1 VIRTUAL REALITY: CONSCIOUSNESS REALLY EXPLAINED! (Why, How, Where and What: A Radical Proposal) Jerome Iglowitz [email protected]www.foothill.net/~jerryi Note: I decided to restore this earlier version, (8-08-08), of this book to hold the original symmetry. This book is meant to be augmented with my later book: “Exotic Mathematics…” , which does a better job of explaining some of my ideas. Chapter 2 of this work especially is intended to be augmented with Chapters 1 through 3 of the later work, as it has been greatly misunderstood. Copyright October 23, 1995 All Rights Reserved (Revised December 13, 1998)
Stylistic and Semantic Notes: 11 A Few Practical Matters: 13 A Thesis for the Young: 14
PREFACE TO CHAPTER 1: ON REALISM AND MIND AS A NON-REPRESENTATIVE MODEL 17 The Alternative Positions: 20
CHAPTER 1. WHY? THE BIOLOGICAL PROBLEM: PART ONE, (REPRESENTATIVE MODELS AND THE MIND) 24 Humberto Maturana: 24 The First Hypothesis: A Non-Representational Model in the Brain: 26 The Schematic Model: a New Paradigm for Models 26
A.1. The Simplest and Most General Case of the New Paradigm: 26 A.2. A Deeper Example: Instrumentation, (A Schematic Usage More Closely Related to the Problem of the Brain) 30 A.3. The Richest Example: The "GUI", the most sophisticated example of a schematic model and the most pertinent to the problem of the brain) 31
B. Schematism: The Formal and Abstract Problem and The Argument: 33 B.1. The Problem: Consider, finally, the formal and abstract problem. Consider the problem of designing instrumentation for the efficient control of both especially complex and especially dangerous processes. In the general case, what kind of information would you want to pass along and how would you best represent it? How would you control it? How would you design your display and control system? 33 B.2. The Argument for Schematism: 33 B.3. An Immediate Corollary: The Specific Case of Biology 35 B.4. An Immediate Retrodictive Confirmation: 38
C. Conclusion, (section): 39 Contra: 43
PREFACE TO CHAPTER 2: THE LOGICAL PROBLEM -AND REALISM AGAIN 48 Meaning 53 Knowing: 54 Anthropological and Linguistic, and Logical Commensurability 54 Realism Again: 54
CHAPTER 2. HOW? THE LOGICAL PROBLEM OF CONSCIOUSNESS 62 Let’s Start from the Other End: First Hilbert's "Implicit Definition": 63 Cassirer and Classical Logic: 69
The Classical Concept: 70 Contra the Aristotelian Concept: 71 Cassirer's Alternative: "The Functional Concept of Mathematics": 72 Concept vs. Presentation: 74 Contra The Theory of Attention: 75 Major Consequences: 76 Re Presentation: 77
The Concept of Implicit Definition: 79 Implicit Definition vis a vis Presentation: 82 Why is this relevant to mind? 84
Contra Cassirer: 86 The Crux of the Issue: Presentation 87 Mind-Brain: The Second Hypothesis: 88 A Possible Physical Paradigm: 90 Convergence. 93 A crucial turning point in my argument: 95 Plain talk: 98 Conclusion: (chapter) 102
INTRODUCTION TO CHAPTERS 3, 4 AND 5 103
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(TOWARDS A RESOLUTION OF THE PARADOX) 103 CHAPTER 3. BIOLOGY_PART II: TOWARDS THE WHERE AND THE WHAT? 106 BIOLOGY & EPISTEMOLOGY 106
Closure: 108 Maturana and Varela: 112 The Axiom of Externality 132 An Answer to the New Dilemma: 139
PREFACE TO CHAPTER 4 142 CHAPTER 4: COGNITION AND EXPERIENCE: QUINE AND CASSIRER 144
A fantasy: 146 The Epistemological Problem: 149 Cassirer Revisited: 152 Cassirer's Theory of Symbolic Forms: 154 The solution to the dilemma: 164 Whence Cassirer's Thesis: 167 Contra Cassirer: (What are the real parameters?) 170 [Important Note 6-20-1999: a modification of my conclusions] 179 The Power of Naturalism 180 Quine Speaks to my Proposal 188
PREFACE TO CHAPTER 5, (THE FINAL STEP) 190 CHAPTER 5: WHAT? THE SUBSTANCE OF MIND 191
The Last Hurdle 194 The Third Hypothesis: a formal statement: 195 Philosophical Implications 196
CHAPTER 6: CONCLUSIONS AND OPINIONS 198 Scientific Conclusions: 198 Devil's Advocate: 198 So Why Bother? 200 How do we live? 202 My "Act of Faith": 202
CHAPTER 7: EPILOGUE 204 APPENDIX A, (INFORMATION AND REPRESENTATION) 209
A Little Combinatorial Argument: 209 A Simple Limiting Argument: 211 The Argument: 212
APPENDIX B, (ISOMORPHISM AND REPRESENTATION) 217 APPENDIX C, (MIND-BODY AND ARTIFICIAL INTELLIGENCE: HUBERT DREYFUS) 221
(1) the biological assumption: 222 (2) the psychological assumption: 222 (3) the epistemological assumption: 222 (4) the ontological assumption: 223
APPENDIX D: (ROGER PENROSE) 234 APPENDIX E: DOGMATIC MATERIALISM AND REALITY 239 APPENDIX F: "DENNETT AND THE COLOR PHI" 243
An Extension of the Schematic Model: A Brief Sketch 249 APPENDIX G: AN OUTLINE OF THE SEMANTIC ARGUMENT, (FOR PHILOSOPHERS) 253 APPENDIX H : EXTENDED ABSTRACT 262 AFTERWARD: LAKOFF, EDELMAN, AND “HIERARCHY” 266
Lakoff: 266 The Classical Concept 267 Cassirer and Lakoff’s Logic 271
Edelman: 282 On “Presentation” 285
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Re-entrant Maps 286 The Cartesian Theatre 288
On Epistemology: 291 MATHEMATICAL IDEALS 291
Conclusion 298 APPENDIX I: A FEW ILLUSTRATIONS 300 APPENDIX J: (AN ELABORATION OF THE POSSIBILITIES OF THE DISCUSSION) 304 BIBLIOGRAPHY 312 DEDICATION: 316
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Preface to the Second Edition:
I read recently of a neuropsychological study of the brainscans of fiercely partisan
political adherents. It consisted in the recording of brain scans of fierce democrats, or fierce
republicans when listening to the speeches of their own, or the other party’s candidates. What the
study showed was that the rational sections of the brain were largely suppressed when hearing the
opponent’s views, and the emotional areas were intensified. And conversely, when hearing one
of their own, just the opposite occurred. They were very ready to reason along with their
spokesman, and suppress their negative feelings. I think this is significant for most human
interaction, and it is particularly relevant to a discussion of the mind-brain problem –our deepest,
most important, and most divisive scientific problem.
Most of us have very definite ideas as to where any solution to the mind-brain problem
must ideally start. Any beginning, deviating more than a “comma” away from that ideal triggers
an almost complete dismissal and the creation of an active adversary from the very first page. No
contrary argument will be entertained or admitted. And yet this problem is not yet solved. After
almost three thousand years it is not solved! Is it almost solved? I think not, though you may not
agree with me. Might we be “almost there”? Perhaps the physicists will discover “the
consciousness particle” at the bottom of it all! I think not.
There are certain basic presumptions we all bring to the problem: “mind”, “material”,
“law”, …, but not necessarily with the same priority. My point will be that which order we choose
will not be significant in the end. All perspectives must ultimately meet. How is that possible?
That is the theme and purpose of this book.
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I believe this particular problem will determine our ultimate views and our ultimate actions
in ethics and behavior. I believe it will determine our absolute future or our extinction as a species.
I do not believe that our future is hopeful.
Let me start this work therefore from the simplest perspective –the materialist perspective,
and see where it leads, (we would reach that same end if we were to begin anywhere else).
Jerome Iglowitz, December 2009
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Introduction "Popper [said that] ... hypotheses are interesting only if they are bold -that is, if they are
improbable and thus likely to be falsified. For then, to withstand falsification by rigorous
testing is a triumph, and such a hypothesis is significant. Safe (that is, probable)
hypotheses are a dime a dozen, and the safest are logical truths. If what science is seeking
is primarily a body of certain truths, it should stick to spinning out logical theorems. The
trouble with such safety, however, is that it doesn't get us anywhere." (P.S. Churchland,
1988, P.260)
Is anyone really interested in an answer to the mind-body problem? And why should they
be? If science is able one day to deal with all of the ravages of mental illness, and to explain the
whole of human behavior as biological phenomena -as it surely will- then the problem would seem
fit for the debates of philosophers with philosophers alone, and of interest to no one else.
But, as in science generally, there is also a problem of organization - how do we organize
these biological phenomena? And more -how do we predict and integrate them? It is one thing to
catalogue prior experiment, and it is quite another to integrate it into a comprehensive and
predictive framework useful to empiric practice. Ptolemean vs. Copernican cosmology is the
prototypical illustration of the distinction. Ptolemean theory was quite capable of cataloging any
celestial movement, but it could not lead to Kepler's laws. It was sterile for the progress of future
deep science. Heisenberg and Schroedinger1 supply a more modern instance. Heisenberg’s matrix
conception of quantum mechanics was comprehensive, but not predictive. Schroedinger’s
alternative was.
1 Cf , for instance, Cassidy, David. "Uncertainty: the Life and Science of Werner Heisenberg", 1992 for a lucid
discussion of the problem.
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There is a fundamental prejudice in the history of human thought: it is that the large-scale
organization of reality is simple. The whole history of science seems to confirm this premise.
From Euclid to Copernicus, from Galileo to Newton to Maxwell and Hertz to Einstein to
Heisenberg and Schroedinger and Bohr, from Aristotle to Darwin and Pauling..., this is our central
premise.
The problem of the organization of the brain, our central and self-referential problem, is
then either the exception to this rule, (paradoxically it is also the center of our understanding, i.e.
man’s organization, of all the other organizations), or it will itself be organized on such a principle.
But is the Copernican center of that organization to be found in the fundamental principles -and
organization- of biology and chemistry, or in principles unique to the brain itself? In short, is a
"Newtonian physics" of the brain possible? If it is, then the problems of "mind", and "mind-brain"
become crucial as they supply critical clues to that organization.
But there is another aspect to the general problem presented here. It is not only that no
solution has yet been presented for the mind-brain problem, but rather that the consensus of
contemporary scientific opinion seems to be that there is no solution possible consistent with our
ordinary, (i.e. "folk"), understanding of mind and perception. The consensus, (in the community of
“hard scientists”), is that only actions and mechanical processes are possible, that "understanding"
and "perception" must necessarily be reduced to the mechanical vocalizations, (and the precursors
of such vocalizations), of linguistic automatons. I do not claim that this is not a formally consistent
solution, but its center of organization lies clearly in the principles of biology and physics, and not
of the brain itself.
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If another solution is submitted, it must be appraised in terms of the new possibilities it
opens. To be worthy of serious consideration, it must promise -and specifically suggest- new and
powerful empirical results: philosophy is not enough. Though it may offend basic dogma, though
it may profoundly offend our sensibilities, if it also proffers deep and profound scientific advance,
then it must be considered seriously. The solution I will present here, though highly esoteric, (in a
mathematical sense of the word), has definite and specific implications for the directions of
empirical research. Though scientifically and philosophically radical, I believe it resolves the
whole of the mind-brain problem for the first time. It is, moreover, eminently compatible with the
very same sort of radicalness which grounds modern physical science.
Let me be very clear. My purpose is passionately empiric and my conclusion pointedly
scientific, not merely philosophical. I postulate a deep reorientation of the foundations of
neuroscience with an unswerving focus on productivity. But as Cassirer, for instance, has amply
illustrated, it is the case for all the crucial turning points in the history of science that deep progress
necessitates serious re-examination of what were, before, philosophic certainties. Those prior
"certainties" have always precluded the profoundest leaps of our greatest scientific theories.
Philosophy has been the crucial business of the greatest of our scientists –at the very points where
their most significant work was done. 2
2 Let me duplicate a footnote from Chapter 4 here that makes the point:
Cassirer sums up the case:
"A glance at the history of physics shows that precisely its most weighty and fundamental achievements stand in closest connection with considerations of a general epistemological nature. Galileo's 'Dialogues on the Two Systems of the World' are filled with such considerations and his Aristotelian opponents could urge against Gallilei that he had devoted more years to the study of philosophy than months to the study of physics. Kepler lays the foundation for his work on the motion of Mars and for his chief work on the harmony of the world in his 'Apology for Tycho', in which he gives a complete methodological account of hypotheses and their various fundamental forms; an account by which he really created the modern concept of physical theory and gave it a definite concrete content. Newton also, in the midst of his considerations on the structure of the world, comes back to the most general norms of
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Stylistic and Semantic Notes:
Because of the complexity of my conception and because it is so far removed from the
accepted paradigms, I have had to solve severe artistic and semantic problems to give what I hope
will be a lucid exposition. 3 My thesis is a synergistic and multidisciplinary combination of three
very radical ideas. Each of these is, by itself, capable of a linear, (though not simple), exposition
and argument. Each, however, raises profound new difficulties which must be answered. It is only
in their combination that a plausible and, I think, a convincing rationale can be made. I therefore
face a difficulty of much the same sort that Kant, (for instance), faced in the exposition of his ideas
which faced a similar difficulty and which he illustrated with the problem of explaining the parts of
the body. To understand the hand, (he argued), the arm and the heart and the brain must be
understood, -and conversely. The parts are only truly intelligible in their integration into the whole.
I had originally tried, (reasonably I thought), to present an overview and synopsis of my individual
themes and their interconnection in an introductory chapter, giving at least a general answer to the
problems they raised.
physical knowledge, to the regulae philosophandi. In more recent times, Helmholtz introduces his work, 'Uber der Erhaltung der Kraft'... with a consideration of the causal principle... and Heinrich Hertz expressly asserts in the preface of his 'Prinzipien der Mechanik'.. that what is new in the work and what alone he values is 'the order and arrangement of the whole, thus the logical, or, if one will, the philosophical side of the subject.' But all these great historical examples of the real inner connection between epistemological problems and physical problems are almost outdone by the way in which this connection has been verified in the foundations of the theory of relativity.... Einstein...appeals primarily to an epistemological motive, to which he grants...a decisive significance." (Cassirer: "Einstein's Theory of Relativity",P.353-354)
This case can be made over and over again, and is particularly transparent in modern times concerning quantum mechanics. Cassidy’s “Uncertainty: The Life and Science of Werner Heisenberg”, (Cassidy, 1991), lays out the epistemological dilemma of that time succinctly. The paradigm case, however, remains that of Copernicus which I feel is even now still underrated in this regard.
3 As an aside, let me remark that “hypertext” would have made some sense as a format for my book. It is frankly beyond me at this point, and I doubt, as well, that it is a proper medium for a serious treatise. To a very real extent, however, I have used footnotes and the multiple appendices to the same end. This was done in an attempt to give at least preliminary answers to the “obvious” objections that must occur almost everywhere.
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When I circulated early versions of my thesis for comment, I received numerous initial
reactions of high interest from persons whom I considered bright and able, (not because they were
interested!) But most of these contacts just "died away", with no further response. A few brave
souls, (or those with more background in the field), managed to get past the initial statement and
into the "meat" of my theory, and they have helped me enormously with their criticisms and
suggestions. I do not think the others dropped out because of a lack of ability or willingness -or
because of disbelief. It is my experience that most people are not shy about expressing
disagreement, but that never happened. Those I contacted told me they simply "bogged down" in
the Introduction and Synopsis, (the original Chapter 1), and got lost.
I think this was a fault of my presentation. I concluded that the sheer density, the innate
complexity, and the necessary abstractness of such a synopsis, undertaken without prior
familiarity, was enough to "boggle" almost any mind. If these were not my own ideas, I would
probably stand likewise. They are simply too far from the standard paradigm to be presented in
such a form.
The alternative presentation raised difficulties of its own, but I concluded that it was the
only way to make my ideas comprehensible in a lucid form. That alternative was to just "dive in",
to give just a very general statement -which I give here- to the effect that I will present three
radical themes, (1. a biological rationale for the brain, 2. a logical rationale for the mind, and 3. an
epistemological rationale which reconciles the first two), that each is unsettling, and that it is only
in combination that they become convincing. Or, rather, each is individually plausible, but the new
difficulties each raises are resolved and plausible only in their synergistic combination. Each
offers a specific and constructive counterproposal to accepted wisdom. My biological thesis, for
13
instance, proposes that "cognition" and human reality, (viewed from a contemporary Naturalist
perspective), is virtual. It is a schematic and internally organizational, (rather than a
representational), artifact of evolutionary metacellular process. My argument is considerably more
complicated than that, however, postulating original logical and epistemological dimensions to the
problem and ultimately suggesting a home for “mind” itself.
I will therefore present each of the theses in order, each as a separate chapter,4 and ask for a
suspension of judgment until all three are completed. This is asking for a lot, I know, but it will
allow a linear comprehension, and should be within the scope of a diligent reader.
The very (logical) form of my argument, especially at certain key turning points, is quite
complex and might be confusing however. This complexity is not of my doing but is a necessary
reflection of the complexity of the problem itself. I have therefore provided a logical outline and
synopsis of the argument as Appendix G. You may refer to it as needed, but I discourage it, (at
least until after completing the first two chapters), for the reasons cited above.
The one reader who might properly be excepted from this injunction is the Philosopher
who might want to turn to the outline before starting the body of the book. There are a number of
apparent self-contradictions in my argument which might induce such a reader to dismiss my thesis
out of hand. They are, however, only apparent as I will make clear in the outline.
A Few Practical Matters:
Let me conclude this introduction with a couple of practical matters. “Who is my intended
audience and what are the prerequisites?”, I have been asked.
4 the third thesis as three chapters
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I speak to an imaginary audience which includes the best of the Naturalist philosophers and
scientists,5 but the ghosts of the "old ones" -Des Cartes, Hume, Kant, Newton, Darwin, Hilbert,
Einstein, Bohr, Quine ... are there as well. At the deepest level, it is written for the most serious
workers in the field, but even from them I do not expect an easy reception. The problem I
anticipate derives from my multipli-radical as well as multidisciplinary approach –i.e. it proposes
radical (but commensurate) solutions within all the disciplines it encompasses. It is my hope that
these workers will see the plausibility of my ideas as regards their own specialties and that this will
make them open to question conventionality in disciplines outside their own. Too often this is not
the case –respectability is many times bought at the price of conformity everywhere else. My
thesis is not “multidisciplinary” just because it cites several disciplines; it is multidisciplinary
because it is grounded across several disciplines. The subject requires it.
I assume that all serious workers in the field, no matter which aspect is their special
interest, will have mastered at least all of the major popular works about it6 as well as those of
the classical thinkers. The sheer size and variegation of the issues – i.e. the ground we must
cover, (our subject is the human mind and human cognition itself after all), makes it necessary
to assume a familiarity with that material.
A Thesis for the Young:
There is another level on which this book may be read, however. It may be read “naively”.
By this I mean that it may be read as a simple exposition of a thesis, rather than as the answer to
5 I especially court mathematicians; I especially court biologists.
6 E.g. Dennett, Churchland, Maturana, Edelman, etc. I believe the cases they make are profound and compelling, and they should be familiar to any serious student of the subject. My task is to answer those cases and propose a viable alternative, not to restate them.
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the profound objections which have been raised against all previous attempts at explicating the
mind-body problem.7 On such a first reading you may skip the footnotes, the references and even
the appendices, though you must go back to them ultimately. For this kind of reading, the actual
prerequisites are small. I require only, (as many a mathematical text begins), a "mathematical
maturity". By this I mean that my ideas are to be taken literally and precisely. This is an argument
from fundamentals, very much in the Kantian spirit, but informed by modern mathematics and
biology. Even on such a reading it remains a difficult theory however because it is conceptually
complex and novel, not because it is full of details to be mastered. It does not require prior
knowledge so much as an openness of understanding.
It is, therefore, a thesis for the young -or the young at heart. If I am fortunate enough to
capture their genuine attention, however, then they must broaden their reading to appreciate its full
and far reaching implications. This is not an elementary text. The Bibliography is just a
suggestion of where to start. As a minimal beginning I would recommend Maturana and Varela's
"Tree of Knowledge", at least the first chapter of Cassirer's "Substance and Function", Cassirer's
"Einstein's Theory of Relativity", Kant's "Prolegomena to any Future Metaphysics", and Penrose's
"The Emperor's New Mind", (the latter mostly for its summation of modern physics and its criteria
of theories). P.S. Churchland's "Neurophilosophy" would be a next logical step, Dennett's
"Consciousness Explained" the following, probably Lakoff’s “Women, Fire…” and Edelman’s
“Bright Air…” next,8 and from there the choice is yours. (Though I totally disagree with Dennett
7 Which is the way experts must read it. 8 Regretfully I had not read either Lakoff or Edelman till after the completion of the essential draft of my book.
Because of time and life constraints, I have been unable to give both of these profound conceptions the service they are due. I have gone back and tried to tie their ideas with my own –particularly in the prefaces- and have added a last appendix, (“Afterword”), dealing specifically with their conceptions. To a large extent I agree with their conclusions, (though not necessarily with their mechanics) –though on different grounds. They do not achieve the
16
on the answer, for instance, it is a beautifully reasoned book and lays out the problem in
uncompromising terms.)
This is a wonderful field to enter at this time. It holds, I believe, the “Rosetta Stone” for
the future of humankind and, as such, is the desperate and urgent need of our insane age. It holds
critical and hopeful clues across all the disciplines -not the least of which is ethics.9
This is a very large idea, the distillation of 40 years of independent, (“cloistered”),
thought.10 It is too large and too different to be digested at a single sitting. I would suggest that
you master the first thesis by itself, then the second, and then consider them together as a unit, (i.e.
evaluate their specific synergism –i.e. "the concordance"). Finally I suggest you approach the third
and conceptually most difficult thesis from that secure ground.
"Mind-body" and "cognition" are really a complexity of problems wrapped in a loose
ribbon of words. They are really the problem of everything! Though my solution is (necessarily)
complex in presentation, once understood, it is very simple and natural in concept. I think it’s kind
of elegant!
necessary sophistication to resolve the mind-body problem however. Nor are they internally consistent –they fail in their treatment of a “God’s eye” view of the world. cf Afterword.
9 I think it provides the beginnings of a scientific ethics, and a scientific aesthetics. But the latter is a huge component in the advancement of science as well as history shows. Stephen Hawkins internet question is profoundly relevant, I believe.
10 My particular problem in this book is to translate it into the conceptual language of the current dialogue. Yours is to comprehend a paradigm very different from anything you have seen before.
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Preface to Chapter 1: on Realism and Mind as a Non-Representative Model
Sometimes in the attempt to solve an exceedingly difficult or a seemingly impossible
problem we tentatively adopt what is, on the face of it, an ostensibly absurd or even an outrageous
hypothesis and see where it leads. Sometimes we discover that its consequences are not so
outrageous after all.
I definitely agree with Chalmers11 that the problem of consciousness is "the hard problem".
But I think it is considerably harder than even he seems to think it is. I think its final scientific
solution requires new heuristic principles as deep and as wrenching to our innate preconceptions
as, (though different from), the "uncertainty", "complementarity" and (physical) "relativity" that
were crucial to the successful advance of physics early in this century.12 I think its resolution
involves a profound extension, (though not a refutation), of classical logic as well. A full
consideration of those deep new cognitive principles: "cognitive closure", (Kant, Maturana,
Edelman), "scientific epistemological relativity",13 (Cassirer and Quine), and of the necessary
extension of logic, (Cassirer, Hilbert, Rosch, Lakoff, Edelman, Iglowitz), must await later chapters
however. In a very real sense, moreover, it is a "chicken and egg" problem. I must ask for some
latitude therefore. This is too big a problem to be focused in a single chapter.
In this chapter I will propose, instead, just the first and conceptually simplest part of a three
pronged, (and multidisciplinary), hypothesis for a solution of the problem of consciousness. This
11 Chalmers. 1995 12 For a vivid recreation of that time and the comparable intellectual dilemmas presented by the empirical findings of
quantum physics see "Uncertainty: the Life and Science of Werner Heisenberg". Cassidy, 1992, for instance. 13 This is not an ad hoc relativism, but a scientifically structured one –I will elaborate this point shortly and develop it at
length as the subject of Chapter 4.
18
first hypothesis proposes, ("outrageously"), that the evolutionary rationale for the brains of
biological organisms was not representation14 -nor reactive parallelism -nor transcendent logic!15-
as is generally asserted, but was, rather, an optimizing, (and non-representational), internal
operational organization, (by metacellulars), of their own primitive reactive biologic process
instead. I will argue that our conceptual and perceptual objects themselves are metaphors of that
internal organization. I will propose a specific model and argue that this organization was vital for
the adroit functioning of profoundly complex metacellular organisms in a hostile environment. I
will argue, moreover, that this organization was antithetical to a representative role!
Representation, I will argue, is in conflict with an optimization of biological response!
This is an "outrageous" hypothesis in that it proposes a premise which presumes16 our
ordinary physical and evolutionary world, (ordinary biology), while the consequences of that
selfsame premise are that our ordinary worldview, (to include the aforementioned "ordinary
physical and evolutionary world" in which it was framed), is neither probably, nor even likely, to
be (metaphysically17) correct!18 We humans, after all, are metacellulars too.
14 This is not so peculiar an idea as it may seem but is being advocated more and more frequently by eminent
biologists of our day- e.g. Maturana and Varela, Freeman and Edelman. 15 i.e. an ultimate, objective logic dealing with the ultimate, objective, (ontic), world -the absolute world in which we
exist. This is Kant's distinction between "transcendent" and "transcendental". 16 In its very statement 17 "Metaphysics", as a word, refers not just to historically obsolete scientific ideas such as "final causes", "purpose", et
al, but also to ultimate being -i.e. "ontology". This aspect of metaphysics, (i.e. what is the world really?), still remains at the core of most conceptions of science and philosophy despite Kant's herculean efforts. Though unfashionable to give it a name, that which it names is ubiquitous. I will address the issue at length in Chapters 3, 4, and 5 as its clarification is crucial to the mind-body problem just as it was crucial to the successful advance of modern physics.
18 The same dilemma is shared, clearly, by Maturana and Varela, Freeman, Lakoff, Edelman, … Maturana calls it “the razor’s edge”.
19
not
in.
How is this possible? Why is it not a logical absurdity? I will supply a cogent realist
resolution of this seeming "reductio" in Chapters 3 and 4 drawing from Kant, Cassirer, Quine and
Bohr. The answer lies in an honest-to-God epistemological relativism! I will argue, with
Cassirer, that our science is a relativistic19 organization of phenomena, ("experience"), and not
metaphysically, (i.e. absolutely), referential.20 This proposal, like Bohr’s, will resolve the apparent
self-contradiction of this first premise by placing it as a scientifically significant and useful
relative21, (i.e. organizational), but not metaphysically referential assertion. It is proposed,
(itself!), as a legitimate and scientifically productive automorphism within our ordinary world,
as a metaphysical (objective) mapping to an external, absolute doma
My overall thesis is neither solipsistic nor idealistic, however, but scientific and realist.
Ultimately I will propose that our ordinary world, (our "folk world"22), is a blind working
algorithm, (in just Bohr's sense of quantum mechanics), on the Kantian "Noumea"23 but
incorporating, like physics, a principle of fundamental epistemological uncertainty. It is, therefore,
19 I had probably best clarify mine, (and Cassirer's), meaning of the word "relativism" right here. It does not have the
sense of "cultural relativism", "ethical relativism", or that "anything is as good, (or true!), as anything else". It does not signify an abandonment of truth or legitimacy. Rather, we understand the word in the mathematical and scientific sense -in the sense of Einstein's Special Relativity for instance. It denotes an exact and invariant rule of connection. One set of measurements in a particular frame of reference is not arbitrary as regards another set of measurements in another frame under Special Relativity for instance. Instead it is related to it in a rigid and invariant relation -i.e. via the specific equations of the theory of relativity. This is the sense of "relativism" and "invariance" that Cassirer and I utilize, and it is diametrically opposed to "capriciousness".
20 I will argue that the business of science is the prediction of correlations of events, not about what those correlations ultimately correspond to in some ultimate ontic "nether world". I will argue, with Maturana and Varela, and with Gerald Edelman that brains, (and the product of those brains), are adaptive, (e.g. “ex post facto selective of preexisting internal variation" using Edelman’s terminology -cf Edelman, 1992, p.82), and not information processing. But "adaptation" does not imply isomorphism or objective mapping, it implies competence, which is quite different from implying a "God's eye" knowledge of the world, (information). I will pursue this discussion in Chapter 3. Edelman draws a similar conclusion, but then goes on, inexplicably, to propose exactly such a "God's eye" view himself! I attempt to resolve that difficulty in Chapter 4 in a modification of Cassirer's "Symbolic Forms".
21 see footnote above 22 and ultimately, (as an extension of that world), our science as well 23 ultimate reality
20
a realist24 hypothesis in the essential meaning of that phrase, but embodying a tenet of
metaphysical indeterminacy. It is "Kantian" without the categories.
I will show in later chapters, (though not in this one), how this first hypothesis, (in concert
with ancillary logical and epistemological hypotheses), opens the first real possibility for an actual
and adequate solution of the problem of "consciousness" commensurate with the legitimacy of
science. I will argue that it leads to an actual solution of the fundamental paradoxes of sentiency.
That solution actually explicates those paradoxes rather than merely denying or reducing, (i.e.
eviscerating), them -and "consciousness" in the process -as has been the case heretofore. This is a
crucial measure of a new theory. It foreshadows, moreover, the beginnings of a truly scientific
psychiatry for the first time.
The Alternative Positions:
The nonrealist philosophies: dualism, idealism and solipsism appear to have a certain
advantage in the problem of consciousness. Admittedly, they circumvent certain of the primal
difficulties, but they do so at a price too costly for most scientists and other practical minds.
Because they detach25 physical presentation, (i.e. sensory perception26), from our consciousness,
(or discount it entirely), the problems of "the homunculus" and of how we know clearly disappear -
at least in regard to external perceptions. We know because we know. We begin by knowing.
There is, they claim therefore, no problem of knowing!
24 Contrary to his own (grudging) acceptance of the label of "critical idealist", Kant was very much a realist. His
arguments in "Prolegomena" very clearly and pointedly distinguish him from classical idealism. A more modern classification, I propose, would be "ontic indeterminist". The "categories", I believe, are a different issue, and open to question. See Introduction to Chapter 2 for an elaboration of essential realism.
25 or reinterpret 26 to whatever extent it may exist for them
21
g?29
But it is only an illusory advantage for these philosophies do not solve an even deeper
problem of "presentation" and another "homunculus" implicit in our very logic itself. How can
this part of even a "mental stuff" know that part?27 How, in Leibniz's formulation of the problem,
can "the many" be known to "the one"? Whence comes the integration of the parts? Whence,
furthermore, comes the "abstraction" and "attention"28 at the theoretical foundations of the
classical logical "concept"/”category” –i.e. at the very basis of classical logic itself? What do we
abstract from -and where, and what do we pay attention to -in our formal theory of concepts -and
how? How can there be a logical homunculus? How can there be meanin
This is the problem of logical presentation. I call it the logical problem of consciousness,
and it is the hardest problem. It is a problem that no philosophy has yet answered. It is the
purpose of this chapter to present the first of three synergistic30 hypotheses intended, (at their end),
to answer it fully, (and the core of the mind-body problem as well), in a manner consistent with
science and realism.
27 other than that mind is "nonextensional" and "non-divisible" -i.e. "it just does"!
28 cf Chapter 2
29 A large part of the problem of "mind" and of "consciousness" lies in our inability even to properly and adequately frame it. This ambiguity is pretty much admitted by all parties. I believe it is a consequence of the lack of an adequate underlying conceptual framework, and not because of a lack of substance to the problems themselves. It is only when an adequate substrate theory has been formulated, (or while it is being formulated), that the problems will take on clear and logical form, and solutions will be cogent. There are clear precedents in the history of science to illustrate the case. How, for instance, could the perspectives, (the questions and the answers), of Galilean or Newtonian physics be formulated in the causative framework of Aristotle or the cosmological framework of Ptolemy? The answer is that they could not. It was only in the evolution of a different context and a different science that they could be explicitly formulated at all.
The problems and the answers of "mind" and of "consciousness" are considerably clearer within my thesis -i.e. they can achieve a concise formulation, but not in a prelude to it.
30 and, thereby, individually somewhat perplexing
22
planations.
Ordinary realism, (ordinary materialism), on the other hand, throws away the baby with the
bath. It leads inexorably to the conclusion, as Dennett31 has so forcefully argued, that we can have
no consciousness -we are all automatons -"zombies"! Simply put, there is no way that one part of
a spatially and temporally distributed process32 can know another part.33 There is no "place" that
knowing can be; there can be no "Cartesian Theater"! We are "multiple drafts" published on a
mechanical "demon press". Emergence, supervenance and epiphenomenalism,34 on the other
hand, are profoundly challenged by Occam's razor35 since by definition they can add nothing
causative to physical ex
The real problem for those of us who believe we "have a life" therefore, is how to account
for both consciousness and a reality external to that consciousness in a philosophy of realism and
science. I will argue ultimately that it requires a reduction of the excessive and blatantly
metaphysical36 demands made on realism while retaining the essential core we vitally require.
This (essentially Kantian) realism37 will enable a viable solution to the logical problem in my
second thesis, (and to the problem of meaning as well), and answers our innate demands for both
31 Dennett, 1991. I will not reiterate these kinds of arguments within this book -we have much larger and original
ground to cover. They have been powerfully and beautifully made innumerable times before. (Cf, for instance, Dennett, P.S. Churchland, Paul Churchland, … -even Edelman!) Furthermore I accept their conclusions within the context within which they were made and expect my intended reader to have been strongly challenged by them. It is that context itself we must examine but we must do so without presupposing our conclusions, “heterophenomenologically”, as Dennett would say
32 the process of the brain, for instance 33 (though it can react to it!) 34 and property dualism ... 35 The principle that entities are not to be multiplied beyond necessity, i.e. beyond explanatory sufficiency. 36 i.e. ontological –see footnote above defining “ontology” 37 see prior footnote concerning Kant’s realism
23
science and consciousness. My third hypothesis38, (in conjunction with the first two), undertakes
to supply the actual "substance" -the "matter of mind”- within the context of that same realism.
Consciousness without realism and science is inconsequential. Science and realism without
consciousness is pointless.
Sometimes it is necessary to walk around a mountain in order to climb the hill beyond. It
is the particular mountain of "representation", and the cliff, (notion), of "presentation" itself, (to
include logical presentation), embedded on its very face, I will argue, which blocks the way
towards a solution of the problem of consciousness. This first chapter points out the path around
the mountain so that we may approach the more manageable grades beyond. "Presentation", I
hold, is not implicit in consciousness nor is it innate in realism.
Let me now present just the first of three synergistic hypotheses whose combination I will
ultimately propose as a scientifically plausible solution for the problem of consciousness. This
first hypothesis is not intended to stand on its own. Though it opens new and fruitful
perspectives on the problem, it raises very large problems itself. The latter are the subject of
the second, (Chapter 2), and third hypotheses, (chapters 3, 4, and 5). Their adequate resolution
involves a paradigm shift of monumental proportions and is dependent on the whole of the
three hypotheses. It is the latter fact, I believe, which has made the problem so long
intractable.
38 Chapters 3, 4, and 5
24
Chapter 1. Why? The Biological Problem: Part One, (Representative Models and the Mind)
Humberto Maturana:
"The plastic splendor of the nervous system does not lie in its production of
'engrams' or representation of things in the world; rather, it lies in its continuous
transformation in line with transformations of the environment as a result of how
each interaction affects it. From the observer's standpoint this is seen as
proportionate learning. What is occurring, however, is that the neurons, the
organism they integrate, and the environment in which they interact operate
reciprocally as selectors of their corresponding structural changes and are coupled
with each other structurally: the functioning organism, including its nervous
system, selects the structural changes that permit it to continue operating, or it
disintegrates." 39 40
"… the nervous system ...is not solipsistic, because as part of [its] organism, it
participates in the interactions [with] its environment. ... Nor is it representational ...
[it] does not 'pick up information' from the environment, as we often hear... The
popular metaphor of calling the brain an 'information-processing device' is not
only ambiguous but patently wrong." (Maturana and Varela, 1987, pp.170-171, my
emphasis)
39 Consider also Edelman: “…recognition is not an instructive process. No direct information transfer occurs…
Instead, recognition is selective.” (Edelman, 1992, p.81) 40 See also Edelman, 1992, pps. 190-191, for a conception comparable to Maturana’s “structural coupling”
25
Humberto Maturana and Francisco Varela's "The Tree of Knowledge"41 is a detailed and
compelling argument based in the necessary structure of physical explanations, against even the
possibility of a biological organism's possession of a representative model of its environment.
They and other eminent modern biologists, (Walter Freeman and Gerald Edelman for instance),
argue even against "information" itself moreover! They maintain that information never passes
between the environment and organisms; there is only the "triggering" of structurally determinate
organic forms.42 I believe that theirs is the inescapable conclusion of current science and I will
argue that case as the subject of Chapter 3.
It is not my intention to present that argument in this chapter however. Here, instead, I will
present an explicit and constructive counterproposal for the existence of a different kind of model
in the brain, "the schematic operative model". This model, I believe, (and contrary to the case of
the representative model), does remain viable within the critical context of modern science. I
believe that we, as human organisms, do in fact embody a model. I believe it is the stuff of mind!
Let me now present an inductive argument –and a concrete counterproposal- that the brain
embodies a scientifically viable, (and biologically efficacious), model of internal process rather
than a representational model of its surroundings. Representative models are not the only possible
kinds of models. Nor is representation a model's only conceivable or best use.
41 Maturana and Varela, 1987. 42 Edelman makes an argument to the same conclusion based in embryology and the actual size of the human genome
for his theory of "Neural Darwinism”. He concludes that the brain is an "ex post facto" adaptive rather than an "informational" system. Freeman argues similarly "that perception does not consist of information reception, processing, storage, and recall.." -that the brain is not representational.
26
The First Hypothesis: A Non-Representational Model in the Brain:
Normally, when we think of “models”, we mean a reductive, or at least a parallel model. In
the first we think of a structure that contains just some of the properties of what is to be mirrored.
When we normally use the term “schematic model”, we talk about the preservation of the
“schema”, or “sense” of what is mirrored. Again it is reductive, however- it is logically reductive.
It is, as was claimed against me, “just a level of abstraction”. There are other uses for models,
however, those that involve superior organizations! This is the new sense of a “schematic model”
that I propose to identify.
The Schematic Model: a New Paradigm for Models
A.1. The Simplest and Most General Case of the New Paradigm:
Even our most simplistic models, the models of even our mundane training seminars for
instance, suggest the possibility of another usage for models very different than as representative
schemas. They demonstrate the possibility of a wholly different paradigm whose primary function
is organization instead.
Consider: " 'Motivation' plus 'technique' yields 'sales'.", we might hear at a sales meeting.
Or, " 'Self-awareness of the masses' informed by 'Marxist-dialectic' produces 'revolution'! ", we
might hear from our local revolutionary.43 Visual aids, (models), are ubiquitous. The lecturer
stands at his chalkboard and asks us to accept drawings of a sundry set of shapes: triangles,
squares, … even cookies, horseshoes44... as objects -with a "calculus"45 46 of relations between
43 The single quotes are meant to parse the "objects" as will become clear shortly.
44 Mathematicians love to be cute like this!
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them. These shapes are stand-ins for concepts or processes like "motivation", "the nuclear threat",
"sexuality", "productivity", "evolution", ... in the diagrams on his board. In these presentations, the
"objects" often do not stand in place of entities in objective reality, however. What is "a
productivity" or "a sexuality", after all? What entities are these?
Another lecturer might invoke different symbols however, and a different "calculus" to
explicate the same topic. In analyzing the French Revolution in a history classroom, let us say, (a
classroom is a kind of training seminar after all!), a fascist, a royalist, a democrat might
alternatively invoke "the Nietzschean superman", "the divine right of kings", "freedom", ... as
"objects" on his board, (with appropriate symbols), redistributing certain of the explanatory
aspects, (and properties), of the Marxist's entities, (figures) -or rejecting them as entities
altogether.47 That which is unmistakably explanatory, (“wealth”, let us say), in the Marxist's
entities, (and so which must be accounted for by all of them), might be embodied, instead, solely
within the fascist's "calculus" or in an interaction between his "objects" and his "calculus". Thus
and conversely the Marxist would, (and does in fact), reinterpret the royalist's "God"-figure, (and
his –the Marxist’s- admitted function of that "God" in social interaction), as "an invention of the
ruling class". It is taken solely as an expression of his "calculus" and not as a distinct symbol, (i.e.
object). Plainly put, their objects -as objects- need not be compatible!48 Usually they are not!
What is important is that a viable "calculus"-plus-"objects", (a given model), explain or predict
45 Footnote: Webster’s defines a “calculus” as a method of calculation, i.e. any process of reasoning using symbols. I
mean it in this sense -in contradistinction to “the calculus”, (i.e. differential and integral calculus). 46 Webster's defines "calculus", (math): "a method of calculation, any process of reasoning by use of symbols". I am
using it here in contradistinction to "the calculus", i.e. differential and integral calculus. 47 Is this not the usual case between conflicting theories and perspectives?
28
"history".49 It must be compatible with the phenomena, (in this particular example the historical
phenomena). In Chapter 4, I will argue, (with Hertz and Cassirer), that the same accounting may
be given of competing scientific theories, philosophies, and, indeed, of any alternately viable
explanations.50
The very multiplicity of alternatively viable calculuses, (sic), and the allowable
incommensurability of the "objects"51 of their models, however, suggests an interpretation of those
"objects" contrary to representation or denotation. It suggests the converse possibility that the
function and the motivation of those objects, specifically as entities/objects in what I will call these
"schematic models", is instead to illustrate, to enable, -to crystallize and simplify the very calculus
of relation proposed between them!52
I propose that the boundaries -the demarcations and definitions of these “objects”, (their
“contiguity” if you will)- are formed to meet the needs of the operations. They serve structure- not
the converse!53 I suggest that the objects of these “schematic models” –specifically as objects-
serve to organize process, (i.e. analysis or response). They are not representations of actual objects
or actual entities in reality.54 This, I propose, is why they are "things"! These objects of
48 Consider Edelman: "...certain symbols do not match categories in the world. ... Individuals understand events and
categories in more than one way and sometimes the ways are inconsistent." Edelman, 1992, pps. 236-237, his emphasis.
49 more generally: the phenomena 50 Hertz, for instance, argues that science makes symbols whose one essential quality lies in the generation of a
parallelism with experiential consequence but that “we do not know and have no means of finding out whether our ideas of things accord with them in any other respect than in this one fundamental relation.” (my emphasis) cf Chapter 4: Hertz, Cassirer, Quine
51 together: the possible conceptual contexts 52 cf the arguments of Chapters Two and Four for a detailed rationale 53 cf Afterword: Lakoff/Edelman for a discussion of mathematical “ideals” which bears on this discussion. 54 this directly relates to the issues of “hierarchy” which I will discuss shortly, and at greater length later
29
schematic models functionally bridge reality in a way that physical objects do not. I propose that
they are, in fact, metaphors of analysis or response. The rationale for using them, (as any good
"seminarian" would tell you), is clarity, organization and efficiency.
(But how is this even conceivable?55 How are “objects” even possible independent of
some ultimate “reference”? I will argue shortly that a "calculus"-plus-"objects"56 can be freely
formed, (ad hoc rather than contingently, referentially formed), as an interface –a “front end”- to
efficiently organize57 a domain of correlation, (experience for instance, or a mathematical
domain).58 This conclusion will impose consequential and severe constraints on the nature of the
correspondence however. I will propose that it is redressed in the constitution, (correspondence),
of the "objects" themselves!59)
Though framed in plebian terms, the "training seminar", (taken in its most abstract sense),
defines the most general and abstract case of schematic non-representative models in that it
presumes, (as presented), no particular agenda. It might as well be a classroom in nuclear physics
or mathematics, the boardroom of a multinational corporation, -or a student organizing his leisure
time on a scratchpad.
55 This is specifically a logical question –i.e. it is a question of logical possibility, and my detailed answer is the subject
of Chapter 2. 56 a model 57 i.e. predict, analyze or control 58 rather than being constrained by the contiguous, (object-contained), properties of real, (or possible), metaphysical
objects 59 That the combined model must so correlate, (to have any value), is, of course, a given. But must it correlate in its
parts? Must the "objects" of the model correlate as objects to objective objects? Must the operations of the model, ("the calculus"), correlate to objective relations between them? Can we not conceive of a more abstract situation, suggested by higher mathematics, wherein the whole of the model correlates to its domain in a distributed sense?
30
A.2. A Deeper Example: Instrumentation, (A Schematic Usage More Closely Related to the
Problem of the Brain)
Instrumentation and control systems provide another, somewhat more respectable example
of the possibilities of schematic, non-representational models and "entities". Consider the most
general case of instrumentation for instance. Here "objects" need not mirror objective reality
either. A gauge, a readout display, a control device, (the "objects" of such systems), need not
mimic a single parameter -or an actual physical entity. Indeed, in the monitoring of an especially
complex or critical process, it should not! Rather, "an object", (a readout device for instance),
should represent an efficacious synthesis of just those aspects of the process which are relevant to
response, and be crystallized around those relevant responses!60 A warning light or a status
indicator, for instance, need not refer to just one parameter. It may refer to the composite of
electrical overload and/or excessive pressure and/or... Or it may refer to an optimal relationship,
(perhaps a complexly functional relationship!), between many parameters! It may refer to a
relationship between temperature, volume, mass, etc. in a chemical process, for instance.
The exactly parallel case holds for its control devices. A single control "object" may
orchestrate a multiplicity of (possibly disjoint) objective responses. The accelerator pedal in a
modern automobile, as a simplistic example, may integrate fuel injection volumes, spark timing,
transmission gearing...
"The calculus"61 of this joint system of readout and control is the relationship between the
objects of the readout and the necessary actions upon the objects of control. It is the calculus of
Transformations, after all, are not defined on the domain of "spaces", but of abstract sets -i.e. without an a priori presumption of order.
60 Precisely because it is complex and critical, (or dangerous) –e.g. it may explode with very little warning! 61 Like the “calculus” of our lecturers before
31
response and, for especially complex and critical, (or dangerous), processes, coherence and
simplicity of that calculus is absolutely crucial.
Ideally -for maximal simplicity and speed- instrumentation and control might unify in the
same "objects" in a single contextual frame. We would then manipulate "the objects" of the
display, which would themselves be the control devices as well. (We might, in a simplest example
for instance, grasp an errant pointer on a gauge –on a speedometer, let us say- and force it back into
the “safe” range to effect a necessary correction. The pointer would be both the speedometer and
the accelerator/brake in one.) Think about this possibility as applied to our ordinary "objects of
perception" -in relation to the sensory-motor coordination of the brain and the problem of naive
realism! Consider the fecund and profoundly simplifying possibility62 that our "naive objects",
(our sensory objects), could be the unified "objects", (for readout-plus-response), of "the calculus"
of biological instrumentation. The brain is a control system, after all. It is an organ of control!
The process it controls is both profoundly complex and dangerously urgent, the extreme and
A.3. The Richest Example: The "GUI", the most sophisticated example of a schematic
model and the most pertinent to the problem of the brain)
Consider finally the graphic user interface, (the "GUI"), of a computer. The use of
"objects", (icons), in GUI's is perhaps the best example of a “schematic” usage presently available,
and suggests its deepest potential. It is also the most pertinent to the problem of cognition.
In my simplistic manipulation of the virtual objects of my computer's GUI, I am, in fact,
effecting and coordinating quite diverse and eclectic -and unbelievably complex- operations at the
physical level of the computer, operations impossible, (in a practical sense), to accomplish directly.
32
What those virtual objects represent and what my virtual and naive manipulation of them actually
does, (at the physical level of the computer), need not even be known to me. The disparate
voltages and physical locations, (or operations!),63 represented by a single "object", (icon), and the
(possibly different) ones effected by manipulating it, correlate to "an object" only in this
"schematic" sense. Its efficacy lies in the simplicity of the "calculus" it enables!
The pragmatic criterion for a GUI is that the rules be simple or intuitive,64 consistent with
proper function. Its value, (its goodness as an interface), is measured by the simplicity of the
calculus it embodies.
Current usage is primitive, admittedly. Contemporary software designers have a limiting
preconception of the "entities" to be manipulated and of the operations to be accomplished in the
physical computer by their icons and interface. But GUI's and their "objects", (icons), have a
deeper potentiality of "free formation" -they have the potential to link to any selection across a
substrate, i.e. they could "cross party lines". They can cross categories of "things in the world",
("objectivist categories" in Lakoff’s term65), as I will argue shortly.66
How does one make a "GUI", after all? One constructs a system of objects, (icons), plus
rules in such a way that the application of those rules on the objects will allow the accomplishment
62 which I will argue in Chapter 2 63 In my computer, I have icons for "things", (text files or databases, for instance), processes, (print the screen or run a
program), script files, (which may execute any combination of things I choose: e.g.: wait 30 secs; run wordprocessor; calculate spreadsheet; search a database for someone who owes me money, search my wordprocessor documents for a misspelling of the word "thought", wait till 6:00 am; get email, turn on the coffee pot, ...), etc.
64 The name of the user interface on my old Amiga is actually called "intuition". 65 Cf Lakoff, 1987. Also see my “Afterword: Lakoff, Edelman…” 66 See Appendix J for an elaboration.
33
of some desired goal. It allows the operation of my computer, for instance, or the control of a
machine, or the control of a process.
Ultimately, of course, the combination of "objects" and "calculus" must accomplish the
purpose desired. Since it is the primary intent of a GUI that the "calculus" be simple however,
then the "objects" must then be defined dependently in terms of it. It is the distribution of function
in the objects themselves, I argue, which allows the simplicity of the calculus.
B. Schematism: The Formal and Abstract Problem and The Argument:
B.1. The Problem: Consider, finally, the formal and abstract problem. Consider the
problem of designing instrumentation for the efficient control of both especially complex and
especially dangerous processes. In the general case, what kind of information would you want to
pass along and how would you best represent it? How would you control it? How would you
design your display and control system? 67
B.2. The Argument for Schematism:
It would be impossible, obviously, to represent all information about the objective physical
reality of a, (any), process or its physical components, (objects). Where would you stop? Is the
color of the building in which it is housed, the specific materials of which it is fabricated, that it is
effected with gears rather than levers, -or its location in the galaxy- necessarily relevant
information? (Contrarily, even its designer's middle name might be relevant if it involved a
67 Alternatively, how would you organize control?
34
computer program and you were considering the possibility of a hacker's "back door"!)68 It would
be counterproductive even if you could as relevant data would be obscured and the consequent
"calculus", (having to deliberate all that intricacy!), would become too complex and inefficient
thereby for rapid and effective response.69 Even the use of realistic abstractions could produce
enormous difficulties in that you might be interested in many differing, (and, typically,
conflicting), significant abstractions and/or their interrelations.70 This would produce severe
difficulties in generating an intuitive and efficient "calculus" geared towards maximal response.
For such a complex and dangerous process, the "entities", (instrumentation), you create
must, (1) necessarily, of course, be viable in relation to both data and control -i.e. they must be
comprehensive in their necessary function. But they would also, (2) need to be constructed with a
primary intent towards efficiency of response, -towards a simplistic "calculus", (rather than
realism), as well -the process is, by stipulation, dangerous! They would need to be fashioned to
optimize the "calculus", (pattern of required response), while still fulfilling their (perhaps
consequently distributed!) operative role.
Your "entities", (instrumentation), would need to be primarily fabricated in such a way as
to intrinsically define a simple operative calculus of relationality between them -analogous to the
situation in our training seminar or a computer’s GUI. Maximal efficiency, (and safety), I argue
68 cf Dennett on the "frame problem" 69 This is precisely Dreyfus' "large database" problem: “a problem on which no significant progress has been made”.
Dreyfus 1992 Also see footnote to Appendix A. 70 This is typically the case! A working project manager, for instance, must deal with all, (and often conflicting),
aspects of his task -from actual operation to materials acquisition, to personnel problems to assuring that there are meals and functional bathrooms! Any one of these factors, (or some combination of them), -even the most trivial- could cause failure of his project. A more poignant example might involve a U.N. military commander in Bosnia. He would necessarily need to correlate many conflicting imperatives -from the geopolitical to the humanitarian to the military to the purely mundane! See also Lakoff on conflicting frames, (ICM’s).
35
therefore, would demand crystallization into schematic virtual "entities" -a "GUI"71- which would
resolve both demands at a single stroke. Your "objects" could then distribute function so as to
concentrate and simplify control, (operation)! These virtual entities would be in no necessarily
simple (or hierarchical -i.e. via abstraction) correlation with the objects of physical reality.72 But
they would allow rapid and effective control of a process which, considered objectively, might not
be simple at all. It is clearly the optimization of the process of response that is crucial here, not
literal representation. We do not care that the operator knows what function(s) he is actually
fulfilling, only that he does it (them) well!
B.3. An Immediate Corollary: The Specific Case of Biology
Biological survival is exactly such a problem -it is both (a) especially complex, (indeed
biology is the paradigm case of complexity), and (b) especially dangerous. For the metacellular
colossus, life is a moment by moment confrontation with disaster! The problem for the
"evolutionary engineer" therefore was exactly that detailed in the formal and abstract problem of
B.1! It is a schematic model in just the sense of B.2 that I conclude evolution constructed
71 the objects of which must be logically, but not necessarily visually resolved 72 But how does the schematic model present a better solution to the problem of conflicting abstractions? The answer
is that it does not improve the conflicts per se, but it does better deal with the practical problem as it does not lose "data", (i.e. detail), as does a model built on abstraction. Think about an example based on a military chain of command. A general makes decisions based on many levels of abstraction presented progressively from sergeants, to lieutenants, captains, majors, colonels, etc. At each level detail is lost in abstractions, (in a hierarchical model). But those details, (or a combination of them), -or conflicting abstractions- may decide the course of a battle. This is typically the complaint of lower-level managers, (from sergeants to shop foremen) -that upper management does not live in the "real world".
The schematic model is theoretically capable of preserving all this complexity so that a best overall solution, (towards some goal), based on the actual situation may be reached on the highest level. Cassirer's functional concept shows that we need not lose detail in abstraction, (for synthesis), but may preserve it in a functional synthesis.
36
therefore,73 and I propose that it is the basis for both the "percept" and the "mind". I conclude that
our "natural world", our naive world, is a "GUI" evolutionarily constituted for maximal operational
efficiency.
But it is just the converse of the argument made above that I assert for evolution. It is not
the distribution of function, but rather the centralization of disparate atomic biological function
into efficacious schematic -and virtual- objects that I urge that evolution effected while
compositing the complex metacellular organism.74
But let's talk about the "atomic" in the "atomic biological function" of the last paragraph.
There is another step in the argument to be taken at the level of biology. The "engineering"
argument, as made above, deals specifically with the schematic manipulation of "data". At the
level of primitive evolution, however, it is modular (reactive) process that is significant to an
organism, not data functions.75 A given genetic accident corresponds to the addition or
modification of a given (behavioral/reactive) process which, for a primitive organism, is clearly
and simply merely beneficial or not. But that process is itself informationally indeterminate to the
organism -i.e. it is a modular whole.76
No one can presume that a particular, genetically determined response is informationally,
(rather than reactively), significant to a Paramecium or an Escherichia coli, for example, (though
we may consider it so). It is significant, rather, solely as a modular unit which either increases
survivability or not. Let me therefore extend the prior argument to deal with the schematic
73 To prove a corollary, it is necessary only to demonstrate that the conditions of the theorem- in this case profound
complexity and profound risk- are met which I have. 74 See third following footnote re: complementary perspectives 75 cf Maturana or Edelman, for instance 76 Compare this argument with Edelman’s on immunology or his own theory of TNGS.
37
organization of atomic, (modular), process, rather than of primitive, (i.e. absolute), data.77 It is my
contention that the cognitive model, and cognition itself, is solely constituted as an organization of
that atomic modular process, designed for computational and operational efficiency. The atomic
processes themselves remain, and will forever remain, informationally indeterminate to the
organism.
The purpose of the model was computational efficiency! The calculational simplicity78
potentiated by a schematic and virtual object for dealing with a multifarious environment
constitutes a clear and powerful evolutionary rationale. Such a model, (the "objects" and their
"calculus"), allows rapid and efficient response to what cannot be assumed, a priori, to be a
simplistic environment. From the viewpoint of the sixty trillion or so individual cells that
constitute the human cooperative enterprise, that assumption, (environmental simplicity), is
implausible in the extreme!
But theirs, (i.e. that perspective), is the most natural perspective from which to consider the
problem. For five-sixths of evolutionary history, (three billion years), it was the one-celled
organism which ruled alone. As Stephen Gould puts it, metacellular organisms represent only
77 These are clearly just the complementary perspectives on the same issue. My thesis is one of organization after all
and the argument above was made on those specific grounds. The identical argument can be made step by step for an organization of primitive process as was made for an organization of data, based alike in efficacy. The conditions are the same: (1) profound complexity and (2) extreme and immediate risk. In the earlier case, we sought to consolidate enormous and conflicting data to maximize response. In this case, we seek to integrate multitudinous and conflicting "atomic processes" to the same end. The arguments and the conclusion are the same: a non-topological schematism. It is an issue of perspective and these are complementary perspectives on the same issue of organizational efficiency. In the context of the a priori human (organism's) cognitive perspective, for instance), it can be considered as distribution of topobiological "objects". From a more abstract, less preconceived perspective, however -from the mathematical standpoint of multivariate statistical analysis, for instance, (cf Lara, 1994), it can be considered centralization. Crudely put, it depends on which end of the "telescope" you are looking through. From the perspective of "the operator", (function), the system is distributive, whereas from the standpoint of "the engineer", (design), it is concentrative.
78 alternatively, the operational organization
38
occasional and unstable spikes from the stable "left wall", (the unicellulars), of evolutionary
history.
"Progress does not rule, (and is not even a primary thrust of) the evolutionary
process. For reasons of chemistry and physics, life arises next to the 'left wall' of its
simplest conceivable and preservable complexity. This style of life (bacterial) has
remained most common and most successful. A few creatures occasionally move
to the right... "
"Therefore, to understand the events and generalities of life's pathway, we must
go beyond principles of evolutionary theory to a paleontological examination of the
contingent pattern of life's history on our planet. ...Such a view of life's history is
highly contrary both to conventional deterministic models of Western science and
to the deepest social traditions and psychological hopes of Western culture for a
history culminating in humans as life's highest expression and intended planetary
steward."(Gould, 1994)
B.4. An Immediate Retrodictive Confirmation:
Do you not find it strange that the fundamental laws of the sciences, (or of logic), are so
few? Or that our (purportedly) accidentally and evolutionarily acquired logic works so well to
manipulate the objects of our environment? From the standpoint of contemporary science, this is a
subject of wonder -or at least it should be. (c.f. contra: Minsky, 1985) It is, in fact, a miracle!79
79 The "anthropic principle", sometimes cited, is clearly self-serving and tautological: "if it were not so, it would not be
so"! My thesis supplies a specific counterproposal.
39
From the standpoint of the “schematic model”, however, it is a trivial, (obvious), and necessary
consequence. It is precisely the purpose of the model itself! This is a radical teleological
simplification!80
C. Conclusion, (section):
Evolution, in constructing a profoundly complex metacellular organism such as ours, was
confronted with the problem of coordinating the physical structure of its thousands of billions of
individual cells. It also faced the problem of coordinating the response of this differentiated
colossus, this "Aunt Hillary", (Hofstadter's "sentient" ant colony.81) It had to coordinate their
functional interaction with their environment, raising an organizational problem of profound
proportions.
Evolution was forced to deal with exactly the problem outlined above. The brain,
moreover, is universally accepted as an evolutionary organ of response. I argue that a schematic
entity, (and its corresponding schematic model), is by far the most credible here -to efficiently
orchestrate the coordination of the ten million sensory neurons with the one million motor
neurons,82 and with the profound milieu beneath. A realistic, (i.e. representational / informational),
"entity" would demand a concomitant "calculus" itself necessarily embodying83 the very
80 Just one of many effected by my thesis. 81 cf Hofstadter, 1979 82 Maturana and Varela, 1987 83 which again raises Dreyfus' "large database problem" -i.e. how could [a brain/computer] deal with huge amounts of
information in a reasonable amount of time? ..."a problem on which no significant progress has been made" (paraphrase, Dreyfus, 1992)
40
complexity of the objective reality in which the organism exists, and this, I argue, is
overwhelmingly implausible.84 [See Appendix A: An elaboration of the argument]
Aside: The "schematic brain" is a "big hunk", admittedly! And there are still larger hunks
of the puzzle not yet in place. Specifically there are the considerations of "cognitive closure",
(Maturana), "logical closure", (Quine), and "scientific epistemological relativism", (Cassirer), that
must be addressed to validate plausibility. I do not ask that you accept the truth nor even the
plausibility of this admittedly radical first hypothesis at this juncture therefore. That must await
the presentation of the rest of the argument in Chapters 2 through 5. What I do ask, however, is
that you be willing to acknowledge its biological and evolutionary and operative strengths and be
open to at least seriously consider it in the context of the larger problem of consciousness.)
Evolution faced an engineering problem of profound proportions, and I propose it solved it
exceedingly well. I propose that it was evolution's progressive coordination of the reactive neural
ensembles of primitive organisms that created the "objects" of those organisms. But I further
propose something far stronger. I propose it created those objects -even the "perceptual objects" of
those organisms- specifically as coordinative nexuses85 of disparate and distributed atomic
response rather than as explicit referents to environment!86 I propose that those objects are
internally and organizationally significant, not referentially so. They are virtual and schematic
only. Representation is the "parallel postulate" of evolution!
84 cf Appendix A. Appendix A was originally incorporated here, but I removed it to an appendix as I felt it interrupted
the flow of the argument. Edelman argues to the same end, (as Appendix A), that the human genome is insufficient by many orders of magnitude to the purposes of "information".
85 i.e. intersections and coordinators 86 I will distinguish this more clearly from Maturana and Varela's thesis in Chapter 3.
41
I conclude therefore, as an evolutionary consequence, that even the human brain's
"objects"87—our objects, i.e. the objects of knowledge and perception- are specifically virtual and
coordinative as well. I conclude that they are evolutionary optimizations -and artifacts- for the
coordination of internal process. We, after all, are biological organisms too. I propose that even
the human brain's objects, then, are schematic. I propose that even our ordinary objects of
perception are schematic artifacts of process. They are in no simple correlation with objective
reality!88
This conclusion, though startling, (and at first even bizarre), drastically simplifies the
profound logical problem of the "percept"89 however. Its origin90 and function is no longer
enigmatic and epistemologically self-serving. It becomes instead a clear and foreseeable
consequence of ordinary, (rather than extraordinary), evolutionary process. It is the simple,
cumulative, and linear result of incremental organizing and optimizing refinements to structure.
(In the next chapter I will demonstrate how it radically simplifies the logical paradoxes of
sentiency as well.)
I have argued that91 it is not important that the "operator"92 of such a (complicated) process
knows what it is, (specifically), that he is doing, (only that he does it well). It is important that he
87 See Chapter 4 to resolve the seeming obvious self-contradiction 88 I will postpone raising the obvious objections that occur here, (i.e. non-referentiality and a seeming self-
contradiction), until I have developed the context to do so. A Copernican revolution in our very conception of "knowledge" is necessitated by this hypothesis, (as developed in my third hypothesis). It will turn out, however, to have very positive implications for science. Please bear with me for a little. This is a very large and complex thesis.
89 (and of “presentation”) 90 This is a point in standard theories where, using Dennett's phrase, "then a miracle occurs". For P.S. Churchland, it is
“the good trick”. 91 from the designer's standpoint 92 I will exorcise this "homunculus" shortly by virtue of my second thesis.
42
l
does it diligently, however. It is important that he be locked into the loop of his virtual reality -that
he "pay attention". This introduces the necessity of an inbuilt realistic imperative -i.e. a
mechanical guarantee of his dedication.93 The universal and dogmatic belief in the (simple) reality
of our natural world is thus itself a consequence of my thesis -and the greatest obstacle to its
acceptance.
This (first) thesis supplies an immediate and naturalistic biological rationale for "mind".
"Mind",94 (the "objects" and their computational relationality), becomes a natural and, for the first
time, (in contrast with the Naturalists' story), a necessary rather than an incidental95 consequence
of evolution. It is the consummation of evolution's incremental extension and organizationa
optimization of primitive (reactive) neural arrays.96 Given my thesis however, its "objects" now
clearly function as metaphors of process, and not as informational units of environment. The
"large database" and the related problems of "information"97 encountered in the field of artificial
intelligence, for instance, are thus not problems for the human brain at this level -save internal to
the metaphor itself.98 This thesis greatly simplifies other crucial aspects of the mind-body problem
as well,99 and, contrary to all current paradigms, suggests the beginnings of, (i.e. a legitimate
93 Hume postulated such an imperative long ago, (cf P.S. Churchland, 1988, p.247). But this "realistic imperative" will
be seen, (by virtue of my second thesis), to be an inherent of operative function rather than being imposed upon it. 94 I am keeping the connection between "mind" and "brain" quite loose at this point. I feel it is admissible at this early
stage of an attempt at explicating precisely this distinction. I will specify my definitions at the end of Chapter 2, and in Chapters 3, 4 and 5.
95 i.e. Naturalists say that an organism, at some stage, began not only to react to its environment, but to embody that environment in parallel! Cf P.S. Churchland, for example.
96 The "How?" of this is supplied in the second thesis, and the "Where?" and "What?" of it is supplied in the third. 97 (and reference) cf chapters 3, 4 & 5 98 cf Appendix B 99 It is a key element in the resolution of the problems of the "Cartesian theater", (see Chapter 2), and has profound
implications for the fundamental epistemological problem as well, (Chapters 3,4 and 5).
43
context for), a definite "Galilean mechanics" appropriate to neuroscience.100 The "objects" of our
perceptual world are no longer metaphysical "givens", but, rather, are operationally continuous
with, and open to explicit and precise resolution in terms of the overall (operative) brain function
of which they form a part.101 I propose, then, brain as an operational continuum! In the next
chapter, we will find a close parallel -and a synergism- with the continuum which we will discover
in mind and logic.
Contra:
Conversely however, this (first) hypothesis significantly complicates our conceptions of
objective reality! It violates, (or rather, stretches), almost every paradigm in our current
intellectual universe as well.102 But why, given the level of "strangeness" in modern science,
would we expect that our most fundamental problem of "measurement", i.e. that of human
cognition itself, would fall to a simple "naturalistic", (and naive realistic), approach in the first
place? Why would we expect that its solution would have only minor repercussions? My answer
admittedly leaves us in a dilemma however, because the "events", the relationality of experience
embodied in the Naturalistic picture -and its rendering of empirical science- are the very subject of
our discussion - or any other discussion! It raises, as well, the question of the consistency of my
own arguments. I have based them in Darwinian evolution and that presumes the legitimacy of our
naive view. My third thesis will address this problem directly, building on arguments of Kant,
100 And for the foundations of the first scientific psychiatry! 101 My "object" might be likened to the second, purely internal and procedural component of Hofstadter's "symbol" but
discounting or at least drastically subordinating his primary, representative component. Hofstadter appreciates that his "symbol" has a large, purely internal and operational function besides its representational role.(Hofstadter 1979, P.570) I will address the issues of "representation" and "isomorphism" presently.
102 I will develop these aspects in Chapters 3, 4 and 5
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Cassirer, Maturana,103 and Quine to justify my usage and suggest a convincing and plausible
conclusion consistent with the perspective of modern science.
Briefly, the solution I will propose, (in my third thesis), is that, though we must preserve
the invariant relationality, (the predictivity), of empirical science and of common experience, we
needn't preserve their primitives, their "objects", nor even their hierarchical organization104 as ontic
referents.105 I will suggest a very different correspondence between mind and "externality" than
isomorphism, (and reference). I will propose that our human world is a blind working algorithm,
implicit in the optimizing organization of process. Mathematics, biology, and epistemology
suggest alternatives more plausible than simple parallelism.
The very complications of this (first) thesis, however, are commensurate with, they are of
the same order and the same type as, the complications already necessitated by the conceptual
dilemmas of modern physics, (and are subject to the same resolving strategies as well).106 They
force us to look at the ground and even the very meaning of "a theory of reality", (as do their
counterparts in physical science). They force us to a revised view of science itself. Science and
theories of reality generally, are, ultimately I will propose, operative rather than descriptive, (i.e.
103 and of Edelman 104 Returning to the "Macintosh" analogy I used earlier, because "the letter is in the trashcan" does not imply that that
aspect of computer process which is "the letter" is physically or logically inside that aspect of computer process which is the "trashcan". It does not imply that they are hierarchically organized.
105 Just as a good Copernican was obliged to accept the data of the Ptolemean astronomer before him, (the angles and times recording the motion of Venus, for instance), so are we required to accept the relationality of experience -the data of naive cognition, i.e. apples, tigers and railroad trains and all the things they do. But we are not required , (no more than he), to accept the ontology in which it was understood! I propose, then, a real "heterophenomenology", (cf Dennett, 1991), i.e. a neutral ontic commitment!
106 I am most definitely not arguing a QM, (quantum mechanics), solution to the mind-body problem. Rather, I will argue that our perceptual world stands in the same relation to reality as does modern physics, (including QM). Both, I argue, are algorithms! The latter is an intellectual algorithm, the former an organic one. Both algorithms coordinate response. But the dynamic algorithm embodied in naive realism, (which is the computational calculus), -
45
referential), enterprises. This is hardly a new suggestion, but was the conclusion of many of the
pioneers of modern physics. In the context of the "schematic object", however, it takes on a new
clarity and force. Science, (with its "objects"), becomes an immediate corollary of my theorem for
our perceptual world. It is just our ultimate, (and, ultimately, schematic), scheme for coordinating
reactive process. It is our species' ultimate strategy, and ultimate metaphor, of biological response.
Naive-realism, (and Naturalism as well -at whatever level of sophistication), as a world-
view, demands our belief because it makes our existence simple and our "objects" real -really!107
My hypothesis is disturbing, however, because it makes them unreal -really! I propose that our
ordinary objects of perception are convincing, and the relations we find between them simple,
precisely because the brain's calculus has been evolutionarily optimized108 for them!109 They are
the utilitarian artifacts effective in our prior evolutionary history.110 But now this is changing.
They no longer adequately serve their prior role. The calculus they optimized can no longer utilize
them as proper "objects" in the larger experience -the experimental and theoretical context of
current science, nor in the technology it enables. Ordinary objects will not serve quantum physics,
(or the transistor television it generated), -nor do they allow the solution of the mind-body
problem!
I wish to propose the schematic model, rather than the representative model, as a serious
alternative for our perceptual world. Would evolution "equip its creatures" with a representational
and perception, (the objects) - is the one that evolution supplied us with. (I will resolve the obvious difficulty in my third thesis.)
107 cf Fine 1986 108 This is not the self-contradiction it might seem. I accept the relationality, (i.e. the predictivity), of evolution, but not
necessarily its ontic primitives. I will develop this theme in Chapters 3 and 4. 109 Cf. Lakoff on Rosch’s “basic level categories”. 110 Compare Lakoff’s discussion of “prototypes”.
46
ive.
ve
model of reality? Could it?111 I think the case for a schematic model is the stronger one.
Primitive neural systems are, in point of fact, operational and reactive rather than representat
The incremental refinement of an operational, (schematic), model is, then, linearly consistent with
the principles of evolution. It is a simple consequence of evolutionary process, a progressi
organization and optimization of reactive response. The origin of a representative, (Naturalistic),
model, however, involves significant logical discontinuities. No one credits representative models
to evolutionary primitives. Who will posit such a model to the nervous system of a hydra or a
planarian worm, for instance? Representationalism must maintain, therefore, that at some discrete
point in evolutionary history an organism's internal process somehow came to parallel its
environment112 rather than simply reacting to it -which is quite a different case. This is a very
large assumption, -a very good "trick"- lacking any incremental or physical rationale other than "it
must have" or "it would be beneficial if it had". But is this not simply petitio principii, (assuming
what you have to prove)? How?
The case for the reactive role of brain throughout evolution is overwhelming, but nowhere
is there any case at all for a representative role.113 Indeed, there is not even a viable conception of
such a role -it is the essence of the mind-body problem itself.114
My first hypothesis seems to fit very well with what we know so far. Do we perceive
mathematical magnitudes, (wavelengths), of light waves or "colors"? Do we perceive molecular
111 see the argument of Appendix A 112 this is P.S. Churchland's "good trick"! 113 other than the one which assumes its own conclusion. If our perceptual world were, in fact, representative of
reality, then the representation of the brain would, therefore, be efficacious! The argument confuses consistency with necessity.
114 See Chapter 2, "The Logical Problem".
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density or "hardness"? Do we perceive mean molecular energy or "heat"? We are dealing with a
model. I propose that it is even more of a model than we suspect -to include our "objects" as well!
My conception is a direct and linear extension of the historical progression of science away from
naive realism. Our sensations are no longer "knocking at the surface of our brain", but, rather,
affect it at the system level to yield schematic artifacts -the "objects of perception". The
"perceptual object", I argue, is a schematic artifact of process!
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Preface to Chapter 2: The Logical Problem -and Realism Again
In a problem as complex as this one is and as complex as I propose its solution to be, it will be
important to have signposts to look at periodically so that we can orient ourselves. These chapter
prefaces are intended to serve as those signposts. So then, where have we gotten to at the end of
Chapter 1?
In the first chapter I presented a concrete alternative to the representative model of
cognition. It was not really intended to stand alone as an argument however, nor do I really expect
anyone to be convinced at this point. (Those arguments are in chapter 3, 4, and 5 and in the
Appendices.) Indeed, it goes against almost everything we know or believe and, at first blush, it is
absurd. Chapter 1 was intended only to explain and to show a certain plausibility of the theme.
But discursive arguments would not serve in any case to change the minds of realists and
practical scientists on the issues of our most fundamental paradigm –of our realistic worldview
itself. Yet I speak to none other than those –realists and practical scientists! Realists question their
most fundamental paradigm only when innovative perspectives illuminate vast new areas or
simplify whole aspects of important problems leading to pragmatic results –and then only to the
extent implicit in the gain. (The theories of Relativity and Quantum Mechanics are profound
recent examples of just such a modification of the realist paradigm.) What realists will never
question however, -nor will I as I stand with them- is realism itself.
But what is “realism”? To be a realist, does it mean that we must assume all the baggage
that comes with the name at this particular moment in history? Was it not identical, then, with the
realism of the Ptolemean/Aristotelians who stood against the counter-intuitive theories of
Copernicus? Had Dr. Johnson lived then, might he not have kicked the nearest rock, rejoining
49
Copernicus: “Now it is moving!”115 But is it identical, now, with the realism of Pierce’s chalk,
which he threatened to drop and break and thereby prove its reality? Does realism mean today
that, besides an inviolate faith in the existence of an absolute ultimate reality, we must assume the
possibility of absolute knowledge of that (ontic) reality as well –even at some coarse scale?
Physicists, (the penultimate realists), have been forced to embrace algorithmicity and
epistemological uncertainty at the very small, the very large and the very fast scales. If our middle
scale objects were taken as the objects of a biological algorithm –prototypes116 of biological
logic117 as well, then continuity would be reestablished to epistemology across the board. But was
not even fundamental epistemological uncertainty, (i.e. the general case), as well as physical
uncertainty always a possibility within the basic confines of realism?
Gerald Edelman, (following Putnam and Lakoff), lists the three essential tenets of what he
calls “scientific realism”, (Lakoff calls it “basic realism”, Putnam "internal realism"): “(1) a real
world (including humans but not depending on them); (2) a linkage between concepts and that
world; and (3) a stable knowledge that is gained through that link.”118 The combination of my
three themes will confirm Edelman’s first and second postulates,119 but the “knowledge” in his (3)
will be argued as mathematically and scientifically relativistic120 in its significance and pragmatic,
(i.e. algorithmic), in its justification. In Chapters 3 and 4 I will argue on biological and Kantian
115 Johnson, of course, is famous for his demonstrative argument against idealism. He is said to have kicked a rock
saying: “I refute it thus!” 116 Cf Rosch, Lakoff, Edelman 117 (process) 118 Edelman 1992, p.230 119 I argue that the “linkage” in Edelman’s second postulate is real but blind however. Cf Chapters 1, 3, 4, 5 and
Appendices A & B. 120 see below
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grounds for just two fundamental “axioms” of realism however: (1) the “axiom of externality”,
(Chapter 3), and (2) the “axiom of experience”, (Chapter 4), which roughly correspond to
Edelman’s first two requirements. Together they define the absolute minimum and necessity of the
realist position. In Chapter 4, I will argue for a rigorous scientific relativism of knowledge in
general, a special kind of relativism however, based (in seeming contradiction) on an absolute! It
is based on an invariant -the invariant of experience. Invariants, the mathematical conception of
that which does not change under varying (relativistic) perspectives, (varying coordinate systems
for instance), are the basis of Einstein’s Special Relativity, of course. The rigid, i.e. unvarying and
concrete equations of that theory supply an explicit illustration of the kind of relativism and
stability121 I wish to argue, (following but modifying Cassirer), for knowledge in general. It is
diametrically opposed to “capricious relativism”, “specious relativism”, “Whorfian relativism”,
“cultural relativism”, or the relativism of Solipsism, for instance. Nor is it “idealism”. Anything
does not go! Knowledge must be commensurate with experience, (to include the experience of the
results of scientific experiment), but its organization, its “co-ordinate system”, (of which I argue
“objects” are a part), is not innately fixed thereby. It is experience itself, i.e. that which must be
accounted for,122 and not any particular organization of that experience which is a necessary
(second) metaphysical, (i.e. ontological), posit of realism.
Edelman, basing his arguments in Lakoff’s, (and, ultimately, Putnam’s), argues –as I will
argue- against the further extension of the realist position into “metaphysical realism” –against its
incorporation of “objectivism”. (I have used the name “Naturalism”):
121 in agreement with Edelman’s third postulate of realism. 122 In the sense of chapter 1 and which I will argue explicitly as the subject of chapter 4. See especially the “King of
Petrolia” fable.
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“objectivism assumes, in addition to scientific realism, that the [actual] world has a definite
structure made of entities, properties and their interrelationships….[that] the world is
arranged in such a fashion that it can be completely modeled by what mathematicians and
logicians would call set-theoretical models. … Symbols in these models are made
meaningful (or given semantic significance) in a unique fashion by assuming that they
correspond to entities and categories” [which themselves exist] “in the world. Ibid, p.231-
2, my emphasis
Edelman, like Lakoff and Putnam, argues against this “objectivism” –against a privileged
“God’s eye view of the world”. His arguments constitute a critique of logic –based in Lakoff's
synthesis of extensive empirical studies of actual humans, actual cultures, and actual languages
which challenge the classical theory of the category. Thereby they question classical logic, (of
which it is the foundation), itself. Edelman’s motivation, however, derives from his theory of
neuronal group selection, (TNGS), -“Neural Darwinism”- wherein he argues that the brain is not
informational but “ex post facto selective”.123 Brains, Edelman argues, are not commensurate
between individuals at the finest scale –even between genetically identical individuals. They are
therefore not the sort of things that information or programs run on. He argues the human genome
is too small to create such an “information machine”.124 Edelman’s arguments are made in support
of his theory of “Neural Darwinism”. While it is a very plausible theory, (and the sort of thing my
thesis would suggest), it has yet to be confirmed. In chapter 3, I will base my arguments to the
123 i.e. brains select from pre-existing internal variation on pragmatic rather than informational grounds as the immune
system does 124 Edelman, 1992, P. 224. His argument is very similar in form and purpose to my argument of Appendix. A.
52
hapter 2.
same end in Maturana and Varela’s. Their arguments are made from the fundamental principles of
biology, (and physical science in general), however and so carry a greater generality and force.
In this second chapter I will show that my first thesis, in concert with my extension of
Cassirer’s logical hypothesis, does accomplish the kind of expansion and illumination –the
explanatory power- that realists require to seriously re-examine their premises. For one, it allows a
viable and natural theory of meaning for the first time.125 More significantly it also supplies a
realistically tenable theory of what, (were the word not pre-empted), I would be tempted to simply
label “cognition”. By this I would mean not “performance” or “problem solving”, (in the sense
used in Cognitive Science), but knowing!126 How is it possible to know? How is it possible for
one part of a physically and temporally separated process, (the process –or material- of the brain
for instance), to know, (rather than merely interact with127), another part? How would it be
possible for one part of even a mental space to know another part? This is the problem that
Leibniz characterized as the problem of “the many and the one”. How can the many be known to
the one? How can there be knowing without a homunculus? How can there be knowing without a
mystery? How can there be a "Cartesian Theatre"?128 This is the target of C
125 Putnam and Lakoff argue against even the logical consistency of the standard solution –a truth-functional mapping
from a formal system to a model. 126 There is, of course, a definitional problem here. “Knowing”, “awareness”, “cognition" +are all often understood as
referential, operational, et al. But the other sense: i.e. conscious knowing, conscious awareness, conscious cognition, is precisely the problem we are here to solve. It does not consist in showing how an automaton, a “zombie”, a Turing machine –or even a biological organism- can be constructed to be indistinguishable from a human respondent. Dennett, and almost every other realist writer on the subject, (even Edelman sidesteps the problem), thinks that our ordinary sense of these words is impossible. The “homonculus”, the “color phi”, etc. argue against a “Cartesian theatre”. It is the subject of this chapter to show how just such a “theatre” can be constructed, consistent with scientific logic.
127 “Interaction” is process/doing; it is not “knowing”. 128 After Dennett's usage
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Meaning
The adoption of my first thesis enables the utilization of perhaps the most profound
proposal ever suggested for the problem of meaning: Hilbert’s “implicit definition”. (It is very
important that this not be confused with mathematical “formalism” –a theory of proof- of which he
was also the author.)129 Hilbert proposed that the “things” of mathematics –for mathematics- are
solely a function of the laws, (axioms), in which they are framed and that their “meaning” is
exactly their role (function) in those laws. Its “objects” are “implicitly defined” by its axioms. 130
They are logical objects!
My first hypothesis enables Hilbert’s “implicit definition” to function as a general theory
of meaning however as opposed to its present limited usage as a theory of specifically
mathematical meaning. If our (human) model is internal and algorithmic rather than referential,
(the first hypothesis), if our “objects” are metaphors of process, if even our very logic is taken as a
biological rule of function vis a vis environment, (as a “constitutive logic” in Kant’s terminology),
rather than as transcendent131 revelation, (as I will argue in this chapter), then the meaning of its
(now) “bio-logical” objects may reasonably be understood as their implicitly defined role in that
process. (This is the "metaphor" I referred to previously.) This is very close to our ordinary, naïve
129 This is not a superfluous caution considering, for instance, Lakoff’s treatment of formal systems and meaning, (nor
Edelman’s cavalier dismissal of axiom systems). It is in the assignment of a truth function from a formal system to a model wherein he challenges the logical validity of the objectivist theory of meaning based on Putnam’s argument. “Implicit definition” must be strongly distinguished from “formalism” which was conceived by Hilbert as a theory of proof. Implicit definition”, however, was conceived specifically as a theory of meaning. It derives instead, I think, from his background as the “king of invariants”. The “things” are the logical invariants of the axioms.
130 I.e. They are specified from primitive operations rather than from primitive properties. 131 In Kant’s sense of the word
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sense of “meaning”132 and quite different from its proposed formalistic and counterintuitive
definition as “reference” or truth functional mapping.
Knowing:
The first hypothesis, in combination with an extension of Cassirer’s logical hypothesis and
Hilbert’s mathematical conception, also enables “knowing”. It allows a solution of the problem of
the “many in the one” / the "Cartesian Theatre" without magic by extending the very logic within
which we conceive it. This is a logical problem for which I will propose a concrete logical
solution as the subject of this chapter.
Anthropological and Linguistic, and Logical Commensurability
I have mentioned the commensurability of my first hypothesis with existing empirical
findings reported by Rosch, Lakoff, et al., and will go into the subject further in the “Afterward:
Lakoff, Edelman and Hierarchy”, so I will not belabor the point. I submit that it is a pretty good fit
with the whole of these extensive studies.
Realism Again:
But are the retrodictive solutions of these admittedly profound problems sufficient to cause
a realist to accept such a distasteful diminution of his supposed powers? My answer, (as I would
expect yours to be), is “no”! These kinds of answers –however good they may be133- are at best
132 “Meaning”, normally understood, has to do with connectivity to other meanings. 133 And I think they are very good!
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only hints to the progress of science.134 This is why I argue my answer only as a tentative one. It
is the future of science which will answer this question. It is only in broad new consequences –
pragmatic consequences- that a compelling case could be made. But to conceive consequences, we
must first entertain the premise.135
As a realist then –talking to other realists-, I ask only that you truly practice your own
realism at its strongest. But realism is ruthless. It is concerned, ultimately, only with what works –
no matter how painful that may be to our cherished prejudices. I ask that your realism be a ruthless
–and honest- one therefore, both for and against my hypothesis!
This next chapter will be difficult and technical. For this, I apologize. It will be necessary
to examine the technical foundations of logic itself because the implications of classical logic and
its modern embodiment, (taken as a necessary and sufficient tool rather than as a special case),
force us to abandon an important part of our realism, i.e., ourselves, (normally taken)! Formal
logic also provides an important and specific clue to the nature of mind itself.
The foundations of logic are also especially relevant to the mind-brain problem because
ultimately, (I will argue), logic is itself a biological and evolutionary phenomenon, and not,
(following Kant’s usage), “transcendent”. Logic is not God-given! I will propose a reformulation
of classical logic based in the proposals of Ernst Cassirer who questioned its adequacy and
proposed an extension three quarters of a century ago. I will extend Cassirer’s thesis, and then
134 Conversely, however, these are the kinds of things that we would like any viable theory to explicate. They are
strong and viable clues to any acceptable theory and no proposed realist theory before this has done other than to deny them.
135 I will discuss this issue further in the “Lakoff/Edelman appendix. My thesis has direct implications for neuroscience, but it also has implications for the foundations of mathematics and logic and thereby for the whole of hard science itself. It challenges the adequacy, (but not the validity), of even that lynchpin of modern thought –the mathematical set! In the “Dennett” appendix, I have also sketched what I believe could be the beginnings of a first scientific psychiatry.
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marry it to my first, biological hypothesis to arrive at what I propose as an actual solution of the
problems of the “homunculus” and the "Cartesian Theatre", (the problem of “knowing”). It is a
solution absolutely consistent with the dictates of modern biology. My logical answer superficially
resembles the conclusions of Edelman and Lakoff, but is of a greater generality and depth. That
greater generality will be necessary for the resolution of the obvious epistemological
contradictions136 in which those authors embroil themselves. It is necessary for the resolution of
the logical paradoxes of sentiency.
Cassirer’s logical thesis was in many respects driven by the same forces as Lakoff’s, but it
was a more rigorous, realistically plausible and cogent solution I believe. The problem with
Lakoff’s proposed solution137 is that concepts/categories138 can be anything at all! They are
arbitrary and dependent on history. How, then, can a logic, (or a worldview), based on categories
be formed? Lakoff’s conception is considerably better than this,139 I admit, in that it is grounded in
empirical considerations –in anthropological and linguistic findings. But at the base –wherein are
we to ground and evaluate these findings? There is no possibility of a formalism. If anything is
provable, then it is a triviality that nothing is provable! We stand on quicksand.
Cassirer’s extension of the classical concept/category however was grounded firmly in the
history of the successful advance of mathematics and physical science but it was not arbitrary. He,
136 They both emphatically disclaim the possibility of a “God’s eye view” of the world, and then both proceed to supply
exactly that –a (sophisticated) “naïve realistic” , (i.e. “objectivist”), answer in a “naïve realistic” , (“objectivist”), world! Both embed their answers precisely inside the particular “container” schema! Maturana and Varela encounter the same difficulty.
137 Cf Afterword: Lakoff / Edelman 138 I will use these interchangeably
139 More accurately, it is based in ICM’s, (“idealized cognitive models”), derived from bodily function. But all of these ICM's are defined precisely within the particular “container schema”, (the set-theoretic ICM), of the body in
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like Wittgenstein, Lakoff and Edelman, challenged the set-theoretic foundation of logic. He
argued that our concepts, (categories), in the most general case –and especially in the case of
mathematics and science- are not grounded in a commonality, (an intersection), of properties of the
members. The logical concept of “metal”, he argued for instance, does not ignore, (or exclude),
the element of “color” even though there is no color common to all metals. Even though gold is
yellow, and steel is silver and copper, well, “copper-colored”, the logical concept of “metal” does
not exclude color thereby, (as set-theoretic abstraction would suggest), but retains it as a
function.140 This function assumes the value yellow for gold, silver for steel, etc. X(gold) =
yellow, X(steel) = silver. There is, of course, no “metal” without a color. The case is identical for
conductivity, (Y), specific gravity,(Z), etc. The legitimate concept of “metal” is then the function,
M(X,Y,Z,…). The actual logical and scientific concept, (category), in general is then, (Cassirer
plausibly argues), a rule of rules, a function of functions which assume definite values and fully
encompasses its extension. It is only in the special case, the limit case of the concept that the
classical definition obtains. That is the case where the rule is specifically “identity”, e.g. the
concept of all men whose hair is ( = ) blond,141 or the series, 3,3,3… rather than 2,4,8…. It is the
simplest case of the functional rule: where all the elements of a series are the same.
But limit cases in mathematics have a privileged place and a strict rationale. In general,
they are not ad hoc definitions or artificial impositions. In general, they are the result of taking a
general case at the limit –but only in the special and particular instance where that action results in
space! It supplies therefore the very “God’s eye view whose possibility he disclaims. Lakoff’s relativism does not satisfy the paradox he creates. cf “Lakoff/Edelman Appendix”
140 defined on a series 141 [blond, blond, blond,…]
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a plausible and fruitful continuity of concept. (A “circle”, for instance, can be taken as the natural
limit case of the “ellipse” -wherein the foci are the same.) The study of limits provides an
abundance of examples where that is not the case however.
Usually, (and preferentially), that process results in a quantum simplification of the
discipline wherein it is adopted. The “zero” case in integer arithmetic, (how “many” is zero, after
all?), allows the whole spectrum of the integers, (positive, negative and zero), and the possibility of
free computation beyond the simple counting or aggregation of the positive integers. Cassirer’s is
alike a natural and plausible extension of classical logic itself. It retains classical logic as its truly
natural limit case142 in just this sense of the limit cases of mathematics. It is neither ad hoc nor
“mathematics”), is a function of functions, a rule. I will postulate a further but still natural
extension of Cassirer’s logical hypothesis in this chapter: “the Concept, (category), of Implicit
Definition”. It too is rule-based, but it is based in the unified rule of an axiom system, (i.e. the
conjunction of the axioms). It too is a lawful conception.
I will conclude this chapter with an assertion of “concordance” which I argue is the
strongest present argument for my hypotheses. 143 The form of the solution attained by my
biological argument for the brain, (chapter 1 and argued in chapter 3 and the appendices), and the
form of the solution for mind, (attained independently on purely logical grounds in chapter 2), are
142 Classical logic represents the special case of a rule of series wherein the rule is identity. 143 There are other strong grounds as well. In line with the “productivity requirement” I referred to above, it yields
new insights into the foundations of mathematics and logic. These are not trivial concerns in light of the acknowledged discordances in set theory and logic. Rosch’s and Lakoff’s empirical findings are a strong fit as well.
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perfectly commensurate! Mind, I will argue therefore, is the unified rule of behavior144 –but that
rule, (as I will argue for my logical hypothesis in this chapter), knows its “objects” –they are
implicitly defined! Leibniz’s problem is solved.
At this point, (at the conclusion of Chapter 2), I will have satisfied the logical and
organizational requirements of mind-brain problem. I will not at that point have provided an
answer to the “substance” of mind however. That requirement will be addressed in my third and
final hypothesis, the subject of chapters 3, 4 and 5.
As realists, we require an assumption of externality roughly equivalent to Edelman’s first
tenet of scientific realism, but as just the same sort of realists we require an assumption of self and
knowing as well. If we kick a stone, (with Johnson), or drop a piece of chalk and expect it to
shatter, (with Pierce), we expect to know these things. (We also fear the possibility of a broken toe
or the inability to continue our lecture!) The specifically metaphysical, (ontic), existence of our
experience is part of that selfsame realist demand. How else do we, (as realists), judge the viability
of theories of that externality except by their compliance with experience?
As a realist, and if a choice were forced between the two, I suppose my tendencies would
tend, (barely), toward “externality”. But this is precisely the kind of choice, forced by logic, which
would make me, (also as a realist), question logic itself. It is probably the only situation,
moreover, -wherein a crucial aspect of our realism is challenged –where such a suggestion would
be entertained seriously at all. Discursive arguments, logical antinomies, mathematical anomalies,
“cats on mats”145, anthropological and linguistic research, … –all these, (to the extent they are
plausible or even compelling), would be, (and have been), walled off and isolated from our basic
144 In a more general sense, (using the terminology of Maturana), of “ontogenic coupling”
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realism and the logic in which we conceive it. Who cares who shaves the hypothetical barber,
after all?
The predominant Naturalist school of neuroscience feels that it has been forced to make the
very choice I have described –and with very compelling (logical) arguments.146 It feels it must
choose between “externality” and self. Best and most frankly framed by Dennett, it concludes that
we are physical automatons, “zombies”.147 But the context –the comprehensive worldview- in
which we, (you and I), are right here enmeshed in considering this problem does not exist
according to Dennett! This “Cartesian theatre” is not a part of these zombies –you or I or Dennett
himself. The only place it might exist –and Dennett makes explicit mention of the fact- is in logic
itself, (in the robot Shakey’s program148). Dennett's worldview which contains his solution to the
mind-brain problem does not, (for Dennett), exist in Dennett! It exists, (as a particular draft), in the
logic of his book! This is linguistic idealism.
Naturalists cannot admit even the possibility of a “mind”149, (Dennett calls it a “figment”),
because they cannot solve the problems of the homunculus and the Cartesian Theatre. Specifically
they cannot solve the logical problems inherent therein. For there to be a whole, (“a one”), there
must be a “little man” inside who sees it as such. But for him to see it, there must be another little
man inside… This infinite regression, and the framing of the problem which generates its
necessity –as well as the logical difficulties of the “Cartesian Theatre” are the result of the
145 see Lakoff re: Putnam 146 Cf P.S. Churchland, or Dennett for instance 147 My apologies to Dennett, but, as I reflect in a later footnote, his “unfair to quote this out of context” prohibition does
not refute the fact that after several hundred pages, he says just that. 148 Cf Dennett 1991, P.130 149 normally taken
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limitations of the classical, set-theoretic (“container” 150) logic in which they are conceived. And
yet, as I think Dennett conclusively shows, they are the necessary result of applying that logic to
the mind-brain problem. If, as realists, we accept the adequacy of classical logic, and of the
Aristotelian concept/category which is its foundation, then the “self”, and the “experience”,
(normally and not behaviorally and mechanistically taken), which are profound parts of our
selfsame realism must die!
I consider Dennett’s, Churchland’s, … arguments convincing. In fact, I consider them as
conclusive when taken in conjunction with the classical logic within which they are framed. But
this conclusion was always implicit within classical materialism –which I also take very seriously.
Simply put, and to repeat myself, there is, (under the presuppositions), no way that part of a
spatially and temporally separated process –or material- can “know” another part. If ordinary
classical logic is definitive, then my form of realism, (ours?), is dead. I choose, however, to
question the premise. I, as a realist, choose to question logic.
150 In Lakoff’s terminology, it is a hierarchical “container schema”.
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Chapter 2. How? The Logical Problem of Consciousness
(Cassirer- Hilbert- Maturana: an Archimedean Fulcrum)
(Note, December, 2009: this whole chapter has been vastly re-oriented and expanded in my later
book: “Is the Incorporation of Exotic Mathematics Necessary for a Solution of the Mind-Brain
Problem? I think it is!” (In PDF) The first three chapters of the latter are specifically relevant to
and validate my perspective in this current chapter.)
"... Every attempt to transform logic must concentrate above all upon this one
point: all criticism of formal logic is comprised in criticism of the general doctrine
of the construction of concepts."151 (Ernst Cassirer)152
The problem of "consciousness" and the profoundest paradoxes of the mind-body problem: the
"Cartesian theater", the "mind's eye", and the "homunculus" are logical problems. They are
151 Compare also Lakoff: 1987, p.353. “Most of the subject matter of classical logic is categorization.” 152 Cassirer 1923 pps.3-4
He continues: "The Aristotelian logic, in its general principles, is a true expression and mirror of the Aristotelian metaphysics. Only in connection with the belief upon which the latter rests, can it be understood in its peculiar motives. The conception of the nature and divisions of being predetermines the conception of the fundamental forms of thought. In the further development of logic, however, its connections with the Aristotelian ontology in its special form begin to loosen; still its connection with the basic doctrine of the latter persists, and clearly reappears at definite turning points of historical evolution. Indeed, the basic significance, which is ascribed to the theory of the concept in the structure of logic, points to this connection. ..."
[But] "... The work of centuries in the formulation of fundamental doctrines seems more and more to crumble away; while on the other hand, great new groups of problems, resulting from the general mathematical theory of the manifold, now press to the foreground. This theory appears increasingly as the common goal toward which the various logical problems, that were formerly investigated separately, tend and through which they receive their ideal unity."
problems of logical possibility. How could cognition, how could mind, ordinarily taken, even
exist? It is not so much a problem of what it is that they actually are, but rather a problem of how
is it even possible that they could be! How, as Leibniz framed it, could "the many be expressed in
the one"? How could we know? In the context of realism, ordinary logic allows not even a
possibility -other than an eliminative reduction, (a denial), of the problem -and of sentiency itself.
The "schematic model" of my first hypothesis cuts to the core of these problems. Coupled
with Ernst Cassirer's extension of traditional logic, (his "Functional Concept of Mathematics"),
itself extended again in light of the expansion of logical possibility innate in David Hilbert's
"implicit definition"153 for the axiom systems of pure mathematics, it illuminates them and
demonstrates a specific "how" for the first time. The answer turns on an extension of the formal
logical Concept154 and with it, of logic itself. Surprisingly that answer will allow us to retain our
normal, ("folk"), conception of mind as well.
Let’s Start from the Other End: First Hilbert's "Implicit Definition":
1. David Hilbert's book, "Foundations of Geometry"155, is a recognized milestone in the history of
mathematics. In it, he proposed a new axiomatic foundation for Euclidean geometry. His novelty
lay in his methodology however.
It is just this "general mathematical theory of the manifold" to which he refers at the end which, I will argue, forces an
even further extension of Cassirer's own arguments. 153 as strongly distinguished from his "Formalism" which is quite a different issue 154 I will be employing a convention of capitalizing the word “concept” when it denotes the formal, technical notion of
the concept to avoid such verbiage as “the concept of the concept”, etc. 155 "Foundations of Geometry", Hilbert, 1910.
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His axioms, (as usual), referred to certain objects: "points", "lines" and "planes" and to
relations between them: "to belong to", "between", and "congruent to". Hilbert's radical
innovation, however, lay in the fact that he quite purposefully never specified, (and never had to
specify), what "point", "line" and "plane" were to be or the meanings of the specified relations. He
never required a specification of properties. He stipulated that the sole significance and exclusive
consequence of his "objects", (undefined terms), was to be in their operationality as expressed in
the axioms. They were to be "implicitly defined" by those axioms. The success and the fertility of
the subsequent extension of his approach across the whole of modern mathematics illustrated
thereby that mathematical axiom systems, insofar as they are mathematical, need define their terms
and their elements, (their "objects"), only operationally and internally, not referentially. They do
not define those terms in terms of set theoretic operations on primitive properties.
Consider the "integral domain" of Modern Algebra as a typical application of Hilbert's
ideas. Axiomatization begins with the simple assumption, (conditionally) of a set of "elements",
(objects), -its "domain"- which obey a set of rules, (axioms). These objects, (of its domain -and
"existence" terms generally), are assumed only, (as Wilder points out) "presumptive(ly)" and
"permissive(ly)" however. We are told nothing about them in an objective sense.
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The only objects posited explicitly and definitionally are the identity elements '0' and '1',
the additive and multiplicative identity objects respectively. But these identity objects are
presumptive and permissive as well. They are wholly specified as just the identity elements under
these operations and no more - they are not the real(?) 0 and 1 or any other real objects.156 No
properties can be derived from the fact. Indeed, they are preferentially named otherwise -"e", for
instance or placed in quotes by mathematicians to divorce them from real experience. The
"addition" and "multiplication" operations, ('$' and '#', for instance), are conceived as totally blind
operations as well.
What are we given about the "e" object, ("1", for instance, or "0")? What properties are
assumed? Only that under the unspecified operations '#", ("multiplication"), or "$", ("addition"),
the result of combining any other objects with them, (e.g. [ e # x, or "0" $ y], x,y any members of
the domain), that the result is again x or y respectively.
x # e = x, y $ "0" = y
This is the whole of their definition and it is totally operational. What is conceptually
significant about the Integral Domain is that there are two distinct operations, connected by the
distributive law, not that they are some special operations.
In Modern Algebra, "equality", ("="), is unqualified and axiomatized as well. It is taken
specifically as an "equivalence relation", (under the rules/axioms of reflexion, symmetry and
transitivity), but it is the basic (and equally blind) equivalence term under which all other
156 These terms presume only existence, not any particular properties of that existence. This, I suggest, is what it means
for them to be "permissive".
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equivalence relations, ("≡"), are defined. It is not necessary to assume, (a priori), for instance, that
"4" and "3 + 1" are "names" for, (i.e. denote), the same object, only that they are equivalent under
the basic equivalence relation of "equality", (i.e. that "4" = "3 + 1").
We are allowed to derive the other elements of the domain solely operationally as well - in
terms only of these two givens, the '0' and the '1', (subjects of the only specific existence
postulates). Thus '1' + '1' = '2', for instance, and '2' + '1' = '3', etc.157 We can derive another
element '-1' as the additive inverse, (under the conditional "existence" axiom of the additive
inverse), and 'negatives' of the others as well. Continuing this (conditional) process, solely in
terms of the axiomatic laws, (operationally), we can build the whole of an integral domain and it
relates158 to the real integers "up to isomorphism".
“Relation”, definable within a mathematical system, (as an n-tuple, for instance), is an
operation of a different order and meaning than the operational, (relational), primitives of that
system which are employed to define that “relation". The primitive operations of an axiom system,
("addition" and "multiplication", for instance), are the constitutive relations of axiomatics. When
axiomatics defines a “relation” internally, however, it is a subsidiary relation and has a different
import –it is defined relative to the primitives.
The point of all this is that the whole process of specification -i.e. the whole of the definitional
content of the elements, (objects), of this integral domain is achieved solely in terms of the blind
operations specified in the axioms acting on property-indiscernible, blind, objects, not by set
theoretic refinements on primitive, (atomic), properties of these elements. Nowhere in this
157 Under the assumption that '0' ≠ '1' 158 given the addition of the Well-ordering principle, itself wholly operative as well
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axiomatic system are the primitive operations identified with real integer operations, (or any other
"real" operations), nor are they dependent upon them. The case is the same for the
elements/objects of the system. Nowhere are they dependent upon any "real" objects, so no real
properties may be legitimately identified with them.159 This is, as Schlick says, a genuine
"Copernican revolution", (after Kant's usage), in the history of mathematics. More, it is a new kind
of logic, distinct from the logic of Aristotle which is wholly dependent on set theoretic refinement
of original properties of its objects.160
Hilbert's conception results in a novel and very different kind of "object",161 one which is
wholly constituted as an expression of the logical relations of the axioms. It is a logical object!
Hilbert's brilliant reformulation of its foundations, almost trivial in appearance, has become the
heart and soul of modern mathematics.162 Mathematics no longer looks to experience for its
159 Compare Cassirer: "…we have in pure mathematics a field of knowledge, in which things and their properties are
disregarded in principle, and in whose fundamental concepts therefore, no general property of things can be contained." , "Substance & Function", p.18 Does this mean that we must follow Hilbert into "formalism" -i.e. the simple manipulation of "marks"? I don't think so, for there is nothing particular about any given choice of marks in an axiom system- e.g. the identity elements might be named by any other marks, so long as the usage is consistent. It is the relationality, the operationality of those marks in a connective system which is significant. What "implicit definition" furnishes, then, is a concept embodying the invariant relationality of the system under all consistent substitutions. What is important about it is that that invariant relationality is non-trivial -e.g. that an " integral domain", (taken abstractly), can correspond with the real (?) integers "up to isomorphism"! (Birkhoff & Mac Lane, 1953, p. 34)
160 Cf. The section immediately following this and the Afterword: Lakoff / Edelman for a further discussion of Aristotelean Logic.
161 Consider the "object" of Chapter 1 in this light. 162 I make a very large distinction between "implicit definition" and "formalism", both products of Hilbert's sweeping
intellect. The latter deals with a formal and mechanical methodology of proof while the former deals with actual and internal logical implication -which is not the same as its formal expression. Most working mathematicians are not particularly committed to "formalism", but they are very definitely committed to "implicit definition". Every time a mathematician goes to definitions, (which is all the time), he goes to the undefined terms of the system he is dealing with -and no further!
Hilbert was a "catholic" mathematician in the small "c" sense -he had enormous scope. It is the "king of invariants" who sired "implicit definition", I believe, and not his twin –i.e. the father of "formalism".
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substance163 or its validity. It concerns itself, rather,164 solely with the fertility and the rigorous
internal consequences of systems of explicit ideas. Ultimately, it is the science of the total
possibility of order.165
Schlick characterized Hilbert's innovation this way:166
“The revolution lay in the stipulation that the basic or primitive concepts are to be
defined167 just by the fact that they satisfy the axioms.
[They] "acquire meaning only by virtue of the axiom system, and possess only the
content that it bestows upon them. They stand for entities whose whole being is to be
bearers of the relations laid down by the system.", (my emphasis)168
This is the description of a genuine and profound "Copernican Revolution" in logic itself.
Here "relation"169 logically defines "entity", not the converse. This entity is a function of (logical)
process. But "implicit definition" has another deep logical significance. It does not define its
"objects" within the dualistic and oppositional context implicit in the foundations of classical
163 As Cassirer commented, this does not mean that it does not look to experience as the origin, the suggestion for its
ideas, but rather that it does not accept experience as the arbiter of its substance. 164 as is clearly visible in the evolution and reassessment of modern geometry -in the grounds for the resolution of the
"parallel postulate" problem and Non-Euclidean geometries, for instance, and in the whole of Abstract Algebra. 165 This is the lesson of Abstract Algebra. I will make this case later in this chapter as part of the argument for the
Concept of Implicit Definition. 166 See also Einstein (1954), P.234, and Wilder (1967), Pps.3-8 167 It is crucial to understand that "defined" is used in a very different sense in mathematics than in the sense of
ordinary "dictionary definition". It specifies the actual, the whole and exclusive existence -for mathematics- of the entity defined. Mathematics students are ingrained in this as the very first step towards "mathematical maturity".
168 Please note the close parallel to the argument I made in the "training seminar" of Chapter 1 169 i.e. the constitutive relations specified in the axioms
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f
y problem.
Aristotelian logic. It does not define them within the classical schema of presentation170 /
attention171 abstraction172 of properties.173 It defines and resolves its objects, rather, by internal
and logical resolution of its fundamental operations, and therein supplies the first clue to a logical
possibility for sentiency -i.e. for the many-in-the-one.174 Cassirer's analysis, (and actual
reformulation), of the formal logical Concept175 is crucial to an appreciation of the full
implications however. Hilbert and Cassirer together, in company with the "schematic object" o
Chapter 1, supply a new logical ground -the logical ground necessary for a resolution of the
problems of sentiency, and, finally, for a resolution of the mind-bod
Cassirer and Classical Logic:
2. Cassirer argued that “the object” of modern mathematics, and “the object of mathematical
physics” as well, (their "ideal" objects), are conceptual objects (only). He maintained that the
Concept they actually embody in modern science is not the classical (Aristotelian) "generic
Concept" however, but is rather a new "Functional Concept of Mathematics", (Cassirer’s Concept).
He argued that modern mathematics and modern physics have already reconceived the formal
logical "Concept" itself, albeit tacitly.176
170 cognition of objects/sets of atomic properties 171 attention to specific properties of the former 172 abstraction = set theoretic intersection of those properties 173 The problem of the "homunculus", I will argue shortly, is already implicit in this (classical) framing of the concept. 174 –i.e. that our objects are not perceived or referential objects, but created ones!. 175 Cassirer, 1923, Pps.3-233, especially Pps. 3-26 176 ibid. Also see his "Einstein's Theory of Relativity"
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The Classical Concept:177
Cassirer summarized the genesis -and the still-continuing usage- of the classical generic
Concept as the simple abstraction and the idealization, through "attention", of a commonality of
"marks", (properties), in a series of presentations.
"But what was beyond all doubt, as if by tacit agreement of the conflicting parties, was
just this: that the concept was to be conceived as a universal genus, as the common element
in a series of similar or resembling particular things."178
A series of presentations with characteristics: (a,b,c,d), (a,c,d), (a,c,e), for instance, is held
to bring forth the classical concept: {a,c}. From mere abstraction, (via attention), the whole of the
doctrine of the classical Concept follows from these simplistic origins. "Every series of
comparable objects has a supreme generic concept, which comprehends within itself all the
determinations in which these objects agree, while on the other hand, within this supreme genus,
the sub-species at various levels are defined by properties belonging only to a part of the
elements."179
But the successive broadening of a concept necessarily correlates to a progressive lessening
of its content; "so that finally, the most general concepts we can reach no longer possess any
177 See also “Afterword: Lakoff, Edelman…” for another discussion of the classical concept. 178 "Substance and Function", p.9 179 ibid p.5 This passage, (delineating, incidentally, the mathematical "power set"), suggests also the absolute hierarchy
of concepts, (and theories), implicit in the classical conception. Cassirer's alternative, (which I will discuss shortly), reveals a new possibility, developing into his theory of "symbolic forms" which I will elaborate in Chapter 4.
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definite content."180, [at all!]. The ultimate genus -"something"- is totally (and logically) devoid of
specific content!
Contra the Aristotelian Concept:
The Concept in this form, however, is clearly not adequate or consistent with scientific, nor
even with ordinary usage:
"When we form the concept of metal by connecting gold, silver, copper and lead, we
cannot indeed ascribe to the abstract object that comes into being the particular color of
gold, or the particular luster of silver, or the weight of copper, or the density of lead;
however, it would be no less inadmissible if we simply attempted to deny all these
particular determinations of it."181
It would not suffice to characterize "metal", for instance, "that it is neither red nor yellow,
neither of this or that specific weight, neither of this or that hardness or resisting power"; but it is
necessary to add that it "is colored in some way in every case, that it is of some degree of hardness,
density and luster." Similarly, we would not retain the general concept of "animal", "if we
abandoned in it all thought of the aspects of procreation, of movement and of respiration, because
there is no form of procreation, of breathing, etc., which can be pointed out as common to all
animals."182
180 op. cit p.6 181 ibid P.22 182 ibid P.22
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Cassirer's Alternative: "The Functional Concept of Mathematics":
Cassirer proposed an alternative and considerably more plausible basis for a different
technical logical Concept -borrowed from mathematics - "the Functional Concept of
Mathematics":
"Lambert pointed out that it was the exclusive merit of mathematical 'general concepts'
not to cancel the determinations of the special cases, but in all strictness fully to retain
them. When a mathematician makes his formula more general, this means not only that he
is to retain all the more special cases, but also be able to deduce them from the universal
formula."183
But this possibility of deduction does not exist in the case of the scholastic, (Aristotelian),
concepts, "since these, according to the traditional formula, are formed by neglecting the particular,
and hence the reproduction of the particular moments of the concept seems excluded."184
"The ideal of a scientific concept here appears in opposition to the schematic general
presentation which is expressed by a mere word. The genuine concept does not disregard
the peculiarities and particularities, which it holds under it, but seeks to show the necessity
of the occurrence and connection of just these particularities. What it gives is a universal
rule for the connection of the particulars themselves.... Fixed properties are replaced by
183 ibid P.20-23 184 ibid P.20-23, my emphasis
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universal rules that permit us to survey a total series of possible determinations at a single
glance."185
We do not go therefore from a series: a-alpha1-beta1, a-alpha2-beta2, a-alpha3-beta3...
directly to their common element a, (Cassirer argues), but replace the alphas by a variable x, and
the betas by a variable y. Therein we unify the totality in the expression "a-x-y", (actually w-x-y,
where "w" is the constant function w(p) = a, (for all p), of the "generic concept"). This expression
can be changed into the "concrete totality" of the members of the series by a continuous
transformation, and therefore "perfectly represents the structure and logical divisions of the
concept"!186
Cassirer's "series" may be ordered by radically variant principles however: "according to
equality", (which is the special case of the "generic concept"), "or inequality, number and
magnitude, spatial and temporal relations, or causal dependence"187 -so long as the principle is
definite and consistent.
185 ibid P.20-23 186 ibid, P.23 As one of Kant's commentators urged about one of the latter's arguments, I find this argument as
"mirabile dictu". It is the clear and true expression of what we mean by a "Concept". It is the functional assemblage of a set of rules. Rosch and Lakoff have argued in more recent times, (based in hard empirical data), that the categories of actual human beings, actual human cultures, actual human languages are not, in fact, grounded in the classical Aristotelian "Concept" but are based, instead, in prototype, metaphor, metonymy, association, radial categories, etc. But what are these, (in their anthropological totality), but the free posit of rules of category formation? Cassirer has provided a more classical and rigorous conceptualization. It incorporates the possibility of all (consistent) rules in a classical formulation.
Clearly this does better correspond with ordinary and scientific usage than does the classical concept. It is the functionality of our definitions which specifies the concept. The mathematical "subset" is the limiting, rather than the typical, case therefore.
187 ibid P.16
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Thus he fundamentally reconceives the formal Concept, this our ultimate logical building
block, as "the "Functional Concept of Mathematics". It is the functional rule, F(x,y,z,...), which
organizes and embodies the totality of its extension.
Concept vs. Presentation:
Cassirer's new formal Concept is no longer logically derivable from its extension however:
"The meaning of the law that connects the individual members is not to be exhausted by the
enumeration of any number of instances of the law; for such enumeration lacks the
generating principle that enables us to connect the individual members into a functional
whole."188
If we know the relation according to which a b c . . . are ordered, we can deduce them by
reflection and isolate them as objects of thought. "It is impossible, on the other hand, to discover
the special character of the connecting relation from the mere juxtaposition of a,b,c in
presentation."189 190
"That which binds the elements of the series a,b,c,... together is not itself a new element,
that was factually blended with them, but it is the rule of progression, which remains the
same, no matter in which member it is represented. The function F(a,b), F(b,c),..., which
188 ibid P.26 189 ibid P.26, my emphasis 190 cf. Stewart, 1995, "Fibonacci Forgeries". Stewart's article illustrates the case. The "insufficiency of small
numbers" leads to an indeterminability of any finite series.
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determines the sort of dependence between the successive members, is obviously not to be
pointed out as itself a member of the series, which exists and develops according to it."191
This is the definitive argument against “abstraction” as the general case and “presentation”
as an ultimate foundation for logic. The association of the members of a series by the possession
of a common "property" is only a special case of logically possible connections in general. But the
connection of the members "is in every case produced by some general law of arrangement
through which a thorough-going rule of succession is established."192
Contra The Theory of Attention:
The "theory of attention"193 therefore "loses all application in a deeper phenomenology of
the pure thought processes", (i.e. cognition). The similarity of certain elements, (under the
classical view), can only be (conceptually) meaningful when a certain point of view has already
been established194 from which the elements can be distinguished as like or unlike. This identity
of reference under which the comparison takes place is, however, "something distinctive and new
as regards the compared contents themselves."195
191 ibid P.17 192 ibid P.17, my emphasis 193 It is "presentation" vs. "attention" which is at the basis of the oppositional orientation of classical logic, and which
is ultimately, I will argue, the origin of the problem of the homonculus. 194 Compare Lakoff: “Category cue validity defined for such psychological (or interactional) attributes might
correlate“, (his emphasis), “with basic-level categorization, but it would not pick out basic-level categories; they would already have to have been picked out in order to apply the definition of category of category cue validity so that there was such a correlation.” (Lakoff: P.54, my emphasis) See Afterword: Lakoff / Edelman. This is surely directly relevant to the context problem as well, (i.e. "the frame problem), in Artificial Intelligence research. (cf. Dreyfus, 1992)
195 ibid p.25
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The distinction between the concept and its extension, therefore, is categorical196 and "belongs
to the 'form of consciousness'".197 It is "a new expression of the characteristic contrast between the
member of the series and the form of the series".198
Cassirer argued that it is the equivalent of his "Functional Concept of Mathematics", rather
than the generic concept, that is the actual "Concept" which has been employed throughout the
history of modern science.199 He offered a convincing co-thesis, furthermore, that the objects of
mathematics and science are "implicitly defined", (in Hilbert's sense), specifically.200 The
"functional concepts", (their primitive laws), implicitly define their conceptual "objects" -and these
are the actual working objects of science.
Major Consequences:
Cassirer's "Functional Concept" marks a profound advance to understanding, (and our
specific problem), in two respects:
(1) it redefines the formal Concept, fundamentally, as a "functional rule" and,
(2), it isolates the concept as (logically) separate from, -as from a "different world" than -the
"objects" it "orders". The concept is no longer inherent in the elements it orders, (e.g. of
“perception”), nor is it (logically) derived from them. It is:
196 But see my discussion later. 197 op. cit P.25 198 ibid p.26 199 "...the concept of function constitutes the general schema and model according to which the modern concept of
nature has been molded in its progressive historical development." (ibid, P.21) See also especially: Einstein's Theory of Relativity, Cassirer 1923
200 Discussing Hilbert, Cassirer says: "The procedure of mathematics here", (implicit definition), "points to the analogous procedure of theoretical natural science, for which it contains the key and justification." ibid p.94
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"a new 'object' ... whose total content is expressed in the relations established between the
individual elements by the act of unification."201
Re Presentation:
The Concept is a purely intellectual -and original- entity, a "peculiar form of consciousness,
such as cannot be reduced to the consciousness of sensation or perception."202 It is neither a copy
of nor an abstraction from its extension. It is an independent and "mathematically" functional
"ordering" –an act of unification! It is a rule not logically derivable203 from presentation. That
rule, I will argue, is provided by biology, not by revelation.204
Cassirer has removed logic, (in his critique of the formal Concept), from the simple
abstraction of perceptual objects, (i.e. presentation). It becomes instead an internal function of the
mind, (and hence, I will argue, of biology) –i.e. a “new form of consciousness”.
I will now proceed to argue a very natural extension (and, I think, a completion) of
Cassirer’s thesis: “the Concept of Implicit Definition”. This Concept, part of that same “new
form of consciousness” is also internal and logically independent from perceptual presentation as
well. I will argue, in fact, that it creates its very “objects” – its “extension” -within the same free
act of unification. Even our very “perceptual objects”, (as well as our “intellectual objects”), I will
argue, are resolved within the same internal (biological) act. This will remove, (in agreement with
201 ibid P.24
202 ibid p.25, my emphasis
203 i.e. under classical logic 204 i.e. it is not transcendent –nor does it provide a “God’s eye view”!
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Maturana, Walter Freeman, and Edelman), the need for “presentation”, (metaphysically taken),
altogether. It is the (presented) “perceptual object”, I will argue, which has been hypostasized! A
new formulation of the Concept and its subsequent logic will allow the resolution of the logical
paradoxes of sentiency.
Cassirer’s Concept, (the Functional Concept of Mathematics), is unique in that its arguments show
that the fundamental logical Concept is not derived from presentation or perception. It is a free and
independent act (of unification). It is a “new form of consciousness” according to Cassirer and not
dependent on them. But if his arguments are believed, (and I think they are very strong), then there
is a very natural extension of Cassirer’s Concept wherein the rule, (which determines the concept),
can be likened to the conjunction of the axioms in an axiom system and its objects, therefore, to the
objects of implicit definition. That result opens a new possibility –it potentiates the possibility that
objects as well, (and not just intellectual concepts), can be free creations, acts of unification of that
same new consciousness and not dependent on presentation or perception either!
It is clearly in “presentation” itself that the paradoxes of the homunculus and the Cartesian
Theatre arise, after all, and these are specifically paradoxes of presentation. If our perceptions
were presented to us,205 -if mind, consciousness and perception were presentational and dualistic,
(which is implicit in the presentation/attention abstraction of classical logic) -then the paradoxes
of sentiency would be innate and irresolvable. But if those perceptions arose within us, and if
consciousness arose as a whole, (as the unified rule of "ontogenic coupling", after Maturana, as I
will argue), then sufficient grounds for a complete resolution of the problem would be established.
205 as is assumed under the classical view
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This is not an answer from solipsism, dualism or idealism however, but from realism sans
information and presentation.
The Concept of Implicit Definition:
(a natural extension of Cassirer's "Functional Concept of Mathematics")
3. Cassirer's "Functional Concept of Mathematics" does not exhaust the possibilities however -not
even for mathematics. The "implicit definition" of axiomatic mathematics has specific and
converse consequences for the formal Concept. Since, (following Cassirer), an actual concept is
now defined by any (definite and consistent) conceptual rule, I propose that a mathematical axiom
system is itself a perfectly good Concept in Cassirer's sense. Axiom systems embody more
profound rules than Cassirer considered however, and I propose that they define the ultimate
concepts. Here it is a logically complex, (and typically non-serial), rule which defines the concept,
(i.e. the conjunction of the axioms), and conversely, (and significantly), following Hilbert and
modern mathematics, it is a definite, logically precise and consistent rule of generation of its
“extension” -i.e., of its implicitly defined elements as well.206 But axiom systems are not logically
"dimensional", (strictly implied in Cassirer's F(x,y,z...)), nor do they normally define a "series";
they define the raw (broadest) manifold itself.207
There is no a priori presumption of dimensionality in the domain of an abstract axiom
system. Nor can the elements of the mathematical manifold be characterized a priori,
206 I am concerned here with the object of implicit definition only insofar as it is a logical object, only insofar as it is a
mathematical object. This is the actual object of implicit definition. I am not concerned with the (different) objects of models with which it may be made to correspond, i.e. with the objects of its possible realizations. This is quite a different case and quite a different object. It is the logical object per se, I will argue, that solves the homonculus.
207 I.e. the abstract set taken in its broadest, most general mathematical sense
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(dimensionally), as functional values of the individual axioms. Their "objects" are not "objects" of
the sort: (a1(x), a2(y), a3(z), ...). Axioms do not interact dimensionally, they interact
operationally. The combination of axioms, and their rule of generation, (Cassirer's "continuous
transformation"), is purely, profoundly and complexly logical. A mathematical axiom system need
not characterize a "series" or a "series of series" moreover.208 Indeed, this is the exception rather
than the rule. What it must and does embody, however, is the raw manifold itself, (its domain).209
It embodies the "logical continuum" generated by its axioms. It embodies an "order" of a higher
degree of freedom.
The instances of Cassirer's "Functional Concept", (the objects of its extension), are the
continuous generation of its rule. The instances of the implicit definition of mathematical axiom
systems, the implicitly defined "elements" of their manifolds, are logically continuous as well -they
are the continuous generation of a more profound rule which, by definition, exhausts, (and defines),
its extension. The "elements" of the mathematical domain are precisely all and only those "values"
implicitly defined by, (logically generated by), a particular system of axioms -in a sense precisely
parallel to Cassirer's. They are the pure embodiment, (crystallization), of the "order" of its rule.
Its elements are virtual elements expressing its innate order. The whole of their meaning and the
208 Cassirer, like Kant before him, considered the "series", (or a series of series), as the ultimate possible mode of
logical and conceptual organization. He saw it as the ultimate expression, and only possible principle, (rule), for a logical function, (i.e. a logical principle which specifies its extension), other than identity. He based his new formal concept, ("the Functional Concept of Mathematics"), upon that belief.
But that conception is inadequate and inaccurate for the case of modern mathematics. Axiom systems exactly describe, (specify), elements, (their extension), that are not generally, (i.e. not a priori), organizable on a series principle. Axiom systems embody a larger and broader logical principle, (a rule which specifies its instances), and a broader logical concept, (as demonstrated, I suspect, by Goedel). The elements of a mathematical domain are fully prescribed, ("functionally" in Cassirer's sense), by their axioms, (their rule), but this rule is not "series". It is a complex logical rule -not referring to, but internally generating its extension as a virtual expression of its own innate ordering. It is the rule of implicit definition. This rule, following Cassirer, (I will argue), defines a new concept, the "Concept of Implicit Definition".
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whole of their being, (mathematically), is solely such. The manifold, (domain), represents the
functional and conceptual "values" of its system of "generating relations". Its elements are logical
elements.
The "elements", (mathematically conceived), of axiom systems are not "objects" upon
which a system of "generating relations" acts, however, or to which it relates. They are products of
it. There is no a priori presumption of their distinct and separate existence. Wilder, pertinently,
characterizes the "existence" terms of axiom systems as "presumptive" and "permissive" only. 210
Axiomatic "existence" is an operative term only. The elements -the objects- of axiom systems are
logical "invariants" of their generating relations and internal to the rule itself.211 Neither
"presentation", (nor reference), is implicit in them. They are "entities whose whole being is to be
bearers of the relations laid down by the system."
I urge that this -the Concept of Implicit Definition- is the ultimate logical rule, and the
ultimate "ordering". It captures the ultimate functionality, (in Cassirer's sense), of a logical system
and generates its extension, (its abstract "domain"), as a virtual embodiment of its own (logical)
"ordering" -its rule. An axiom system, (conceived mathematically), is a rule which wholly
specifies its "elements" -by definition.212
I propose, therefore, a new and largest formal "Concept": the Concept of Implicit
Definition. I propose it in strict analogy to the case of the mathematical axiom system and in strict
209 which is not, a priori, implicitly dimensional. 210 Wilder, 1967, P.18 211 Contrary to this view, Resnik,(Resnik, 1992), criticized an example of such a "structuralist" conception of
mathematics in terms of the theory of reference. Under my hypothesis, however, the theory of reference itself becomes highly problematic. (cf Quine, 1953, pps.139-159, "Reference and Modality") Also see Chapter 4.
212 See prior "Elaboration" discussion
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extension of Cassirer's Concept. It is the natural extension of Cassirer's Functional Concept of
Mathematics, and embodies, I propose, the ultimate rule, (in Cassirer’s sense), of order. But it is a
generalization of Cassirer's formal concept, not an instance of it. Conceptual "dimensionality", (a
"series of series"), implicit in Cassirer's linear function of functions: F(x,y,z..), is a special case of
the "rule" -and of the formal Concept.
The concept of an axiom system, its "rule" of implicit definition, embodies something
absolutely new and unique amongst concepts however. Its extension is precisely its own analycity.
The "being", (and the "meaning"213), of its elements are, by definition, identical with the purely
logical "singularities" of the (complex) rule -and the concept- itself. They "are ... defined just by
the fact that they satisfy the axioms."214
Implicit Definition vis a vis Presentation:
Like Cassirer's Concept, (its conceptual progenitor), the Concept of Implicit Definition is
not oppositional: i.e. it does not (logically) presuppose "abstraction" or "attention" either. It too is
a "peculiar form of consciousness", an "act of unification ... not reducible to the consciousness of
sensation or perception". But this particular "act", (unlike Cassirer's), does not presuppose
"presentation" either. It does not just logically specify its extension; it logically encompasses it!
The rule of "implicit definition" itself then, following Cassirer, is logical exhaustion and its
"objects" are purely logical objects. They are "crystallizations" - i.e. logical "invariants"215 of and
213 see above --Schlick 214 Wilder quotes Nagel: "Indeed, if geometry is to be deductive ... only the relations specified in the propositions and
definitions employed may legitimately be taken into account." (Wilder, 1967, p.7) 215 cf Cassirer, 1923 pps.36-41
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internal to the rule itself.216 This Concept, I suggest, does not entail "extension" at all -it is a
(complex) unity.
Cassirer’s Concept, (the Functional Concept of Mathematics), is unique in that its arguments
show that the fundamental logical Concept is not derived from presentation or perception but is a
free and independent act of unification. It is a “new form of consciousness” not dependent on
them. The Concept of Implicit Definition, (an extension of Cassirer's thesis), opens a further
possibility, however. It potentiates the possibility that objects as well can be free creations, acts of
unification of that same new consciousness, (and biological organism I argue), and not derived
from presentation or perception either. This is a radical idea admittedly. Though somewhat
repugnant and somewhat astounding to our preconceptions, it is certainly consistent with the
biological conclusions of Maturana, Edelman, and Freeman wherein perception and consciousness,
(whatever those may or may not be for these authors –more generally, the internal biological
function), of an organism do not derive information from the world. But that is just what
perceptual presentation would imply. The positive and the immediate consequence of this new
rendering of the Concept, (C.I.D.217), is that we now have the tools to understand –completely
resolve in fact- the problems of the “homunculus” and the Cartesian theatre. The virtual objects of
implicit definition are known to the system as a whole. For it is only as implicitly defined
resolutions of the system as a whole that they exist at all! This is a major advance on the problem
216 Implicit definition is important when something significant is actually defined. The "objects" of abstract
mathematics, (integers, for instance), are, (in opposition to Mill),"concrete", viable and fruitful. Its element specifies a particular kind of object, and that object is specifically a "crystallization" of a peculiar kind of "ordering"! It embodies the logical and relational essence of that ordering -and that's all! Its "objects" are "crystallizations" of its rule -just like the objects of the training seminar. The rules here, (and there), I argue, define the object, not the converse. But here the actual mechanism of that "crystallization" is transparent. The "calculus" defines the object, and the definitional mechanism is implicit definition.
217 my “Concept of Implicit Definition”
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and enables the only realist solution of the problem yet proposed other than a denial of the problem
itself. It was in “presentation” itself that the unresolvable paradoxes arose after all. To repeat
myself however, the denial of (metaphysical) “presentation” does not result in solipsism, but in
realism sans information and presentation.
Why is this relevant to mind?
4. Why is this significant to the problem at hand? It is because this Concept seems "tailor-made"
to the logical problem of mind: It is capable of solving the homunculus problem and that of the
Cartesian theatre. It can resolve objects without presentation, (without “the homunculus”), and
itself supplies the “theatre”! It also supplies an autonomous theory of meaning.
Cassirer has established the equivalence of "concept" and "rule". If, (1) following the
arguments of chapter 1,218 we are no longer concerned with representation, (nor, with it, of
"presentation"), and (2) if, tentatively, mind were taken as the unified rule, (the "act of
unification"), of brain response,219 -if it were taken as the unified rule of the "structural
coupling"220 of the brain -then (3), (following Cassirer), "mind" might reasonably be identified
with the "concept", (in the larger constitutive sense), of the brain. If that particular concept were
analogous to the "Concept of Implicit Definition" in mathematical axiom systems furthermore,221
218 and of Chapter 3, and of Maturana and Varela, Edelman and Freeman 219 I.E. As an organizational rather than a representative model as I argued in chapter 1 220 See Chapter 3: Maturana and Varela 221 This is consistent, certainly, with the "schematic object" presented earlier. How could evolution crystallize its
(schematic) objects? The implicit definition of process -of "rule"- provides an explicit mechanism and rationale!
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then it would not just "take account" of the elements of its "extension", it would know them!222
Their "meaning" and their "being" would be logically manifest internal to that concept, (and rule),
itself. They would be resolved as virtual expressions of that very rule. They would "acquire
meaning ... and possess only the content that it bestow[ed] upon them." They would be logical
entities "whose whole being [was] to be bearers of the relations laid down by the system." (I argue
that the "logic" just mentioned is a constitutive logic223. I will argue presently that it is the
schematic calculus of Chapter 1!)
But these particular entities -as cognitive and perceptual entities- no longer
(metaphysically) presuppose attention or abstraction -nor do they presuppose presentation.
Therefore, they do not presuppose that which it would be presented to -i.e. a "seer"! The logical
problems of "the object" -the problem of the homunculus, the problem of "the mind's eye", the
“Cartesian theatre”, (which are the principal enigmas of consciousness) -are thereby solved in
principle. The fundamental duality, implicit in classical logic, between "seer" and "seen",
"thinker" and "object of thought", "perceiver" and "perceived", or, more fundamentally, between
cognition and presentation, is bridged. The unity, and the very possibility of cognition of "the
object" -the global perspective of the many in the one- is explained in the unity of its existence as a
virtual object of implicit definition. For it is only globally that such a virtual object even exists as
an object. In our rational universe, then, the Concept of Implicit Definition seems the most
appropriate,224 as a model, to the logical problem of "consciousness". There is no categorical
222 If there is a tendency to characterize my thesis as a variation of functionalism, then it should be noted that it
involves a totally different notion of "function", (and "relation"). 223 after Kant's usage 224 the only appropriate yet suggested!
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disjunction between the "form of the series" -i.e. the "rule" of implicit definition- and its
"elements". They are unified in the concept itself.
Contra Cassirer:
Cassirer "bent" the focus, however:
"there is no danger of hypostasizing the pure concept, of giving it an independent reality
along with the particular things. ... Its 'being' consists exclusively in the logical
determination by which it is clearly differentiated from other possible serial forms ... and
this determination can only be expressed by a synthetic act of definition, and not by a
simple sensuous intuition."225
There are two crucial flaws in his argument, however:
(1): In the axiom systems of pure mathematics, the elements are also expressed by an "act
of definition", (albeit an analytical one) -i.e. that of "implicit definition". They are themselves
manifestations of that "peculiar form of consciousness, such as cannot be reduced to the
consciousness of sensation or perception."
(2): While he states that the application of the Functional Concept is embodied in the
concept itself,226 he argues that concepts are different in kind from their extension. These are
"objects" of a different world from that of the "particular things" -the objects of "simple sensuous
intuition". I argue, (in concert with my first thesis), that the "objects" of "simple sensuous
225 Cassirer, 1923, P.26
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intuition" are themselves ultimately objects of "implicit definition" and part of that same "peculiar
form of consciousness". It follows, then, (given my hypothesis), that there is no simple sensuous
intuition at all -it does not exist. It is the perceptual object which has been hypostasized! His
dichotomy of the "being" of the pure concept and the "being" of the "particular things" need not
stand on either leg.
Cassirer did not generalize the "Functional Concept of Mathematics" into "the Concept of
Implicit Definition". The "new consciousness", furthermore, stopped short of "sensuous
impressions" themselves. For him, the latter were absolute and unknowable. They were, in effect,
the focal point upon which the various forms of knowledge, his "Symbolic Forms",227 were
oriented, but could never reach. They were the rock upon which he erected, in Swabey's
characterization, his "epistemological theory of relativity".228 His "object of knowledge" was a
purely conceptual object, implicitly defined by the fundamental laws of the sciences, -their
"generating relations". The "objects of perception", the "particular things", were of a different and
untouchable world, the rock splitting the intellect in two.
The Crux of the Issue: Presentation
Cassirer did Promethean work, however. He demonstrated the fundamental inadequacies
of the classical Concept, both in its scope and specifically as regards "perception". He illuminated
the profound and expressly logical chasm between the Concept and the perceptual realm, (the
226 "if I know the relation according to which a b c ... are ordered, I can deduce them by reflection and isolate them as
objects of thought" ibid p.26 227 cf Cassirer 1953 and Chapter 4 228 op. cit P.v. I will have much more to say about "Symbolic Forms" in Chapter 4.
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"material" with which it purportedly deals!), and hence the pervasive duality which "perception",
i.e. "sensuous impressions", necessitates for mind and logic. Even Cassirer's "Functional Concept
of Mathematics" was insufficient to the fundamental problem, however, and he remained inside the
"magic circle" of perception. The opposition of "Concept" and "percept", (e.g.
"attention/abstraction" and "presentation" or still even the opposition of Cassirer's "Functional
Concept" and presentation -"sensuous intuition"), and the dualism which is implicit in it, is the
essence of the issue. It is a genuine antinomy and the actual genesis of the problem. Already
contained in "abstraction", already implicit in "attention", already embodied in "presentation" is the
dualistic homunculus: i.e. that to which "presentation" is offered. There was no way heretofore
that we could even conceive of an answer to this problem because it was the formal Concept itself
which generated it. This was the retort in which the "homunculus" was conjured!
"Implicit definition", however, belongs totally to the "new form of consciousness" -as do
the "objects" which it "orders". But here, (beyond Cassirer), there is no longer the assumption of a
presentation of "elements", (psychological impressions or otherwise), from one world to an
intellectualizing, (cognitive), faculty in another. There remains, therefore, no implicit need for the
dualistic homunculus in cognition. This explains why the two worlds are compatible. There are
not two worlds, but one. This "peculiar form of consciousness", this "new consciousness" I
maintain, is the only consciousness.
Mind-Brain: The Second Hypothesis:
"... every transformation of the genuinely 'formal' concept produces a new interpretation of
the whole field that is characterized and ordered by it" (op. cit. p.26)
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6. Let us suppose that "mind" is the "implicit definition" of the process, (rule), of brain response.
Let us suppose that the relationality of brain process is like the system of "generating relations" of
an axiom system,229 and that even the "objects of perception", the "sensuous impressions"
themselves, are implicitly defined within that system,230 (alternatively that our "objects" embody
the "calculus" of evolutionary design as per Chapter 1). The "objects of perception", then, are not
imposed upon the brain, (or presented to it), but are logical invariants of brain process itself.231
The "objects" are products of the "categorical act" -the implicit definition of the brain.
"Implicit definition", as a thesis for mind, does not presuppose "presentation" to generate
its "objects" nor is it antinomical. Its "objects" derive from the logical connection of process.
"Sensuous impressions", therefore, are not presentations to a process, they arise internal to the
process itself.
If we take "the object of perception" as being a specific "object of conception", (taken in
the new, larger sense of "Concept")232 -if it is not, in fact, a copy, a "mirror" of externality, but an
internal functional construct -a schematic artifact of the process of brain response as I have argued
in my first thesis, then we have arrived at a viable solution to the whole of the general problem of
cognition. The unity of the object is the unity of its implicit definition as a virtual element in a
system of fundamental constitutive relationality233. But the "relationality" purported here is not the
229 I will suggest a physical paradigm shortly. 230 i.e., that "perturbation", "triggering" modifies process! cf Maturana and Varela (1987), pps. 166-171, on brain
plasticity. 231 If "mind" is the "concept of brain process", then its rule -implicit definition- is primal logic itself. Conversely, if
"logic", at its root, is the embodiment of that rule, then the relevancy of logic, as the expression of the ontogenic coupling of the brain, requires no teleological presumptions!
232 I.e. within the context of a constitutive logic 233 i.e., in Maturana’s terminology, of “ontogenic coupling”
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relationality of Functionalism. It is not the classical conception, nor even a Cassirerian
"functional" conception of the relationality of fine-grained brain structure, but rather the (logical)
"generating relationality" of implicit definition -of the brain as process.
A Possible Physical Paradigm:
7. What is desperately needed at this point, obviously, is a physical paradigm. How might this
"axiom system" model -which seems to fit the fundamental logical problem of "mind" so well- be
implemented as a biological model? An operational approach seems quite promising. Considering
brain dynamically, -in terms of what it does, (its function), rather than in its fine-grained physical
structure, certainly fits the necessary context of "structural coupling", (response).234 The
perplexing simplicity of the division of the brain into definite gross anatomical substructures, for
instance, is suggestive. (If it were "wired" randomly and incrementally on a "breadboard", as we
would expect if it were developed in response to incrementally acquired evolutionary information,
we would expect an amorphous clutter. Instead, we see very definite gross structure.)
Might not the distinctive, purely and abstractly geometrical function of the cerebellum,235 -
considered as a functional unit of response -provide a pointer in the right direction?236 Might not
these, or some other structural sub-units, considered as modular units of process -of "ontogenic
coupling" -be "axioms"?237 238
234 see Chapter 3 235 i.e. doing tensor transformations. See Churchland, 1986, pps. 412-458 236 The training seminar may still have things to teach us. 237 Or, as another possibility, think about the multiplicity of specific types of neurotransmitters in the brain. If the brain
is monolithically structural –with the axons and dendrites as “wires” of a sort and the synaptic neurotransmitters as a sort of variable “solder”, then why did evolution go to the trouble of making so many kinds?
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If the "objects of perception", the "sensuous impressions" themselves, are "objects of the
intellect",- i.e. implicitly defined purely conceptual entities, ("conception" in the larger sense), then
a Copernican revolution into a new logical world-view, centered in the "Concept of Implicit
Definition", resolves the whole of the problem of cognition. The processes of judgement, intellect,
even "perception" -are not profoundly distinct or separate from the "objects" judged, from the
"objects" with which they deal. Perception, conception,239 logic, and "object" are all aspects of the
same process -the implicit definition of the "generating relations" of brain.
But what of "meaning"? In short, let me repeat Schlick's comment with a different
emphasis: "'point', 'straight line', 'plane', 'between', 'outside of', and the like) ... to begin with, have
no meaning or content. These terms acquire meaning only by virtue of the axiom system, and
possess only the content that it bestows upon them." Meaning itself can be explicated as a function
of "implicit definition". It is an expression of logical "positionality", (order), in the context of
relationality in which it is realized.240 (This is actually very close to the naive sense of "meaning".)
Consider, finally, Patricia Churchland's comment about theoretical systems:
The fact of their multiplicity of type suggests another interpretation: that of multiple, superimposed structures,
(modules?), sharing neurons and distinguished by their response to specific neurotransmitters. This raw speculation would be another possible conception of “axioms”, i.e. functional blocks in the brain.
238 This suggests a very definite line of research, i.e., the detailed investigation of gross substructures in primitive nervous systems. It suggests a line of interpretation in terms of modules of response, i.e. "axioms", whose interaction would define the "objects" of their perceptual worlds! What is it like to be a planarian worm? This may not be a ludicrous idea after all!
239 The "elements" of the manifold are "implicitly defined" by their generating relations, but so is "between", "line", ... Could not the "purely intellectual" object, (concept), -as distinguished from the perceptual object- be conceived as the product of co-definition from embedded axiom systems. It would then be an implicitly defined "object" of a different precision, a different "resolution". The element of a group, for instance, is less "resolved", in this sense, than the element of an integral domain or a field.
240 See Dreyfus 1992 for the context/"frame" problem
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"It emerged that the meaning", (my emphasis), "of the most respectable of theoretical terms
was defined implicitly by the theory the terms figured in, not by the empirical
consequences of the theory. Terms such as 'force field', 'energy', and 'electromagnetic
radiation' were prime examples where meaning was a function of the embedding theory
and where operational definitions were laughable."
"Whole theories have empirical consequences, and it is whole theories that are the basic
units of meaning", (my emphasis), " -not terms, not sentences, and not subparts of the
network. To be acceptable as an account of nature, a theoretical network must, as a whole,
touch an observational base, but not every acceptable sentence or term in the network must
do so." (P.S. Churchland, 1986, pps. 265-266)
I am proposing that the human mind itself is a theoretical (and operative) network, and it is
only as a whole that it touches its base -i.e. its environment. As a whole it determines the meaning
of its terms and implicitly defines its "objects". I propose that not only our theories and the
meanings of their terms, but that our cognitive objects themselves are implicitly defined as well. It
is only in the context of the system of response that they "touch" our environment, ("have
empirical consequences"). The "object" of cognition refers to its, (the system's), own
operationality and not to an external object. I propose that it is not the objects of the system that
touch objective reality, externality; its "axioms" do!
If the brain/mind relationship is like the relationship of the axiom system to its implicit
definition, then "we" do not deal with "presentations" to us, either for abstraction, conception or
perception. Rather, "we" are the system of implicit definition in which the so-called
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"presentations" are created. This completes, I feel, a reasonable and appropriate preliminary
definition241 of "mind".242
Convergence.
8. My (second) thesis furnishes the basis for a coherent biological explication for "mind" and
"consciousness". If even the "percept" is just a special (and natural) aspect of the (extended)
"concept", then mind is clearly a logical243 continuum, (what else is there?) But that logical
continuum would clearly be complementary to the operational continuum proposed under the first
thesis. This concordance suggests an identity: that our "objects" are logical as well as operational
objects244 and vivifies my logical hypothesis of mind.
The evolutionarily argued object of the first thesis is a virtual and schematic object of
process. It is a continuous manifestation of the field of process which underlies it. The
independently argued object of the second thesis, (derived from considerations of formal logic), is
a virtual and schematic object of logic. It, too, is a continuous manifestation of the (here logical)
process which underlies it. This strongly suggests an isomorphic correspondence between the
results of two very different and plausible approaches to the problem. It is the discovery of just
such correspondences that are crucial to the advancement of science.
241 cf Chapter 5 242 Incidentally," implicit definition" suggests another, more mature perspective than those presented in the earlier
discussion on "models". Under this perspective even the schematic models and their artifacts are not (evolutionarily) "constructed" for (efficient) "use". The "objects" arise incidentally -they are implicitly defined as a result of the evolutionary optimization of brain organization around process and response. They are the "undefined terms" of a categorical "axiom system". Under this perspective we do not use our model, we live in it.
243 in the sense of Kant's constitutive logic 244 This correspondence has the potential of supplying a vital and fundamental biological heuristic principle to
psychology itself which, if realized, could be as important to psychology as evolution has been to biology. It could supply a fundamental operative rationale and tool for the investigation of mind and consciousness based in biology.
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But biology itself argues the correspondence. Taking a biological, (and reductive
materialist), perspective,245 logic itself must be taken as a human, (and evolutionary), artifact. The
alternative would be to assign transcendent246 properties to logic, a position clearly contrary to the
very spirit and rationale of materialism itself. From the standpoint of biology, both "logic" and
"concept" must themselves be considered reductively and evolutionarily.
The final biological rationale for human logic itself, (i.e. that aspect of human behavior
which we call logic), is clearly evolutionary, -i.e. it is determined by natural selection. Logic is
then necessarily a pragmatic rule of correspondence, (a procedural rule), between the brain and its
environment. The (primitive) rule of "logic" itself is therefore operational, (rather than
transcendent), and "concept", as part of that logic, must be considered likewise. This suggests a
striking conclusion: the first two theses are equivalent! The "mind" is the "logical", (-i.e. "bio-
logically" operational), "concept"247 of the brain.248 It is the "unified rule" of brain process.
(Within this context, I assert that Hilbert's thesis serves as the clear foundation for a deep and
autonomous theory of meaning.)
This, I propose, supplies the actual basis, grounded in a new formal Concept, for the
"constitutive logic" which Kant postulated to lie beneath our perceptions. I propose that my first
thesis provides its specific and precise biological rationale and my second thesis explicates its
"objects". Our perceptual objects are not objects in reality; they are the implicitly defined logical
245 whose use I will justify in Chapter 4 246 rather than "transcendental" -after Kant's usage. 247 "concept" and "logic" both conceived reductively as biologic processes. 248 This, as I noted before, removes another "miracle", i.e. the startling simplicity and scarcity of the rules of logic and
science. From the standpoint of my theses, the appropriateness of our "objects" and the simplicity of their mutual relationality are precisely the point of their existence!
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objects, (alternatively, clearly now, operative objects), of this constitutive logic. They are objects
of process.
A crucial turning point in my argument:
9. This, I maintain, constitutes the final physical answer to the mind-body problem. Naturalists
can accept this answer as complete, (and the problem as solved), if they like and dismiss any
further questions. But inherent in my thesis as well is the assertion that our objects are not
representative and informational. To believe that they could still remain so becomes, (under my
thesis), equivalent to a hypothesis of "divine harmony", (possible but implausible). This, (right
here then), is a crucial turning point in my argument. I hereby reorient the whole of my argument
up to this point and declare it249 as a reductio ad absurdum of ordinary Naturalism250. By this, I
most definitely do not reject the relationality251 of Naturalism or of Naturalist science. But I do
maintain that I have demonstrated the implausibility of absolute reference and absolute
information.252 The next chapters will elaborate this point explicitly and invoke a variation of
Cassirer's scientific epistemological relativism, which preserves Naturalist science in a deeper
realism. The argument up to this point has been in the demonstration of a counterexample, -a
significantly better counterexample I think- which fits the presumptions of Naturalism and the facts
of the problem as seen from the Naturalist perspective.
249 I have not been "cute" nor, I think, deceptive. It was necessary to establish the language of discussion and a
context. The audience I seek is that of working scientists, and I have addressed myself to them. I seek to extend the field in much the same direction -and to the same purpose - as modern physics extended itself. I will resolve the obvious difficulties in the next three chapters.
250 As distinguished from "relativized Naturalism" -see Chapter 4
251 i.e. the web of implication and predictivity
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The unity of consciousness, the unity of mind is a logical, a conceptual and operational,
rather than a spatial unity.253 The paradoxes of the Cartesian Theater do not derive from an innate
flaw -or fantasy- in "mind"; they derive from a deficiency of ordinary logic.
Hubert Dreyfus254 concluded that the brain cannot be simulated in a digitally based
computer,255 but he explicitly allowed the possibility of an analog implementation. Cassirer
produced, in fact, an analog, (i.e. a functional), concept -"the functional concept of mathematics".
He suggested the requisite (analog) expansion of logic as well:
"..it must become evident that we stand here before a mere beginning that points
beyond itself. The categorical acts which we characterize by the concepts of the whole and
its parts, and of the thing and its attributes, are not isolated but belong to a system of logical
categories, which moreover they by no means exhaust. After we have conceived the plan
of this system in a general logical theory of relations", (my emphasis), "we can, from this
standpoint, determine its details. On the other hand, it is not possible to gain a view of all
possible forms of connection from the limited standpoint of certain relations emphasized in
the naive view of the world. The category of the thing shows itself unsuited for this
purpose in the very fact that we have in pure mathematics a field of knowledge, in which
252 cf Chapters 1, 3 and Appendix A
253 Just "Where" and How this unity exists, (i.e. What), will be addressed in the third thesis, (Chapter 5). Incidentally Dennett also concluded that "mind" is a logical entity! See Appendix F: "Dennett".
254 See Appendix C: "Dreyfus"
255 His arguments are strong but I do not necessarily agree with his conclusion.
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things and their properties are disregarded in principle, and in whose fundamental concepts
therefore, no general property of things can be contained."256
The "general logical theory of relations" he predicts, though it involves an extension of his
own "Concept" is, I propose, the "generating relationality" of implicit definition. The concept of
the axiom system -the Concept of Implicit Definition- resolves the problem Dreyfus so correctly
defined, but it resolves it, (contrary to Dreyfus' expectations), within the platonic tradition.257
My thesis resolves the fundamental problems of "mind" and "consciousness", i.e.
"perception" and the primal logical problems of the "homunculus", the "Cartesian theatre", and
meaning -and it is the only theory yet proposed that does. But these are the greatest enigmas of
mind. (The other is that of providing a possible substance for mind which I have addressed in
chapters 3, 4 and 5.) How can a part of a whole be comprehensible to a whole. How can a mind
"see" its contents without an infinite regress? How can a spatially and temporally distributed
process cognate a part of itself? Other than an eliminative reduction of mind itself -i.e. an actual
negation of mind in our normal sense altogether, (which is the answer of most –realist- modern
theorists), there seems no other possibility. Supervenience, unless taken magically, doesn't really
make a lot of sense. "Grandmother cells" or "pontifical cells", (William James), do not work.
Eliminative reduction, on the other hand, throws away the baby with the bath. Its answer is that
there is no "mind" in our normal meaning of the term. We are linguistic automatons -i.e.
10. Let's talk loosely for a bit. We do not start with absolutes anywhere in our logical and
scientific endeavors. Somewhere we start with beliefs. I, for one, believe that I have a mind and a
consciousness in the naive senses of those words. I think most of you believe that you do too. By
this we do not just mean that our bodies mechanically and robotically produce words and actions
which "cover the territory" -which merely simulate, (substitute for), sentiency in our naive sense of
it, but that there is some universal and unified existence which is aware. But how?
Contemporary Naturalists, (Dennett, the Churchlands, Hofstadter, ...), universally and
necessarily deny naive sentiency -the "mind's eye", the "matter", the "figment" of mind. They
preserve only linguistic and neural process. They forthrightly, (to their credit), reduce mind to
strict mechanism -to spatially and temporally distributed process. Mind, in a non-reductive, (i.e. a
non-reinterpreted), sense, cannot exist for them. In this, I feel, they have completely lost
credibility. They ask me to deny me in order to retain my beliefs about ordinary things.
Even idealism and dualism do not resolve the underlying logical problem however -the
how of Leibniz's "expression of the many in the one", for even then how could this part of even a
mental "substance" know that part? These are logical problems -the problem of the "homunculus"
and the problem of the "Cartesian theatre". Where does there exist even the possibility of a
solution?
Implicit definition, virtual existence -and logic as biology- this is the only example within
our intellectual horizons that seems to hold even any promise for sentiency in this our ordinary
sense of it. It suggests the only scientifically plausible solution to "the mind's eye" and the
"Cartesian theatre" and the only non-eliminativist, (for "mind"), answer to the homunculus
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problem. These are answers which must exist if mind in our ordinary sense is, in fact, to be real.
Implicit definition permits knowing, (as a whole), what are, in some real sense, our distinct and
separate parts -precisely because those parts, (objects), are in fact non-localized and virtual
(logical) expressions of the whole. It opens the first genuine possibility, therefore, for a resolution
of this essential requirement of "naive" consciousness.
But that pathway, (implicit definition), does not make sense from the standpoint of
representation! For implicit definition solves the problem logically -from the standpoint of
constitutive logic -and speaks to nothing other than its own internal structure. "Objects", (under
implicit definition), are known to a system, (i.e. universally/globally), only because they are
specifically expressions of the system. It becomes a viable and natural solution to the problem of
awareness, therefore, only when the objects of consciousness themselves are conceived
operationally and schematically, (and specifically, logically259), rather than representatively.260
When our objects are taken as specifically schematic representations of process however, (as per
my first thesis), the solution becomes both natural and plausible -the logical problem of sentiency
is resolved. 261 I assert that no other actual solution, (other than a denial of the problem itself), has
ever been suggested. This is the argument from the second to the first hypothesis -and different
from the argument from the first to the second presented earlier.
But this conclusion is greatly strengthened by the arguments of the first chapter and of
Appendix A –and by the conclusions of several eminent contemporary biologists. My biological
259 and “bio-logically” 260 That the objects of this constitutive logic would further represent, however, would be a genuine assumption of the
miraculous -possible but difficult. 261 though not the substance problem. That is a separate metaphysical issue addressed by my third thesis.
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thesis, considered biologically, (i.e. aside from its admittedly profound, but purely epistemological
difficulties -which I will make good in chapter 4), is exceedingly strong. How could evolution
organize -as it had to organize- the reactive function of this colossus of sixty trillion cells? Even
this formulation of the question disregards the yet more profound complexity of the reactivity of
the individual cells -also organisms- themselves! It was the overwhelmingly crucial issue in the
evolution of complex metacellulars. My thesis of schematism is both viable and plausible in this
context. But what does this evolutionary development and organization of the reactive process of
complex metacellulars have to do with "information"?
That the progressive evolutionary reactivity of this megacollosus occurred under the
bounds of real necessity is, of course, a given. It is the basic axiom of Darwinian "survival". But
that it could match that possibility -i.e. that it could achieve a (reactive) parallelism to that bound -
i.e. "information!" -is a hypothesis of quite another order and teleologically distinct. [See
Illustration]
It is, I assert moreover, mathematically immature. Objective reality is a bound to the
evolutionary possibility of organisms, but under that bound infinitely diverse possibilities
remain.262 I may, as a crude illustration for instance, posit an infinity of functions under the
arbitrary bound Y = 64,000,000. I may cite semi-circles, many of the trigonometric functions,
planar figures, curves, lines ... ad infinitum. Only one of these matches the bound, and only a
specific subset, (the horizontal lines Y = a, a <= 64,000,000), parallels it. It is a question of the
distinction between a bound and a limit. The reactive evolutionary actuality of an organism
certainly exists within, (and embodies), a lower bound of biologically possibility. But that some
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such, (any such), organism, (to include the human organism!), embodies a greatest lower bound -
i.e. that it, (or its reactivity), matches and meets, (or parallels, i.e. knows!), the real world does not
follow. That premise is incommensurate with the fundamental premise of “natural selection” and
stands as the “parallel postulate” of evolutionary theory. Organisms do not know, organisms do!
Organisms survive!
How much more plausible is it not that the primary and crucial thrust of evolution was
coordination, and specifically a coordination of allowable or appropriate, (rather than "informed"),
reactive response? I submit that, even solely biologically, the schematic object is far more
plausible than the representative one. It involves no "magic", and is totally consistent with our
ordinary conceptions of biology.
In the realm of beliefs, however, my alternative, like the Naturalists', is also bad. It also
goes against gut beliefs when it says that we have no direct, (even a mediated/sophisticated),
referential knowledge of metaphysical reality. But this is exactly the finding of contemporary
physical science. It was the crucial enabling insight of quantum mechanics, for instance. Though
my thesis goes against instinct, the whole course of modern physics stands by its side.
I submit that no other viable, (i.e. non-eliminative or non-dualistic), explanation, i.e., an
actual explanation rather than a prevarication, has ever even been offered for mind and
consciousness as understood in our ordinary sense. The argument, then, is one of demonstration.
If no truly viable alternative can be offered, then this one must be considered seriously.
I argue that the operational process of brain, (and its evolutionarily determined structural
optimization), implicitly defines its "objects", its "entities" in the same sense and in the same
262 As an illustration, (as I quoted Edelman in the "Afterword"), there are numerous different ways that an antibody, for
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manner that the "process" of an axiom system implicitly defines its "objects". The "objects of
perception", I argue, are "mental objects". They are constitutive conceptual objects. But they are
schematic objects, (alternatively, "operational objects"), only, in no necessarily simple
correspondence with objective reality. They are metaphors of response!263
Conclusion: (chapter)
11. Considered physically, I propose that mind is a rule. But it is a rule that internally and
logically resolves objects. Following Cassirer it is, (because it is a rule), therefore a concept as
well. But it is a new and larger form of Concept. This is the reason we were unable heretofore
even to conceive of a solution to the problems of the homunculus, of the "mind's eye", and the
"Cartesian Theatre". It was because our formal Concept itself, (and the rule in which we
encompassed it), was too small!
In the next sections I will correlate my evolutionary and logical hypotheses with the
standard paradigms of biology and physical science -and argue that they are a better "fit" than that
of naive realism or contemporary Naturalism. Maturana and Varela's evolutionary perspective is
absolutely pertinent here, -and their arguments are impeccably drawn. The brain, as brain, is a
reactive system -functioning "with operational closure" -and not a (realistically) representational
one.
instance, can cope with an antigen -see Afterword.
263 Cf Chapter 1
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Introduction to Chapters 3, 4 and 5
(Towards a Resolution of the Paradox)
In Chapter 2, I proposed a concise Naturalistic explanation of mind, i.e. that the mind is the
(materially reduced) "concept", (alternatively, the rule), of the brain! I said that Naturalists could
accept that explanation as the final and conclusive answer to the problem if they chose, but, if they
did, they accepted a profound antinomy therein, as it still does not produce a "live" mind.
Awareness was still not possible except as "awareness" was itself physically reduced. We would
remain, therefore, linguistic automatons.
My third thesis, (chapter 5), will address this problem directly. In the process of its
development, (chapters 3 and 4), I will resolve the admittedly severe epistemological difficulties
raised by the combination of the first two theses. I will resolve them, moreover, in a manner
consistent with the outlook of modern physical science. I will argue a final "Copernican
revolution" away from the purely Naturalistic perspective,264 retaining the results of Naturalistic
science however, (and our ordinary world), under a thesis of scientific epistemological relativism,
(a variation of Cassirer's "Symbolic Forms"). Building on Kant's fundamental insights, I will argue
that the problem of the “substance” of the mind265 is really a problem of metaphysics, and that
Naturalism's own metaphysics, (and it definitely has one), is faulty. Besides its seemingly
irreducible incorporation of reference, it is its overstrong metaphysical assumptions which make
impossible the existence of a "matter" of mind. In the words of Van Fraassen: "Scientism,
264 or, using the terminology of Putnam, Lakoff and Edelman, away from the “objectivist perspective”. It is actually
my third Copernican revolution as each of the theses could be characterized as such. Each reorients the prior terms and arguments as is the usual nature of Copernican revolutions.
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[Naturalist metaphysics] is also essentially negative; it denies reality to what it does not
countenance. [my emphasis] Its world is as chock-full as an egg; it has room for nothing else."266
My thesis has questioned the very basis of cognition. But what are the truly necessary
presumptions of science itself? I will examine those necessary assumptions from the standpoint of
modern biology, (Maturana and Varela), and from the foundations laid by Kant to arrive at the
"axiom of externality", and from the work of Quine and Cassirer to arrive at the "axiom of
experience". These, I maintain, are the two actual primitives of realist reason.
I will employ an extension of Cassirer’s relativism, (a rigorous, mathematically scientific
epistemological relativism), to deal with the problem of reference. On the issue of substance, I will
argue, (in Chapter 5), that the only "really real", (i.e. ontic or metaphysical), supposition that
anyone, (to include behaviorists, material reductionists...-even dualists!), is rationally allowed to
make -yet which all must make- is that of the existence, (however taken), of our interface to
externality itself. But the truly necessary, (i.e. apodictic), part of that interface must be conceived
minimally and mathematically, i.e. it must be conceived as a limit. It is the synthesis of the most
abstract understandings of our necessary realist primitives: "experience" and "externality". As
such, it is implicit in every realist stance in some form –in "memes", in "linguistic coupling", in
"reductionist process", in "behaviorism", .... This is Maturana's "structural coupling"267
reconceived in its most abstract form, i.e. relieved from its specifically Naturalistic setting.
This interface is therefore necessary and, I will argue, it is also sufficient to the problem as
well. It is this minimal interface, itself taken as metaphysically real, (as it must be268), that I will
propose, (going beyond Kant), as a new metaphysical substance. I will argue that it is, in fact and
in itself, the actual "substance" of the mind. If that interface is therefore actual, (i.e. ontic), and if it
is, furthermore, structured as I have proposed in my first two theses, (which is my third and final
hypothesis), then mind exists. It is an actual mind. We are actually aware. We are actually
conscious.269
268 If it does not exist, then there is no link between externality and experience, and the whole, (any), realist intellectual
enterprise collapses. It is therefore itself ontic and apodictic.
269 [An aside: If I were to substantially revise this book, I would have been tempted to base Chapter 3 in Edelman’s “Bright Air, …” , 1992 as it might have provided a simpler basis for the exposition of those ideas. He argues to the same end as do Maturana and Varela that the brain is not informational but “ex post facto selective”. His arguments are based in his theory of neuronal group selection, (TNGS), grounded in embryology and immunology. While I think it is a very plausible theory, it is specific and unproven. Maturana and Varela make the more general case however, based in first principles. It is a more abstract and conceptually difficult approach, but I think it is worth the work. We must endure the arid complexities of the law to finalize the divorce of realism, (and “externality”), from representation.]
106
Chapter 3. Biology_Part II: Towards the Where and the What?
Biology & Epistemology
(Maturana and Varela and Kant)
"If in a new science which is wholly isolated and unique in its kind, we started with the
prejudice that we can judge of things by means of alleged knowledge previously acquired -
though this is precisely what has first to be called in question -we should only fancy we
saw everywhere what we had already known, because the expressions have a similar
sound. But everything would appear utterly metamorphosed, senseless, and unintelligible,
because we should have as a foundation our own thoughts, made by long habit a second
nature, instead of the author's." (Kant, Prolegomena, p.10)
From our ordinary way of looking at things, my third and final thesis, (which will be
formally stated in Chapter 5), will appear convoluted, esoteric and disturbing. When the inverting
glasses of habit are removed and a proper perspective is attained, however, it will become
considerably simpler270, more plausible and profoundly more compatible with modern science than
any proposed alternative. To reach that perspective and before I can even begin to properly state
this thesis however, I must deal with several seemingly divergent, (but actually closely related),
issues. This chapter will discuss the first of them. I must address the epistemological dilemma
created by the conclusion of the first two theses.
Nobody writing meaningfully about the mind-body problem today appears to take
Immanuel Kant as seriously and as literally as I do, and yet he seems to be the thinker most
270 in a mathematical sense of the term
107
pertinent to it.271 The problem of mind-body is, in one profound respect, the problem of knowing,
(epistemology), itself. The questions of what we, as organisms, do know, or even can know -and
how- reflect back on the very knowledge by which we judge the problem itself.
In an ancillary and important respect, moreover, the problem Kant faced in attempting to
communicate his ideas is very similar to the one I face. (I referred to this in the introduction.)
Both theses totally contravene the common wisdom, and (therefore) make sense only as a whole
and not in their parts. Like his problem "of pure reason", (which is clearly a part of my own
problem), my problem:
"is a sphere so separate and self-contained that we cannot touch a part without
affecting all the rest. We can do nothing without first determining the position of
each part and its relation to the rest; for, as our judgment within this sphere cannot
be corrected by anything without, the validity and use of every part depends upon
the relation in which it stands to all the rest within the domain [of reason]. As in
the structure of an organized body, the end of each member can only be deduced
from the full conception of the whole. It may, then, be said of such [a critique] that
it is never trustworthy except it be perfectly complete, down to the minute elements
[of pure reason]. In the sphere of this faculty you can determine and define either
everything or nothing." ("Prolegomena", P. 11)
The combination of my first two theses provides radical and powerful simplifications to the
mind-body problem. It raises a new and seemingly overwhelming difficulty however. If it is true,
271 "This is an advantage no other science", [than epistemology/metaphysics], "has or can have, because there is none
so fully isolated and independent of others and so exclusively concerned with the faculty of cognition pure and simple". Kant, "Prolegomena", Lewis Beck translation, Bobs-Merill, 1950, p.131, my emphasis
108
then what do we know, and what can we know of the reality in which we exist? Since my very
arguments depend, moreover, on accepted knowledge272 of that world, have I not reduced my own
case to absurdity? The path to my third thesis will answer these questions and supply, (at its
conclusion), the single remaining part of my promised complete solution to the mind-body
problem. The latter is the answer to the problem of the "substance" of the mind. What is "mind"
and where is it? How could it be?
Before I can formally state my third thesis which will answer these questions, (in Chapter
5), however, we must look at the problem of knowing, (epistemology), and at the broader problem
of cognition generally, to include perception. It demarcates the problem of "substance". It sets the
bounds and defines the very context within which we must consider it. The pivotal issue will be
"closure"!273
Closure:
A mathematical domain D is called "closed" under operations "*" and "#", (let us say), if
for every x and y in D, "x*y" and "x#y" are necessarily in D as well. The result of all such
operations on the domain is, no matter how far concatenated, always again within the domain. It
never "escapes" itself! I will argue that our human cognitive domain is itself likewise closed,
(though bounded),274 under its operations. This was Kant's, (and Maturana's), conclusion as well.
272 e.g. Darwinian evolution 273 This is, as an emotional issue, the most difficult of my theses and I must expect to lose my credibility with many of
you here. It is a strange and esoteric idea, but, I believe, true. It must, on my part, be presented with the utmost delicacy. On your part, I must ask for a very careful reading as it may not be as it seems at first.
274 A simple mathematical example of a closed and bounded domain would be the domain of the open interval -1 < x,y < 1 under the operation of multiplication. Another would be the open domain bounded by unit circle: for all (x,y): -1 < x,y < 1 with the operation #: (x,y)#(u,v) = (x*u,y*v). The integers are, of course, closed under addition and multiplication, the rationals under addition, multiplication, and division, ...
109
t
ithout."276
Surprisingly it will simplify the problem of "substance" and resolve the intolerable dilemma I (so
innocently) raised as well. It is not that the problem of substance is itself so difficult; it is the
demands that we make on the answer.
Kant was the most scientific, (I might equally say "mathematical"), thinker on this problem,
and he is confirmed more recently, from the logical side by Quine,275 and, from the side of
biology, by Maturana and Varela. Though Kant's arguments belong to another era, his overall
conclusions and his rigorous identification of the basic and necessary assumptions remains intact.
Sanity and plausibility depend on just two, (by definition "metaphysical"), postulates of absolute
existence: "externality" and "experience", ("intuition"). Without them, there is no reason for
reason! But those postulates operate solely within the closed domain of reason: "our judgemen
within this sphere cannot be corrected by anything w
While fully affirming the existence of our external world as a necessary prerequisite to
reason, Kant concluded that we are inherently incapable of knowing any of its independent
properties, (to include time, space, extension, tactility -impenetrability), independent of their
revelation in, and in combination with, human cognitive forms. Kant argued, (in quite a modern
vein), that it is impossible to separate our "instrument", (the peculiarities of biological human
cognition), from what it "measures", i.e. the world it cognates. His genuinely relativistic
conclusion gains modern physical credence from the theories of relativity and quantum mechanics,
and logical credence, (though it contravenes certain of his own, dated, arguments), from the
axiomatic foundation of mathematics. He arrived at a position which I will call "ontic
275 cf Chapter 4 276 ibid
110
indeterminism"277, (i.e. an indeterminism as to properties, but not as to the existence of external
reality). More recently, Quine278 has argued that our "system of knowledge and beliefs" is
logically closed, and Maturana and Varela279 have argued that biological organisms are
operationally and cognitively closed -by definition!
I will argue that our knowledge and, even more broadly, cognition generally280, (to include
perception!), is a closed, (i.e. self-referential), domain whose "boundary conditions"281 are:
(1) the most general, (i.e. the weakest and most abstract), possible assumption of
"externality" itself, and
(2) "experience" as an uninterpreted primitive, i.e. not the interpretation or organization of
that "experience" -not, for example, its interpretation as "sense impressions"282. The
connection between these two assumptions is not necessarily simplistic. This chapter
elaborates the first of them.
In this chapter, I will examine Maturana and Varela's arguments as set forth in "The Tree of
Knowledge". (Maturana and Varela, 1987) They consummate the viewpoint of modern biology
277 Kant himself was never satisfied with "critical idealism" but was forced to retain it for historical reasons. "This
being the state of the case, I could wish, in order to avoid all misunderstanding, to have named this conception of mine otherwise, but to alter it altogether is probably impossible. It may be permitted me however, in future, as has been above intimated, to term it 'formal' or, better still, 'critical' idealism, to distinguish it from the dogmatic idealism of Berkeley and from the skeptical idealism of Descartes." -"Prolegomena", Pps.124-125
278 W.V.O. Quine, 1960. I will elaborate Quine's position in Chapter 4. 279 Maturana and Varela, 1987 280 Cognition has two aspects. Repeating the definition cited earlier, (Websters. "cognition: the act or process of
knowing, including both awareness and judgement". Also, "Perception: (4a) direct or intuitive cognition.") 281 See Chapter 4, re: Quine 282 But if our perceptual objects are cognitions, then how can they be a boundary condition of cognition as well? How
can our perceptual objects and the things they do be "experience" themselves? I will argue that they are not! "Experience" is their invariant relationality across all orientations including even those which might distribute the "objects" themselves! Does perceptual cognition equate with "experience"? No, it is a particular (evolutionarily derived and "pictorial") orientation of that relationality! See Chap.4 and the "King of Petrolia".
111
on the issue of closure. This penetrating work, very much the biological complement of Kant's
"Prolegomena" I feel, defines the secure biological context in which they develop a single heuristic
principle, ("structural coupling"), crucial to the mind-body problem. I will differ strongly with the
conclusions they draw from it, however, as they were unwilling to accept the devastating
consequences of their own arguments. I do.
Maturana and Varela characterize their book as an argument against a representative model
of environment in the brain, against the existence of a current "map" which we use to compute
behavior appropriate for survival in our contemporaneous world. Their argument propounds,
instead, a closed and evolutionarily determined reactive parallelism to environment -i.e. "congruent
structural coupling". They argue that organisms do not behave as they do because of the nature of
their current surroundings; they behave alongside of it!283 Organisms, as reactive physical
systems, are "operationally closed". Their closed ontogenic state is only "triggered" by their
environment. Environment is a "boundary condition" of survival, not a motivation for action.
They conclude there is no current model because there is no flow of current "information".
They develop their fundamental thesis, "structural coupling", at the ground level of
primitive evolution. It is a principle of purely mechanistic coexistence between "organism" and
"environment" which preserves "autopoiesis", (reproduction). It is, I will argue however, weaker
than the strict parallelism, ("congruence"), they demand of it. Their argument, examined more
deeply, is against "information" between an organism and its environment at any stage -to include
that of natural selection! "Congruence"284, however, would clearly be evolutionary
283 Their argument is considerably subtler than this as I will detail below. 284 as in "congruent structural coupling"
112
r.286 They
ent
ve
information!285 "Structural coupling" and the "conservation of autopoiesis", (and Darwin's
"natural selection" itself), are quintessentially principles of raw appropriateness howeve
are not informational. They say: "This works!"; they do not say: "This is what is!" (They do not
exhaust or mirror the whole of possibility). Neither parallelism, ("congruence"), nor embodim
are legitimate consequences of these principles, I will argue, even at the evolutionary level. There
are correlations between domains other than "isomorphism" or "congruence" which preser
pertinency. The mappings and transformations of abstract algebra are obvious counterexamples
disproving the inference. It is only necessary that (some) feature(s) compatible with the milieu of
the domain be preserved. I will argue that the presumed necessity of "evolutionary congruence" is
a human precept and part of the closed and specifically human cognitive model.
I will now attempt to summarize Maturana and Varela's thesis. Please forgive the length of
my citations, but I feel their arguments are profound, subtle, and more concise than any paraphrase.
I believe they are, up to a certain point, conclusive.
Maturana and Varela:
Maturana and Varela,287 make a profound and phenomenologically pure288 argument
proceeding from first principles. It leads to severe epistemological consequences. They begin by
outlining minimal and necessary biological specifications for "living organisms". Those then
e is simply too small for the purposes of information
nditions, not limits!
288 i.e. they do not mix their contexts or the origins of their presumptions
285 cf Edelman, 1992. He argues that the human genom286 i.e. they are boundary co287 afterwards "Maturana"
113
become a sufficient rationale for the whole of metacellular organisms and their (nervous)
behavior.289 The argument is wholly operational and constructive.290
"Our intention, therefore, is to proceed scientifically: if we cannot provide a list that
characterizes a living being, why not propose a system that generates all the phenomena
proper to a living being? The evidence that an autopoietic unity has exactly all these
features becomes evident in the light of what we know about the interdependence between
metabolism and cellular structure."291
Plausibly, they characterize a "living organism" as an "autopoietic unity", i.e. a replicating
(cellular) physical entity. In so doing, they clarify the inherent nature of biological phenomenology
itself, (i.e. its innate categories and operative principles).
"the potential diversification and plasticity in the family of organic molecules has made
possible the formation of networks of molecular reactions that produce the same types of
molecules that they embody, while at the same time they set the boundaries of the space in
which they are formed. These molecular networks and interactions that produce
themselves and specify their own limits are ... living beings."292
289 "And how can we tell when we have reached a satisfactory explanation of the phenomenon of knowing? ...when we
have set forth a conceptual system that can generate the cognitive phenomenon as a result of the action of a living being, and when we have shown that this process can produce living beings like ourselves, able to generate descriptions and reflect on them as a result of their fulfillment as living beings operating effectively in their fields of existence." (op.cit P.30)
290 Please come back and review Maturana's preamble when you have gotten through Chapter 4, particularly Hertz's reflections on the nature of science. I think the connection is important.
291 ibid P.48, my emphasis
292 ibid Pps. 39-40
114
"Autopoietic unities specify biological phenomenology as the phenomenology proper of
those unities", (my emphasis), "with features distinct from physical phenomenology...
because the phenomena they generate in functioning as autopoietic unities depend on their
organization and the way this organization comes about, and not on the physical nature of
their components."293
The legitimate and minimal principles appropriate to biological process are operational
closure and independence.
"Ontogeny is the history of structural changes in a particular living being. In this
history each living being begins with an initial structure. This structure conditions the
course of its interactions and restricts the structural changes that the interactions may
trigger in it", (my emphasis). "At the same time, it is born in a particular place, in a
medium that constitutes the ambience in which it emerges and in which it interacts. This
ambience appears to have a structural dynamics of its own, operationally distinct from the
living being. This is a crucial point. As observers, we have distinguished the living system
as a unity from its background and have characterized it as a definite organization. We
293 ibid P.51
115
have thus distinguished two structures that are going to be considered operationally
independent of each other, (my emphasis), "living being and environment."294
Physical science's primal principle of "mechanism", however, leads to a distinct point of
view on the interactions of the "autopoietic unity" with its environment: "triggering",
"perturbation", and "structural coupling". Organism and environment are coincident, not
operationally dependent!
"Every ontogeny occurs within an environment; we, as observers, can describe both as
having a particular structure such as diffusion, secretion, temperature. In describing
autopoietic unity as having a particular structure, it will become clear to us that the
interactions (as long as they are recurrent) between unity and environment will consist of
reciprocal perturbations. In these interactions, the structure of the environment only
triggers structural changes in the autopoietic unities (it does not specify or direct them)",
(my emphasis), "and vice versa for the environment. The result will be a history of mutual
congruent structural changes as long as the autopoietic unity and its containing
environment do not disintegrate: there will be a structural coupling."295
(I argue that their phenomenology applies to genetic modification as well as ontogenic
modification. A genetic change -randomly and not causally obtained- is retained simply if it is a
benefit to the functioning of the organism -i.e. solely on the basis of appropriateness. It, and the
summation of such genetic changes, therefore, do not actually imply "congruence", but some
294 ibid P.63
116
pertinent, (beneficial or at least non-destructive), correlation between domains. "Structural
coupling" and "conservation of autopoiesis" are not determinate. They are not "specified or
directed" by the environment either; they are bounded by it. Structural coupling is therefore a
weaker and more abstract condition than they presume.)296
Between the living being and the environment there is a "necessary structural
congruence", [but see my comment above], "(or the unity disappears)." But organisms must, (in
the innate phenomenology of biology), be considered as independently reactive to, rather than
determinately, (i.e. informationally), guided by their environment. The conclusion is grounded in
the structure of science itself:
"In the interactions between the living being and the environment within this structural
congruence, the perturbations of the environment do not determine what happens to the
living being; rather, it is the structure of the living being that determines what change
occurs in it. This interaction is not instructive",297 (my emphasis), "for it does not
determine what its effects are going to be. Therefore, we have used the expression 'to
trigger' an effect. In this way we refer to the fact that the changes that result from the
environment are brought about by the disturbing agent but determined by the structure of
the disturbed system. The same holds true for the environment: the living being is a source
of perturbations and not of instructions."298
295 ibid Pps. 74-75 296 Cognition as a coordination of atomic primitives, (as argued in chapter 1), makes a great deal of sense in this
context. The organization is not itself correlative to externality, but is an operative device working on ultimately indeterminate primitives.
297 i.e. informational 298 ibid Pps. 63-64
117
"The key to understanding all this is indeed simple: as scientists, we can deal only with
unities that are structurally determined. That is, we can deal only with systems in which
all their changes are determined by their structure, whatever it may be, and in which those
structural changes are a result of their own dynamics or triggered by their interactions."299
Organisms react! They react, moreover, in the operational closure of their current
(physical) structure. The latter is determined by their "ontogeny", (i.e. on their summed history of
structural change as individuals), which has modified the original phenotypic structure:
"This ongoing structural change occurs in the unity from moment to moment, either as
a change triggered by interactions coming from the environment in which it exists or as a
result of its internal dynamics. As regards its continuous interactions with the environment,
the cell unity classifies them and sees them in accordance with its structure at every instant.
That structure, in turn continuously changes because of its internal dynamics. The overall
result is that the ontogenic transformation of a unity ceases only with its disintegration."300
Maturana goes on to define "second order" and "third order structural coupling" as the
structural coupling of the multicellular organism with its environment, and the coupling of
intraspecies' behavioral interaction, (e.g. linguistic behavior), with environment respectively. But
these are always dependent upon the necessary conservation of the autopoiesis of the germ cell.
299 ibid P.96 300 ibid P.74
118
The scope of the subsequent development, (the operational range), of the metacellular organism301
is determinate from its unicellular stage, and subject to its phenomenology. "The life of a
multicellular individual as a unity goes on through the operation of its components, but it is not
determined by their properties. Each one of these pluricellular individuals...results from the
division and segregation of a lineage of cells that originate ... (from) a single cell or zygote. ...It is
as simple as this: the logic of the constitution of each metacellular organism demands that it be part
of a cycle in which there is a necessary unicellular stage"302. The conservation of the autopoiesis
of that unicellular stage is the necessary boundary condition of the (independent and coincident)
function of any organism, unicellular or multicellular.
"Living beings are not unique in their determination nor in their structural coupling.
What is proper to them, however, is that structural determination and coupling in them take
place within the framework of ongoing conservation of the autopoiesis that defines them,
whether of the first or second order, and that everything in them is subordinate to that
conservation. Thus, even the autopoiesis of the cells that make up a metacellular system is
subordinate to its autopoiesis as a second-order autopoietic system. Therefore, every
structural change occurs in a living being necessarily limited by the conservation of its
autopoiesis; and those interactions that trigger in it structural changes compatible with
that conservation are perturbations, whereas those that do not are destructive interactions.
Ongoing structural change of living beings with conservation of their autopoiesis is
301 i.e. the phenotype 302 ibid Pps. 80-81
119
occurring at every moment, continuously, in many ways at the same time. It is the
throbbing of all life."303
Behavior, from the biochemical behavior of the amoeba to the nervous behavior of man, is
simply an aspect of primary structural coupling. It is the correlation of sensory surfaces with motor
surfaces: "...the sequence of movements of the amoeba is therefore produced through the
maintenance of an internal correlation between the degree of change of its membrane and those
protoplasmic changes we see as pseudopods. That is, a recurrent or invariable correlation is
established between a perturbed or sensory surface of the organism and an area capable of
producing movement (motor surface), which maintains unchanged a set of internal relations in the
amoeba."304
"This basic architecture of the nervous system is universal and valid not only for the
hydra, but also for higher vertebrates, including human beings. ... the basic organization of
this immensely complicated human nervous system follows essentially the same logic as in
the humble hydra ...the nervous tissue understood as a network of neurons has been
separated like a compartment inside the animal, with nerves along which pass connections
that come and go from the sensory surfaces and motor surfaces. The sole difference lies
not in the fundamental organization of the network that generates sensorimotor
correlations, but in the form in which this network is embodied through neurons and
connections that vary from one animal species to the other. ... But we emphasize: ... this is
the key mechanism whereby the nervous system expands the realm of interactions of an
organism: it couples the sensory and motor surfaces through a network of neurons whose
pattern can be quite varied. Once established, however, it permits many different realms
of behavior in the phylogeny of metazoa. In fact, the nervous systems of varied species
essentially differ only in the specific patterns of their interneuronal networks."305
Brain cells do not connect only to motor and receptor cells, however, most of them connect
to other brain cells:"in humans, some 1011 (one hundred billion) interneurons interconnect some
106 (one million) motoneurons that activate a few thousand muscles, with some 107 (ten million)
sensory cells306 distributed as receptor surfaces throughout the body. Between motor and sensory
neurons lies the brain, like a gigantic mass of interneurons that interconnects them (at a ratio
10:100,000:1) in an everchanging dynamic."307
The sensory surface includes, however, not only those cells that we see externally as
receptors capable of being perturbed by the environment, "but also those cells capable of being
perturbed by the organism itself, including the neuronal network."
"Thus the nervous system participates in the operation of a metacellular as a mechanism
that maintains within certain limits the structural changes of the organism. This occurs
through multiple circuits of neuronal activity structurally coupled to the medium. In this
sense, the nervous system can be characterized as having operational closure", (my
emphasis). "In other words, the nervous system's organization is a network of active
305 ibid Pps.157-159 306 cf Appendix A
121
components in which every change of relations of activity leads to further changes of
relations of activity. Some of these relationships remain invariant through continuous
perturbation both due to the nervous system's own dynamics and due to the interactions of
the organism it integrates. In other words, the nervous system functions as a closed
network of changes in relations of activity between its components."308
External perturbations only modulate the constant interplay of internal balances of
sensorimotor correlations. "It is enough to contemplate this structure of the nervous system... to be
convinced that the effect of projecting an image on the retina is not like an incoming telephone
line. Rather, it is like a voice (perturbation) added to many voices during a hectic family
discussion (relations of activity among all incoming convergent connections) in which the
consensus of actions reached will not depend on what any particular member of the family
says."309
"a nervous system...as part of an organism, will have to function in it by contributing to
its structural determination from moment to moment. This contribution will be due both to
its very structure and to the fact that the result of its operation (e.g., language) forms part of
the environment which, from instant to instant, will operate as a selector in the structural
drift of the organism with conservation of adaptation. Living beings (with or without a
307 ibid p.159 308 ibid Pps.163,164 309 ibid Pps. 161-163. Also consider Edelman’s comment on this same issue: “… To make matters even more
complicated, neurons generally send branches of their axons out in diverging arbors that overlap with those of other neurons, and the same is true of processes called dendrites on recipient neurons …. To put it figuratively, if we ‘asked’ a neuron which input came from which other neuron contributing to the overlapping set of its dendritic connections, it could not ‘know’.” Edelman, 1992, p.27
122
nervous system), therefore, function always in their structural present. The past as a
reference to interactions gone by and the future as a reference to interactions yet to come
are valuable dimensions for us to communicate...however, they do not operate in the
structural determinism of the organism at every moment. With or without a nervous
system, all organisms (ourselves included) function as they function and are where they are
at each instant, because of their structural coupling."310
Maturana presents a sufficient and scientifically necessary rationale for the whole of "living
organisms" -to include their "behavior". It is convincing because of the purity and the correctness
of his phenomenology as biology. At each step of evolution, on each fundamental aspect of the
functioning of an "organism", on the reconciliation of the metacellular, (in all its functions), with
the germ cell, these are the biologically definitive categories and principles proper to a "living
being". Its "purity" lies in the fact that he never, (and never has to), step outside this
phenomenology -this context- to complete his thesis. It is necessary and sufficient, -and legitimate,
(in the legal sense),- to the whole of "living beings". It is, therefore, completely plausible.
Nowhere does his mechanics involve "representation", however! Indeed, "representation"
is inconsistent with the mechanics itself. He concludes as a necessary consequence of scientific
principle that neither organisms, nor their brains, operate with representations of their
surroundings. "Representation" is inconsistent with the necessary phenomenology of organisms -
and extrinsic, (and inessential), to the "mechanism" of science. The principle of parsimony, (i.e.
least cause), dictates his conclusion. Organisms are structurally closed systems, only "perturbed"
by their environment, never "in knowledge" of it.
310 ibid P.124, my emphasis
123
"The most popular and current view of the nervous system considers it an instrument
whereby the organism gets information from the environment which it then uses to build a
representation of the world that it uses to compute behavior adequate for its survival in the
world. This view requires that the environment imprint in the nervous system the
characteristics proper to it and that the nervous system use them to generate behavior, much
the same as we use a map to plot a route. We know, however, that the nervous system as
part of an organism operates with structural determination. Therefore, the structure of the
environment cannot specify its changes, but can only trigger them. ...Our first tendency to
describe what happens .." (is in) "... some form of the metaphor of 'getting information'
from the environment represented 'within'. Our course of reasoning, however, has made it
clear that to use this type of metaphor contradicts everything we know about living
beings."311
His argument is not specifically against models in general, however, but, rather, against
representative models, and in this I think it is conclusive.312 It leaves very little room for
objection. It is consistent, convincing and in the mainstream of science. It leads, perplexingly, to a
disastrous paradox: "We are faced with a formidable snag because it seems that the only alternative
311 ibid Pps.129-133, my emphasis 312 I have proposed a very different, and plausible, alternative model in chapter 1. I proposed that organisms do use
models, but that those models are schematic; their "objects" schematic objects only, aspects of operationally closed process. The "objects" of that model are not "entities" in reality; they are optimizing loci of process itself.
I propose that models do, in fact, exist in the human brain, but they are schematic models. Their virtual "objects", (in no necessarily simple correlation with externality), are evolutionarily derived schematic artifacts of process like the "objects" of the training seminar of chapter 1. They effectively coordinate the sensory and motor faculties of the brain!
124
to a view of the nervous system as operating with representations is to deny the surrounding
reality"!
"Indeed, if the nervous system does not operate -and cannot operate -with a
representation of the surrounding world, what brings about the extraordinary functional
effectiveness of man and animal and their enormous capacity to learn and manipulate the
world? If we deny the objectivity of a knowable world, are we not in the chaos of total
arbitrariness because everything is possible? This is like walking on the razor's edge. On
one side there is a trap: the impossibility of understanding cognitive phenomena if we
assume a world of objects that informs us because there is no mechanism that makes that
'information' possible", (my emphasis). On the other side, there is another trap: the chaos
and arbitrariness of nonobjectivity, where everything seems possible."313
"In fact, on the one hand there is the trap of assuming that the nervous system operates
with representations of the world. And it is a trap, because it blinds us to the possibility of
realizing how the nervous system functions from moment to moment as a definite system
with operational closure. ... On the other hand, there is the other trap: denying the
surrounding environment on the assumption that the nervous system functions completely
in a vacuum, where everything is valid and everything is possible. This is the other
extreme: absolute cognitive solitude or solipsism. ... And it is a trap because it does not
313 op.cit p.133
125
allow us to explain how there is a due proportion or commensurability between the
operation of the organism and its world."314
Maturana and Varela have honed their "razor's edge" with the same care and meticulous
skill with which, as biologists, they would undoubtedly hone a microtome. I suggest they are
proposing that we stand, therefore, not on a razor's edge, but on a microtome's! That, as any
biologist should surely know, is an invitation to suicide.315 They have created a full-blown
antinomy. The usual method of dealing with antinomies is to examine the presuppositions.
Wait though, you must surely be thinking! Couldn't we just deny "mind" in its ordinary
sense, then? Isn't this the simplest solution to the difficulty? Why not just abandon (organic)
"cognition" entirely, and "experience" and "externality", (in our normal meanings of them), right
along with it- and go back solely to parallel and congruent behavior itself -i.e. to parallel reactivity,
predetermined by evolution? Why not just deal with the reactivity and the (reductionist) process of
the brain as part of the world,316 accepting the arguments for the inadequacy and the inconsistency
of organic cognition as a final reductio ad absurdum of "mental states" and deal only with
organisms' (behavioral) function?
Maturana and Varela have, you might correctly continue, specified a phenomenology
specific to organisms, but they have specified it within the context of an actual physical world.
Couldn't we, therefore, just deny the "figment"317 of the mind, (the "consciousness", the
314 ibid Pps. 133-134 315 It is likely to result, depending on the angle of fall, in decapitation or, as seems to have happened here, in a severing
of the corpus callosum. :-) 316 as most current Naturalists, in fact, actually do 317 cf Dennett, 1991
126
"awareness" of the brain -or organism), as "folk psychology" and myth?318 Couldn't we consider
"mind" as just a linguistic and behavioral phenomenon? Sure we could, and it is a necessary
consequence of ordinary Naturalism. But then we are right back, (necessarily), in Maturana's319
dilemma, but invoked at a deeper level! For how then does even the behavioral, and especially the
linguistic320 function, (our descriptive language), of (human) organisms, as behavior, come to be
specifically, (i.e. informationally), relevant to the world? Is this not linguistic idealism?321
Maturana's whole argument -and Darwin's as well - is one of simple appropriateness. It is
"survival" and "structural coupling", not "information". This Naturalist argument presumes that
organisms' reactivity -third order coupling, (language), and behavior- determined from the
beginning by evolution for the phenotype and operationally closed thereafter, is categorical322! 323
This, however, is the only plausible course left to ordinary324 Naturalism after Maturana, but it is a
difficult one. It assumes that whatever evolution determines, (whatever "parallelism" or
"congruency" or "adaptability" that evolution gets for an organism), is embodied in the genotype
and subsequently in the phenotype. From that point on, the argument is necessarily entrapped in
the operational closure of the organism. That closed system must determine its reactivity, (its
supposed "parallel reactivity"), forever after throughout its subsequent ontogenic history.
318 cf P.S. Churchland, 1986, Dennett, 1991 319 and Quine's and Kant's which are themselves the children of an ancient line of legitimate skepticism. 320 for behavioral "knowledge" 321 As I suggested earlier was also the case with Dennett’s thesis 322 any two models are isomorphic 323 This is an astounding conclusion and more than the principles, (and Occam's razor), will bear! At best it is petitio
principii, (assuming what you have to prove), at worst it is magic! 324 cf Chapter 4 for my distinction of "ordinary Naturalism" from "relativized Naturalism".
127
But if even the weather is not determinate from a fixed set of principles and starting point,
then how are we to believe that evolution has embodied the complexity of day to day, week to
week, or year to year physical reality in such a fixed beginning? What model does evolution, (as
embodied in the genotype), itself have that it is trying to parallel? If a butterfly in Australia can
cause a hurricane in Florida then how are we to believe that evolution has a model at all, much less
that it can embody such in closed (behavioral or linguistic) principles and laws of reactivity for the
phenotype.
The argument assumes that evolution launched a closed operational system, (the
phenotype), out into the world. But evolution could not know what that phenotype must be
functional with -i.e. evolution has no model itself! Evolution cannot predict the world -especially
in its human-scale features. It cannot predict the weather, the pattern of rocks, foliage, water and
heat -i.e. "the facts"- in an ecosystem, and, if not them, then it surely cannot predict the more
complex reactivity of the organism's fellow biological creatures -pinching claws, a stalking tiger,
or an infection by vibrio comma, (cholera). "Chaos theory", (for instance), argues that while
cyclical processes, (e.g. the large-scale motions of the planets and stars), produce regular and
predictable results, non-linear processes do not.
But physical process, (the ongoing world), especially at the human scale, is dynamic and
non-linear. Moreover it is, by and large, not cyclical. It is, therefore, not predictable in a
determinate model. To assume that such a correspondence to the physical world can be
implemented throughout the lifespan of an organism in a fixed and determinate, and specifically a
parallel operative model, (an informational model), is a difficult premise. (See specifically the
arguments of Appendix A or Lakoff's arguments in the Lakoff/Edelman appendix). For the
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specifically biological world, the biological ecosystem, it is more than difficult. More plausible is
that evolution works by the creation of dynamic and operative local -and not informational -
functions, that are intimately and locally connected to changing process.
The creation of a multitude of these atomic functions that track, (i.e. trigger from),
incremental change in the physical world is a more plausible evolutionary scenario than the
representationist one. But this is exactly my first hypothesis: that evolution created local functions
like this at the cellular level. The organization of these atomic processes then becomes the real
problem for the "evolutionary engineer", and it is this organization which, I propose, was
accomplished incrementally by the schematic model. Our (biological) "objects" are organizers, I
argue, organizing loci of these atomic processes and not informational representations. The
schematic object is an organization of atomic processes, which latter track we-know-not-what.
For how could even evolution know what that "what" might be? Evolution produces the
operationally closed structural coupling of the phenotype, but that structural coupling must be
specifically dynamic rather than informational. What evolution can deal with are such processes,
not information. It can deal with processes that work on the local, tactical level.
The representationalist schema, (of ordinary Naturalism), is not plausible. No, that is not
quite true, it is plausible inside of our own human cognitive model. It is plausible because it
happens that way! My argument is that it happens that way because it is inside of our model!
To quote Dennett, (a surprising passage for me):
"it is not the point of our sensory systems that they should detect 'basic' or 'natural'
properties of the environment, but just that they should serve our 'narcissistic' purposes in
This is an antinomy. No, more accurately, it is a specific and pointed reductio ad absurdum
of the (ordinary) Naturalist premise!326 What Bertrand Russel says of naive realism applies to
ordinary Naturalism, its (natural) child:
"We all start from 'naive realism'. We think that grass is green, that stones are hard,
and that snow is cold. But physics assures us that the greenness of grass, the
hardness of stones, and the coldness of snow are not the greenness, hardness, and
coldness that we know in our own experience, but something very different. The
observer, when he seems to himself to be observing a stone, is really, if physics is
to be believed, observing the effects of the stone upon himself. Thus science seems
to be at war with itself: when it most means to be objective, it finds itself plunged
into subjectivity against its will. Naive realism leads to physics, and physics, if
true, shows that naive realism is false. Therefore naive realism, if true, is false;
therefore it is false." "An Inquiry into Meaning and Truth", Bertrand Russell, Pp.
14-15
To paraphrase Russell, if we know, then we can't know. Therefore we do not know.
325 I find this a very curious statement –coming from Dennett. 326 but not of relativized Naturalism! cf Chapter 4
130
Maturana and Varela characterized the dilemma incorrectly, however. They specified a
necessary choice between solipsism on the one hand, and representationalism/realism on the other,
and this is not the case.
We needn't deny reality based on their arguments, just our specific knowledge of it! Nor
need we deny "mind". It is the acceptance of an "Axiom of Externality", in its most abstract form,
taken axiomatically, that is demanded here,327 and that is not denied by their arguments. It is the
improper extension of that demand, and its confusion with the particulars of our specifically human
organic process, (to include cognition), that generates the difficulty.
As realists we must grant the presumption of "externality" -the simple posit of an ontic
existence. It is fundamental to sanity and to plausibility. The posit of our world, men and
baseballs and trees and planets as necessary ontic entities, however, is not! Even our perceptual
world is a part of our closed cognitive process. I have argued, (in chapter 1), that it is an operative,
(and dynamic), artifact.
But, you surely object once again, we cannot deny the "objects of our experience" and their
apparent relationality! I agree, it is these objects which provide the stability of our life experience
and ground the very essence of sanity, (my thesis is not solipsism). In the next chapter, I will show
why we need not.
We all want our naive world to be real: trucks, men, planets and baseballs, and all our
normal relations between them -i.e. all the things they do. It is a necessary component of "sanity",
and distinguishes it from dreams, fantasies, and, baldly, insanity. If a rock hits me on the head, it
will hurt! But, contrarily, our best science says that our naive world is not real! What is real for
327 both here and in the foundations of physics
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science are atoms, forces, photons, quarks,... all embedded in some mathematically esoteric spatial
context. For it, myself and the man in front of me are, in fact, biological pluralities, or, deeper still,
atomic amalgams... down to the deepest levels of physical conception.
Naturalism, (the scientifically extended328 form of our naive conception and the verity
Maturana is loathe to lose), allows this heresy only because it says that our natural world is
hierarchically,329 (and isomorphically), embedded in that primitive existence which science posits,
and that those hierarchical entities, (our normal "objects"), act as units. It maintains that this
reduction is specifically a hierarchical330 one which maintains all the spatial and material
relationships down through each and all of the depths of scale -hence their reality! Modern science
has not confirmed, but rather has seriously questioned, that assertion. What are we to embed them
328 to whatever level of sophistication! 329 See Afterword: Lakoff and Edelman for a detailed discussion of hierarchy 330 The reduction of scientific theories, (and theoretic reduction in general), is subject to a fundamental logical
limitation under the classical, (pre-Cassirerian), concept. In the last chapter, (chapter 2), I exhibited Cassirer's arguments that the whole root of the classical formal concept is set-theoretical. Concepts, or concepts of "things", (to include, for instance, our ordinary objects), were reducible only in a set-theoretic sense, i.e. by abstraction, (intersection), of common properties. They are, therefore, subject to Russell's "theory of types". At the bottom level, and there must be a bottom level according to the theory of types, there are atomic primitives. Each of the levels above that must be hierarchically oriented, each containing the one above it, (i.e. the "things" of the next higher level are abstractions -intersections- of the ones below). This theory of types was the logically necessary result of the antinomies discovered in the roots of set theory. The most famous is, of course, Russell's paradox.
Cassirer's fundamental advance on the classical formal concept, "the mathematical concept of function" however, provides an escape. There is no "Cassirer's paradox" in the universal formation of concepts. There is no "concept of all concepts", because concepts are now constituted as an assemblage of (consistent) generative rules, not as a (set-theoretic) abstraction (intersection) of properties -which currently stands for the process of scientific reduction. There is clearly no "rule of all rules" as some rules obviously contravene others. At the level of my "concept of implicit definition", concepts are assemblages of "axioms", (i.e. fundamental and consistent generative rules), and the same situation obtains. But, just as is the well demonstrated case for mathematical axiom systems, it is possible to exchange an appropriate subset of theorems for the pre-existing axioms, (while still absolutely preserving the integrity -the interior relationality- of the mathematical subject), so is it possible to "cross-reduce" theories. We do not have one single preferred perspective.
This is the relativism of Cassirer's "symbolic forms". What remains is the "web" of relationality, the "invariants" of experience that must be preserved under all comprehensive perspectives. But that web, those invariants must be viewed, in Van Fraassen's term, in a "coordinate-free" sense, i.e. they must be viewed in their abstract relationality, not from any particular orientation. cf. Chapter 4 and Afterword: Lakoff / Edelman.
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in? At the bottom level of physics, "matter", "space", even "existence", in the sense in which naive
realism uses them, are anomalous terms. Even "cardinality" as such -the "how many of it"- is
dubious!331
Even ordinary Naturalism332 does not, therefore, maintain the integrity of our naive
objects! But is its insistence on the maintenance of the hierarchical integrity of those objects a
necessary, or even a plausible presupposition at this juncture in our intellectual history?
My hypothesis of the schematic object, contrarily, says that our naive world -to include its
relationality, (its laws and happenings),-is more probably unhierarchically, (but rather
transformationally), correspondent with absolute externality, whatever and however the latter may
be. Ultimately it says that our naive world is in correspondence to "points" of atomic biological
process,333 and not to "points" of ontology. It is a metaphor of response. It says that the further
correspondence between those atomic processes themselves and ontology is completely
indeterminate to us as biological and cognitive entities!
The Axiom of Externality
The acceptance of the raw existence334 of such a correlation, however, constitutes a
necessary requirement for any sane or plausible argument -to include my own.335 This is the
assertion, the "Axiom of Externality" in its most abstract form, and constitutes the first of the two
331 Cf Penrose on the twin-slit experiment, for instance 332 i.e. scientific naturalism = "scientific realism" 333 It is an optimizing organization of primitive, organic process -i.e. of primitive operational process. 334 which assumes, therefore, both the axiom of existence and the reality of experience 335 See Appendix B
133
e
problem:
necessary, (apodictic), premises for realist reason.336 (The other is the "Axiom of Experience"
which I will treat in the following chapter.)
The "realism" Maturana impeaches is, in fact, (ordinary) "Naturalism". Nor has he really
made a case that solipsism is the only other alternative.337 While his case against
representationalism does destroy the claims of ordinary Naturalism,338 a realistic case is still
possible -but it must be a theoretically mature one. Einstein's realism339 is more plausible. That
brand of realism involves simply that "theory be organized around a [some] conceptual model of
an observer-independent realm".340 My thesis takes this "some" in its most abstract form, as the
(pure) limit of reason. This "realism" is certainly more credible in light of today's physics.
Realism is more robust than Maturana assumes, and is capable of greater sophistication than a
mere linear extension of the naive world-view. In Fine's words, it is an "attitude". In disagreement
with Fine however, I believe it is a robust attitude.
Maturana came very close to the answer I propose. His "object" of cognition341 is an
object of process: "cognition does not concern" [external] "objects, for cognition is effective
action." He relapses, however, into the "objects" of the Naturalistic context in which he framed th
ld-views.
338
339 omprehend. ... When we strip the (this) statement of its mystical t we are seeking for the simplest possible system of thought which will bind together the
340
336 Is the "axiom of externality" the same as the "realistic imperative" of Hume? Is it an emotional imperative? Itorients wor
337 Theirs is a structured isolation. It does not support the implication that "everything is valid and everything ispossible"!
Since it assumes the premise of naturalism and ends in a contradiction, it is, in fact, a reductio ad absurdum.
"It is existence and reality that one wishes to celements we mean thaobserved facts." (Einstein 1934, Pps. 112-113)
cf Fine, 1986. p.97
134
"Thus, human cognition as effective action pertains to the biological domain, but it is
always lived in a cultural tradition. The explanation of cognitive phenomena that we have
presented in this book is based on the tradition of science and is valid insofar as it satisfies
scientific criteria. It is singular within that tradition, however, in that it brings forth a basic
conceptual change: cognition does not concern objects, for cognition is effective action..."
"At the same time, as a phenomenon of languaging in the network of social and linguistic
coupling, the mind is not something that is within my brain. Consciousness and mind
belong to the realm of social coupling. That is the locus of their dynamics....Language was
never invented by anyone only to take in an outside world. Therefore, it cannot be used as
a tool to reveal that world. Rather, it is by languaging that the act of knowing, in the
behavioral coordination which is language, brings forth a world. ...We find ourselves in
this co-ontogenic coupling, not as a preexisting reference nor in reference to an origin, but
as an ongoing transformation in the becoming of the linguistic world that we build with
other human beings", (metacellular organisms).342
But "language ... cannot be used as a tool to reveal [the] world." Hence, (accepting his
own conclusion), all his primitives at the final telling are "entities" solely of linguistic (and
ontogenic) coupling, and, as such, have no absolute referent! He maintains that we are wrong in
In fact, they do not actually allow an "object" of cognition, as the following citation shows. I am referring here to that aspect of brain process -the effective action- which corresponds to their object of linguistic coupling -which
xplicitly allow. 342 op.cit Pps.234-244, my emphasis
341
latter is the only "object" they will e
135
order co
at all? What "history of evolution"? These linguistic terms supposedly do not "reveal the
world"!
ct of linguistic
cit
ound of
this ling
he latter
former. We are not justified in assigning a particular ontic
interpre
characterizing the actual world "in reference to an origin". Yet he does exactly that himself. He
frames his primitives: structural coupling, metacellular coupling, intraspecies' coupling, ("third
upling"), and linguistic coupling as interactions of "autopoietic [biological] unities"!
What "autopoietic unities"? And where? Where do these linguistic domains exist -and
between what and whom? Where does his book exist? Does it, and, if so, how is it relevant to
anything
He is, in fact, committed to a Naturalist ground, and it contains real organisms, i.e.
"objects". His "object" is ambiguous however. On the one hand it is solely a produ
coupling, (the object of language), but, on the other hand, (in his presupposition of
objects/biological unities which are coupled), it is also the basis of his ontology. This is an expli
and fatal self-contradiction. Either the object, i.e. the organism, exists -providing the gr
uistic coupling, -or does not -in which case "linguistic coupling" is vacuous!
Does my thesis make our objects not real, then?343 Does it mean that there is no
connection between them and the "externality" we must assume? The answer is an emphatic "No!"
The connection is in the interface itself, ("structural coupling") and "experience". But t
must be understood in terms of the
tation to "experience".344
In my next chapter I will "slice" this problem from another side, (citing Quine and
Cassirer), and argue that "experience", as an ontic posit -and a cognitive primitive -while
343 I will make this case in greater detail in the next chapter.
136
ce, as
not so
tural
e
t exhaustive
possibi
new and larger frame, a new orientation of the whole context of our world and our reality. But the
absolutely justified as such, can be legitimately described only as that which remains invariant
under all possible (viable) interpretations, (and I will argue there is always more than one
interpretation). But "invariants" are in themselves a very concrete form: they stand, for instan
the foundation of the Theory of Relativity. Our human cognitive world, and specifically our
perceptual world: people and baseballs and the things they do, are real, but they are real in the
most general interpretation of their relationality, (them and the things they do). This is
strange a conception -it is implicit in the reductions of science already. But the latter's
requirements of hierarchy and isomorphism are not inherent; they constitute the crux of the
problem. It is those requirements which lead to the disastrous end of Maturana's noble and
profound enterprise. Beneficial connection, pertinent connection between domains, (i.e. "struc
coupling"), does not require "parallelism", it does not imply "congruence", it does not requir
"hierarchy".345 Virtual embodiment demonstrates another, non-hierarchical ye
lity of compatibility, and it is this that I have argued in my first thesis.
Maturana's thesis of "structural coupling" is of profound importance. It is an
epistemological principle of the highest significance.346 It is a necessary consequence of his
Naturalist beginnings -and impeaches them! It precedes and supercedes even its biological origin
in its relation to the fundamental problem of knowledge. Biology, therefore, must integrate into a
34 ole cognitive domain. As I have argued, we
se .
346 It is, in fact, a biological and epistemological principle of relativity. This does not imply that it is a frivolous relativity, (i.e. solipsism), however, no more than did Einstein's Relativity imply a lawlessness in physics!
4 Naturalism's mistake is in trying to assign an ontic reference to our whare justified in making only two primitive ontic, (metaphysical), assertions: "externality" and "experience". Theare the minimal and the maximal legitimate ontic posits. See Chapter 4
345 Could there be a congruent correspondence, (though admittedly not apodictic), however? Sure, but would be"magic" of a high order- "and then a miracle occurs"! Dennett, 1991
137
cts
!
Copernican center of that frame must be structural coupling itself. It is "structural coupling" which
must ground biology; not biology which must ground "structural coupling"!347
I propose to accept absolutely the consequences of "structural coupling": that the "object"
of biological cognition is a function of brain process itself, and not an embodiment of its
environment.348 But this must necessarily translate into a Copernican revolution in our very
world-view: if we are biological organisms, then the objects of our human world-view are obje
of process, of response as well. They are "objects" of "effective action"
Maturana and Varela's profound heuristic principle reduces their premise to absurdity -i.e.
the metaphysical certitude of the ordinary Naturalist world-view from which they started. The
naive-realistic world, (the represented "naturalist" world), can have no internal relevance to the
organism, as organism. But this does not impeach the science, (evolution and biology), which is
their ground -no more than did Einstein's Relativity impeach the physics which was his ground!
The viable relationality, (the viable system of predictivity), of biology and evolution, (and of
science generally), can be, (must be!), preserved, (as was the observed relationality of Ptolemean
astronomy -times and angles and relative positions- in the Copernican system which replaced it),
but it must be "reduced"!349
Are we to throw away the whole of our human enterprise then -to include its science? Of
course not -that would be preposterous! But the most profound and most radical advances in
347 It is not an unusual, (nor inconsistent), practice in mathematics to begin by constructing a new mathematical
discipline from one set of premises, and then to start all over with what were originally derivative consequences as the new, (and more appropriate), primitives.
348 Though this might still seem self-contradictory, please bear with me for a few more paragraphs. I will explain myself fully in the next chapter.
349 Though my reasons for using this word are obvious, it is clearly inappropriate to my conception. "Property-preserving or distributive re-interpretation with conservation of relationality" would be more appropriate.
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human thought, its "Copernican revolutions" and "SUPERB350 theories", have always, (by
necessity), subsumed the viable parts of pre-existing knowledge. In the present case, the
subsumption of the preponderance of naive realism and the preponderance of naturalist science
stand as necessities. They work, after all, with a power and effectiveness which is awesome. My
proposal does not suggest or imply that they be considered any less important. It subsumes the
whole of those vistas, but it subsumes them in their viable relationality,351 and not in their specific
ontic (metaphysical) reference! Their connection to externality is operational, and not referential.
In their whole, they constitute a profoundly effective and complex algorithm of unparalleled
significance whose link to externality is "structural coupling". The latter, however, is referentially
indeterminate, (i.e. metaphysically so).
Science turns recursively back on itself in biology and finds that there is a limitation to
knowledge itself. Structural coupling is the antinomy which forces the absolute relativization of all
knowing -to include "biology" and "evolution" -and even "perception" - themselves. These are
"creatures" of human knowledge, of cognition. They are organizers, not primitives.352 Our true
primitive is "experience", (under the necessary premise of "externality"), not any particular
interpretation -or organization- of it. My hypothesis implies, then, a relativization of epistemology
precisely equivalent to Einstein's relativization of physics. This is what Cassirer concluded as
well.353
350 cf Penrose 351 i.e. their predictivity! I will clarify this point in my next chapter. 352 It is explicit in Maturana's argument, (as we have seen), that "structural coupling" and "the conservation of
autopoiesis", (and "congruence" itself), are specifically part of the closed, human (biological) cognitive process. 353 cf chapter 4
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An Answer to the New Dilemma:
At last I can give a preliminary answer, (which I will complete in the next chapter), to the
disturbing question raised at the beginning of the chapter. How can I presume the naturalistic
world -with its "evolution"- to prove a hypothesis which severely questions them?354 How can I
use a (Darwinian) biological argument, (which presumes a simple correspondence between our
cognitions and the real physical world), against that very simplicity -and embodiment- itself? If
my thesis is true, then our ultimate external reality, (ontology), is not necessarily, (nor even
probably), like the reality of our cognitive model!
The answer is that "evolution" is as much an organizing principle as is "causation". It, (and
the objects it treats), is part of the (closed) model itself. It is not a necessary, (or proper!),
metaphysical presumption, but is, in Kant's words, a “synthetic a priori” proposition. It is not a
necessary part of reality; it is a necessary (plausible), part of our cognition of reality. As such, I
can use it with perfect legitimacy within that closed domain. But I use it, (modifying but keeping
the sense of Dennett's word), "heterophenomenologically", i.e. with a neutral ontic reference!
My epistemological and metaphysical position, therefore, corresponds very much to Kant's,
and ultimately, to Cassirer's. It is neither idealism nor solipsism, but a genuine, (and realistic),
ontic indeterminism.355 The term "indeterminism" refers to the impossibility of knowing the
354 This is also, obviously, a reiteration of Maturana's "razor's edge". 355 "Idealism consists in the assertion that there are none but thinking beings, all other things which we think are
perceived in intuition, being nothing but representations in the thinking beings, to which no object external to them in fact corresponds. I, on the contrary, say that things as objects of our senses existing outside us are", (my emphasis), "given, but we know nothing of what they may be in themselves, knowing only their appearances, that is, the representations which they cause in us by affecting our senses. Consequently I grant by all means that there are bodies without us, that is, things which, though quite unknown to us as to what they are in themselves, we yet know by the representations which their influence on our sensibility procures us. These representations we call 'bodies', a
140
nature of that ontic reality independent of our cognition. It does not, however, assert a doubt as to,
but rather affirms, its existence.
"Matter is substantia phaenomenon. Whatever is intrinsic to it I seek in all parts of the
space that it occupies and in all effects that it exerts, which, after all, can never be anything
but phenomena of the outer sense. Thus I have nothing absolute but merely something
comparatively internal which, in its turn consists only of external relationships. But what
appears to the mere understanding as the absolute essence of matter is again simply a fancy,
for matter is never an object of pure understanding; but the transcendental object that may
be the ground of this appearance called matter is a bare Something, whose nature we
should never be able to understand even though someone could tell us about it. ... The
observation and analysis of phenomena press toward a knowledge of the secrets of nature
and there is no knowing how far they may penetrate in time. But for all that we shall never
term signifying merely the appearance of the thing which is unknown to us, but not therefore less actual. Can this be termed idealism?
Long before Locke's time, but assuredly since him, it has generally assumed and granted without detriment to the actual existence of external things that many of their predicates may be said to belong, not to the things in themselves, but to their appearances, and to have no proper existence outside of our representation. Heat, color and taste, for instance, are of this kind. Now, if I go farther and, for weighty reasons, rank as mere appearances the remaining qualities of bodies also, which are called primary -such as extension, place, and, in general, space... with all that which belongs to it (impenetrability or materiality, shape, etc.)", , (my emphasis), "-no one in the least can adduce the reason of its being inadmissible. As little as the man who admits colors not to be properties of the object in itself, but only as modifications of the sense of sight, should on that account be called an idealist, so little can my thesis be named idealistic merely because I find that more, nay, all the properties which constitute the intuition of a body belong merely to its appearance ,[his emphasis].
The existence of the thing that appears is thereby not destroyed as in genuine idealism, but it is only shown that we cannot possibly know it by the senses as it is in itself." Kant, "Prolegomena" pps. 36-37
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succeed in answering those transcendental questions that reach out beyond nature, though
all nature were to be revealed to our gaze."356
I will, (in chapter 5), however, make the limiting step that Kant did not. I will posit our
cognitive interface, (whatever that may ontically be!), as itself a metaphysical entity. It is a part of
the minimal (realistic) ontic posit. It is the synthesis of "externality" and "experience".357
Knowledge is cognitively closed. It is an organizational system that works. It is Quine's
"body of statements and beliefs", (see Chapter 4), constrained only by its "boundary conditions",
("experience"). But it exists always within the human (biological) cognitive frame. It can never
achieve a "God's eye view"!
"It is by languaging that the act of knowing, in the behavioral coordination which is
language, brings forth a world. ...We find ourselves in this co-ontogenic coupling, not as a
preexisting reference nor in reference to an origin, but as an ongoing transformation in the
becoming of the linguistic world that we build with other human beings."358
In the next chapter I will explore the other axiom of reason, (the Axiom of Experience), and
conclude my answer to the epistemological problem I have raised. Quine and Cassirer show the
way. This will then allow a brief and succinct statement of my third and final thesis in Chapter 5.
356 Kant, "Critique of Pure Reason", 2nd edition, 333, translated by Woglom and Hendel, and cited in Cassirer: "The
Problem of Knowledge", 1950, Pps. 101-102 I prefer this to Smith's rendering. 357 cf Chapter 5 358 op*.cit Pps.234-244, my emphasis
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Preface to Chapter 4
Because we have reached a crucial point, and before going further, I would like to recap
our current status -i.e. to go back and "touch home". I have presented a plausible and, I believe, a
compelling resolution of the mind-body problem, but I have presented it within a context of
ordinary Naturalism. But Naturalism, I have argued, is thereby itself, (by virtue of my answer),
problematic.
How, once again, can I maintain the legitimacy of my thesis when it seemingly questions
its very premises? Cassirer, in his "Philosophy of Symbolic Forms", supplies the grounds for a
solution: his thesis of scientific epistemological relativism. He argued that we retain our
knowledge, our science, not as reference to an ultimate metaphysical reality, but as relativistic
organizations of phenomena. Under this interpretation, the (Naturalistic) primitives of my thesis
do not then require what would otherwise be a further, (and self-contradictory), metaphysical
presumption of reference -i.e. they are taken as organizational but not as metaphysical primitives.
Cassirer argues, moreover, that there are alternative and equipotent organizations possible even
within "nature", (i.e. science), itself. Just as in the field of mathematics there are generally
differing subsets of axioms which can generate the relationality of a given subject, similarly
Cassirer maintains that there is a plurality of alternative and equipotent "Symbolic Forms" which
can generate the relationality of experience. Naturalism,359 (to include my scientific thesis of
mind-brain which is framed within it), is just one such relative, (but legitimate), form. What is
359 as embodied in mathematical physics
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truly absolute, however, are the "invariants" of experience! Underlying the whole problem is the
issue of "experience" itself. Let me therefore begin with the latter.
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Chapter 4: Cognition and Experience: Quine and Cassirer
(The Epistemological Problem: What do we know?)
"The totality of our so-called knowledge or beliefs, from the most casual matters of
geography and history to the profoundest laws of atomic physics or even of pure
mathematics and logic, is a man-made fabric which impinges on experience only along the
edges. Or, to change the figure, total science is like a field of force whose boundary
conditions are experience. A conflict with experience at the periphery occasions
readjustments in the interior of the field. Truth values have to be redistributed over some
of our statements. Reevaluation of some statements entails reevaluation of others, because
of their logical interconnections- the logical laws being in turn simply certain further
statements of the system, certain further elements of the field. Having reevaluated one
statement we must reevaluate some others, which may be statements logically connected
with the first or may be the statements of logical connections themselves. But the total
field is so underdetermined by its boundary conditions, experience, that there is much
latitude of choice as to what statements to reevaluate in the light of any single contrary
experience. No particular experiences are linked with any particular statements in the
interior of the field, except indirectly through considerations of equilibrium affecting the
field as a whole....... Furthermore it becomes folly to see a boundary between synthetic
statements.. and analytic statements...Any statement can be held true come what may, if we
make drastic enough adjustments elsewhere in the system... Conversely… no statement is
immune to revision… even the logical law of the excluded middle... and what difference is
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there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or
Einstein Newton, or Darwin Aristotle?"360
"Experience"! I have argued it as an axiom of sanity, and a minimal realist assumption.
But what is it and what does it mean? Is it the same as "sensuous impressions"? Does the posit of
absolute experience demand an immediate further commitment to reference? In this chapter I will
examine these questions in the light of Quine's and Cassirer's ideas and conclude that the answer to
each is "no". I will propose an answer of rigorous and scientific epistemological relativism, (an
extension of Cassirer's), which preserves both the phenomena and the validity of the whole
dialogue of Naturalism, (including, therefore, that of my first two theses), as organization. It will
preserve them without a commitment to metaphysical reference however. "Experience", I will
argue, is exactly that which remains (relativistically) invariant under all consistent and
comprehensive worldviews. Experience is the phenomena we must preserve and account for, but it
is not the specific organization by which we do so. The primitives of a given organization are not
legitimized, therefore, on the basis of reference, but on a (relativistic) basis of empirical adequacy.
In the previous chapter, I began a discussion of cognitive closure and asserted an "Axiom
of Externality". In this chapter I will continue with the issue of closure and confirm the other
necessary, (apodictic), prerequisite of cognition, i.e. the "Axiom of Experience". Quine's epigram
illuminates both. It validates an absolute and ineradicable multiplicity of interpretations for
experiment and experience.
360 Quine, 1953, pps.42-43
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To start, let me propose a fantasy, which I think, clarifies the relationship between
knowledge, cognition generally, and "experience". It will suggest a viable working definition of
the latter.
A fantasy:
The remote and newly discovered atoll of Petrolia, deep in the south pacific islands and
never before touched by modern civilization, was visited by a geological survey party. It was
found to lie above enormous undersea oil reserves. Its king and high priest, a primitive but highly
intelligent man, asked to see our "magic".361 Seeking to humor him, (and, I am ashamed to tell,
selfishly induce him to assign drilling rights to an American company at a ridiculously low price),
he was given a "red carpet" tour of the Supercollider Accelerator, our greatest scientific marvel.362
The king was mightily impressed. He saw "magical worms", (traces on oscilloscopes), "dancing
arrows", (pointers on analog gauges), and tiny "animal tracks", (particle tracks under a
microscope), in this "cavern of the gods". He was convinced that the whim of our gods provided
the "magic", (the "physical laws"), of his experience there, as it, (they), seemed quite different from
his own! He subsequently engaged in a long and heated debate with one of the technicians over
the significance of it all, ending, sad to say, with his casting a set of boar's knuckles and a shrunken
head, (hidden in a bag under his robe), onto the cable-strewn floor with disastrous consequences!
Though whimsical, this fable helps to clarify the purest, (weakest), and the minimum,
(necessary), assumption of "experience". There are clearly aspects of the situation that the king
361 He was awed when watching reruns of "Gilligan's Island" on the exploratory party's television. 362 cf heading above!
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may have considered significant, (i.e. explanatory), that the scientist did not, (and conversely). The
color or shape of an instrument, or the way the technician cleaned his glasses before initiating the
experiment, for instance, are things that the king might have considered as ritual, (or physical),
necessities, essential to the result. Even the number of floors of the facility, the time of day, or the
route by which he entered might be relevant. The technician, of course, considered the king's
multicolored ritual headdress, and his pouch of magic bones, (he was doing his best to be of help),
totally irrelevant. What I will call the "abstract frame" of the experiment he witnessed, however,
was the same for him as for the scientist conducting it. The abstract frame, (the total data and the
"boundary condition"), for both the scientist and for the King of Petrolia was identical with the
abstract, (from interpretation),363 of the whole of the actual experiment itself, (i.e. the whole of the
experimental situation).364
The "abstract frame" must include the "background situation" however, i.e. all the details -
to include the observers! We do not know, a priori, which of these or what of these is relevant.
This is one reason why, (other than the issues of personal integrity or error), experiments must the
reproducible. It is to eliminate unique factors deriving from the particular experimental context365
and to isolate the essentials through a multiplicitous duplication, hopefully random regarding what
is (unknowably) extraneous. We are never on certain ground in that process however. We are
never sure that our historically dictated -and contextually limited- design of an experiment does not
implicitly incorporate such factors, or that there are not broader, (or different), frames, isolating,
363 alternatively, the experiential invariant 364 "Experiment" is clearly an extension, albeit a refined and defined one, of "experience" itself. 365 e.g. a magnetic field from the coffee-maker, a power surge from the factory down the block, the crumb from an
assistant's lunch contaminating a culture
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(or incorporating), other factors as incidental and irrelevant, (or pertinent and important), in which
it could be implemented.366 Following Quine, we are in a process of dynamic reorientation only
bounded by the abstract frame! Any theoretical description really compatible with the overall
experimental situation367, however, is clearly a legitimate, (i.e. logical), interpretation in Quine's
sense!
Consider: was the King of Petrolia's interpretation of the data of the experiment into his
theoretical scheme, (worldview), patently false? Not necessarily, according to Quine. Was the
scientist's translation into "laws of physics", "particles of matter" -or as an expression of the
"primitive building blocks of reality" inherently, (i.e. logically), better? Also not necessarily!
Each could use the data to integrate, reinforce or modify his theoretical basis -his world-view.368
The fable, (in concert with Quine I maintain), helps us to see that "experience" as such is not, (a
priori or a posteriori), identifiable with any of its organizations or orientations. Rather, it must be
identified with the invariant relationality -i.e. with that which remains fixed- under all global,
366 The lack of free ferrous iron in ordinary differential bacteriology plates when looking for Legionnaire's Disease was
an example of a too limited context and was the reason for its long mystery. 367 including one which might dissolve -i.e. redistribute- but exhaustively account for- the apparent relationality of our
primitives. Virtual systems clearly suggest a new logical possibility. 368 Even the cumulative body of scientific experiment can be accounted for by the King. Given an unending stream of
counterexamples, he can, via Quine, incrementally account for each. The presumption that this cumulative body rules out any other consistent world-view, that eventually he will be backed into a contradiction is not justified.
This is not to say that any consistent theory is just as good as any other consistent theory. The king's theory, spirits and witchcraft, let us say, while it may very well be consistent and capable of accounting for any given fact, clearly falls far short in many aspects, perhaps the most important of which is predictability. The scientist will make strong
and definite projections into the future which, by and large, will be clearly and precisely confirmed. He will be able to predict wide ranges of phenomena correctly and efficiently. There are other criteria of good theories as well. Roger Penrose, in his "Emperor's New Mind" has outlined a reasonable standard very concisely. (See Appendix D)
The issue, which I will postpone for a little, is whether there cannot be, under the thesis of epistemological relativism which I will assert, multiple, equipotent and comprehensive "SUPERB", (using Penrose's classification), theories of reality. The proven equivalence, for example, between Heisenberg's and Schroedinger's (widely divergent) theories of quantum mechanics seems to imply that this may be the case.
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comprehensive and consistent orientations. "Experience", (TENTATIVE WORKING
DEFINITION), is that for which both the king and the technician must account in some manner!369
It is not itself an orientation, however. It is, rather, that ("thing") which must remain fixed, and I
argue that it is a primitive of reason. Scientific experiment extends, (generates), experience and
thereby bounds (and shapes) the scope of such consistent theories. It adds new invariant
relationality to the abstract frame, (and the history of abstract frames). Following Quine however,
it never determines them.
The Epistemological Problem:
At the conclusion of Chapter 2, I asserted the definition: The mind is the "bio-logical", (i.e.
materially reduced), "concept" of the brain. (Alternatively, mind is the rule of the brain.) This
scientific conclusion, (and the schematic model), of my first two chapters, however, raises
profound philosophical and epistemological difficulties, seemingly contradicting itself. It raises
questions, moreover, which offend the very foundations of our rational sensibilities. This,
however, is not so unusual a circumstance but has always been the case, historically, at the major
turning points of science. Deep progress has always necessitated radical, (and often distasteful),
reorientations, (rather than mere polishings), of our fundamental worldview -often with the loss of
cherished convictions. Most recently, this is seen very clearly at the invocations of Relativity and
Quantum Mechanics in modern physics which, incidentally, raise much the same sorts of questions
as does my thesis, i.e. "realism vs. empiricism/algorithmic" questions. I urge that the problems
raised by my thesis are not inherently more difficult -or of a radically new and different type- than
369 This identifies, I propose, a viable and legitimate -and theory independent- working definition of experience.
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have been raised, (and answered), before in the cause of science.370 The real issue is productivity -
to whose ultimate judgement I hereby submit my thesis. It is to legitimize and justify my
conclusion, however, that I am forced to philosophy and a study of the metaphysical and
epistemological presumptions of science -and there are such.
There are really two problems involved with the mind-brain problem. There is a scientific
and empirical one, and there is a philosophical and metaphysical one. The combination of my first
two theses solves the scientific problem, and my third thesis will explicate the metaphysical
problem. This chapter will resolve the apparent paradox created by the first two hypotheses, i.e.
the epistemological problem.
I shall now propose a specific answer to the problems which I have raised. This is not the
only answer possible. I might as easily have adopted the empiricist, "anti-realist" stance common
amongst physicists, for instance. My philosophic answer has something in common with that
stance, but I think it is a positive advance on it, as it leads, (in Chapter 5), to a plausible and
pointed answer to the question of the substance of mind. Let me emphasize, however, that my
370 Though admittedly painful, how are the epistemological implications of my thesis so much more difficult than those
of modern physics, for instance? At the scale of the very small and at the scale of the very large, physics says that our physical world is profoundly strange and, at the small scale at least, that the picture of science is essentially algorithmic. My thesis proposes that our human scale world is very much the same -but that it is itself a biological and organic algorithm. It is a "tactile" algorithm wherein the "data" we receive and the instrument we manipulate to control it are one and the same. (See Chapter 1). Its elements, however, are purely and abstractly logical, (alternatively "operational"), elements! This is a very different and radical way to look at our "objects", (to include perceptual objects), to be sure. It is, I believe, however, far more compatible with the outlook of modern physics than is ordinary Naturalism. I maintain that our "tactile", "spatial", "extensive" et al. objects are logical, (alternatively "operational"), rather than representative. (cf. conclusion to Chapter 2) But the "logical" here is a (Kantian) "constitutive logic" rather than an "ordinary logic".
I will argue a necessary detachment of knowledge from reference -a necessary relinquishment of our ordinary assumption of the independence of our (cognitive) "instrument" from what it measures. This does not require a denial of reality, however, but of our absolute knowledge of reality. But physical science has already reached this conclusion, hasn't it?
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real and central claim remains the scientific one, i.e. the result of the combination of my first two
theses; my philosophic answer is solely its rationale.
If my scientific conclusion is true, (and I believe the concordance of my first two theses,
amongst numerous other reasons, strongly suggests it is), then there seems to be an inherent
paradox in knowledge itself, -and my (Naturalist) premises! If both our perceptual and intellectual
objects are solely artifacts of biological coordination, then on what ground can knowledge, (and
my own argument), stand? If the very language, (to include the very "biological coordination" and
"evolution" of my argument), in which I describe the problem, (being part of that self-same human
reality), is only internally organizational and not referential, then what is it that am I describing.
How can I even discuss the problem itself? Doesn't my theory actually eat itself? How, then,
could there be science at all? Notwithstanding the apparent paradox, (which is not unique to my
thesis371 and to which I will here propose a solution), I maintain that mine is a very strong and a
very pure Naturalist argument and that its conclusion, as such, is valid.
Chapters 1 & 2 might be considered as a constructive reductio ad absurdum of the
Naturalist premise. (Chapter 3 is a direct argument to the same effect, building on Kant and
Maturana.) Less kindly, they might be considered as constituting a "straw man". Combined,
however, they are much more powerful than that as they actually do resolve the whole of the
Naturalist dilemma, (other than the epistemological one I just raised), and explicate the actual
mind-brain problem in absolutely legitimate, (and empirically promising), Naturalist terms.
Clearly, there might be something wrong with the Naturalist program, but need it be fatal?
371 This problem is inherent in pretty much the same terms in the whole of Kantian and Neo-Kantian philosophy of
science, and in the philosophical dilemmas of modern physics as well. I urge that my solution, in a form very close to that offered by Cassirer, fits with the whole of modern science in a way that none other does.
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My argument turns now then, not to argue against the whole sense of Naturalism, but
against the part of it I believe is flawed. I base those arguments in an extension of Kant's,372 and,
ultimately, of Cassirer's Neo-Kantian position, i.e. his "Theory of Symbolic Forms". The thrust is
to split Naturalism from its over-strong metaphysical presumptions.
Cassirer Revisited:
My prior arguments do not, however, reduce the system of Naturalist organization, (i.e. its
predictive schema), to absurdity, (nor, therefore, the corresponding organizational, i.e. Naturalist,
validity of my own first two theses which are framed within it), but only its claim of absolute, (i.e.
metaphysical), reference.373 Nor do they question the profound effectiveness of Naturalist
science.374 Cassirer suggests a way to preserve that overwhelmingly successful relationality, (i.e.
the predictive efficacy), of Naturalism in a relativized sense, not as reference, but as organization,
i.e. his thesis of rigorous and scientific epistemological relativism.375 He proposes Naturalism, (and
materialism),376 as just one (among several) of the possible -and equipotent- "Symbolic Forms"
372 Kant's work was concerned primarily with the problem of cognition and therefore has a special relevance here.
"This is an advantage no other science", [than epistemology], "has or can have, because there is none so fully isolated and independent of others and so exclusively concerned with the faculty of cognition pure and simple." Prolegomena, P.131
373 again, at whatever level of sophistication the latter is postulated 374 The Naturalist organization can be taken within contemporary anti-realism, (i.e. anti "scientific-realism" -the
position that scientific theories do not directly describe ultimate, metaphysical reality). I am making a distinction between naturalist organization and naturalist metaphysics. Cassirer I believe, like Van Fraassen, is essentially an antirealist. This is not so surprising, given the fact that they both have Kantian roots, (cf., for instance, Van fraassen's "Laws and Symmetry".) I will most definitely not argue in favor of Naturalism, (i.e. metaphysical naturalism ==scientific realism), but will argue for the (relative and equipotent) naturalist organization. I will argue, therefore, for the structure, but not the reference of that organization.
375 Cassirer's is clearly a mathematical perspective, with its roots in modern algebra. 376 as embodied in mathematical physics
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comprehensively organizing experience. It is only experience itself,377 (the phenomena), that is
preserved as a known metaphysical absolute and to which (relativized) reference can be made.
"Experience", (Naturalist connotations notwithstanding), must not be confused and identified with
its characterization under any particular one of the possible symbolic forms however.
It is the confusion of a particular "frame of reference", i.e. form, (and the assumption that
there is only one comprehensive frame possible378), with the invariant relationality of experience
in the abstract, (i.e. under all consistent frames), that is the heart of the issue. It results in a
confusion of a specific organization (of experience) with the experience itself,379 which is
organized. It results in an (improper) assignment of (unique) metaphysical reference rather than a
(legitimate) judgement of empirical, (i.e. experiential), adequacy for the primitives of the theory.
Cassirer's reformulation of the formal logical concept allows a new logical possibility and an
escape from the dilemma.
Just as Einstein relativized measurement and disembodied the ether, so did Cassirer argue
for a relativization of knowledge, and a disembodiment of direct reference. But Cassirer's is not a
frivolous, laissez-faire relativism, (nor is it solipsism); it is an explicit and technical
epistemological relativity rigorously grounded in the phenomenology of science.380
377 Experience is not necessarily, therefore, the same as its Naturalist interpretation, (organization), as "sense
impressions". Nor, under my thesis, does experience refer to externality. It is an expression of process. 378 i.e. Naturalism 379 to include scientific experiment as an extension of ordinary experience 380 Why is Einstein not saying that any measurements, (at all!), are valid? Why is Einstein's itself not a laissez-faire
physical relativism? It is because there is a rigid structure at the core of his assertion -i.e. the specific, (and precise), invariant equations of relativity. It is the rigid and invariant "equations", (alternatively "the topology"), of experience that structure valid theories. These "equations", this "topology", must be retained as invariant(s) under all viable theories. This is why neither mine, nor Cassirer's, is an irenic relativism.
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What, exactly, is the length of a rod to a physicist? It depends on the measurements, the
frames of reference and the (absolute) equations of the theory of relativity relating them. What is
the relevance of a theory, (including a scientific one)? It depends on the experience, the "form",
(e.g. physics/Naturalist science), and the (absolute/invariant) relations, ("equations" -i.e. the web of
implication), which must be preserved in it. What is constant, under all frames, are the invariants,
(in a mathematical sense), which must be preserved in them, i.e. "experience". I have argued a
working (and non-referential) definition of "experience" as that which must be maintained under
all comprehensive worldviews.381
But what exactly could a relativized substance be then? What could Naturalism's material
be under such a conception? It would be an implicitly defined term, (alternatively "symbol"),
under a particular interpretation -i.e. it would itself be an "object" implicitly defined by the
"generating relations" of the science which specifies it. Even materialism need not, therefore,
necessarily carry a metaphysical commitment. It is an organization of experience using the
(implicitly defined) terms of "substance".
Cassirer's Theory of Symbolic Forms:
Cassirer suggests a new way to look at the relation between theory and experience. He
proposes a rigorous epistemological relativism innate in the phenomenology of modern science.
"Mathematicians and physicists were first to gain a clear awareness of this [the] symbolic
character of their basic implements. The new ideal of knowledge, to which this whole
381 Though this is clearly somewhat circular, it is perfectly consistent with my assertion that "experience" is, in fact, an
epistemic primitive.
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ctly:
development points, was brilliantly formulated by Heinrich Hertz in the introduction to his
'Principles of Mechanics'. He declares that the most pressing and important function of our
natural science is [simply] to enable us to foresee future experience"382
It is the method by which it derives the future from the past which is significant, however.
We make "inner fictions or symbols" of outward objects, and these symbols are "so constituted that
the necessary logical consequences, [my emphasis], of the images are always images of the
necessary natural consequences of the imaged objects".383 But this analysis -and "image"- must be
interpreted carefully:
"...[though] still couched in the language of the copy theory of knowledge -... the concept
of the 'image' [itself] had undergone an inner change. In place of the vague demand for a
similarity of content between image and thing, we now find expressed a highly complex
logical relation, [my emphasis], a general intellectual condition, which the basic concepts
of physical knowledge must satisfy."384
Its value lies "not in the reflection of a given existence, but in what it accomplishes as an
instrument of knowledge,"385 [my emphasis], "in a unity of phenomena, which the phenomena
must produce out of themselves." Hertz formulated the distinction very succin
382 Cassirer, 1953, p. 75
383 ibid, p.75
384 ibid
385 ibid
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"The images of which we are speaking are our ideas of things; they have with things the
one essential agreement which lies in the fulfillment of the stated requirement, [of
successful consequences], but further agreement with things is not necessary to their
purpose. Actually we do not know and have no means of finding out whether our ideas of
things accord with them in any other respect than in this one fundamental relation."386
A system of physical concepts must reflect the relations between objective things and their
mutual dependency, but, Cassirer argues, this is only possible "in so far as these concepts pertain
from the very outset to a definite, homogeneous intellectual orientation",387 [my emphasis]. It is
only within a distinct logical framework that these "images" are significant at all.388 The object
cannot be regarded as a "naked thing in itself", independent of the essential categories, (and
framework), of natural science: "for only within these categories which are required to constitute
its form can it be described at all."
This change of perspective, (a genuine "Copernican Revolution" in Kant's sense),
necessitates and validates Cassirer's conclusion of the innate symmetry and a relativity of
interpretations for phenomena. "With this critical insight ... science renounces its aspiration and
its claim to an 'immediate' grasp and communication of reality."389
386 H. Hertz, "Die Prinzipien der Mechanik", p.1 ff, my emphasis 387 Cassirer, op cit p.76 388 Please note the similarity of this situation, as formulated by Hertz and Cassirer, with that I laid out in Chapter one
for the training seminar. The objects, ("images"), in a very real sense, are a function of the calculus. Insofar as they are justified, it is on the conjoint basis of utility.
389 ibid
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It realizes that the only objectivization of which it is capable is, and must remain,
mediation, [my emphasis]. And in this insight, another highly significant [critical]390
idealistic consequence is implicit. If the object of knowledge can be defined only through
the medium of a particular logical and conceptual structure, we are forced to conclude that
a variety of media, [my emphasis], will correspond to various structures of the object, to
various meanings for 'objective' relations.391
This is the assertion of symmetry and the foundation for his thesis of "Symbolic Forms".
Even in 'nature',392 [my emphasis], the physical object will not coincide absolutely with
the chemical object, nor the chemical with the biological -because physical, chemical,
biological knowledge frame their questions each from its own particular standpoint and, in
accordance with this standpoint, subject the phenomena to a special interpretation and
formation.393 It might also seem that this consequence in the development of [critical]
idealistic thought had conclusively frustrated the expectation in which it began. The end of
this development seems to negate its beginning -the unity of being, for which it strove,
390 Everywhere, where Cassirer uses "idealism", it must be understood as "critical idealism" in the sense that Kant used
it. This is very different from ordinary idealism, and, as I discussed in Chapter 3, is a real misnomer. I have suggested "ontic indeterminism" as a more modern alternative, and one I think both Kant and Cassirer would have been happy with. Also compare the "mere X", (below), with my discussion in Chapter 3.
391 Cassirer, 1954, p.76 392 i.e., "science" as opposed to the "cultural forms" -see discussion later. 393 But even within Cassirer's primary "natural forms" -in physics, for instance, I argue -beyond Cassirer- that the exact
parallel obtains. There are arguably alternative Hertzian formulations of the problem. Alternative objects and alternative calculi are possible. Fine suggests that Relativity and Quantum Mechanics may represent such alternatives, and certainly Schroedinger's and Heisenberg's conceptions of quantum theory illustrate the plausibility.
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threatens once more to disintegrate into a mere diversity of existing things. The One
Being, to which thought holds fast and which it seems unable to relinquish without
destroying its own form, eludes cognition.394
It is the phenomena, (experience), not reference, however, that is the fulcrum of, (and
reunifies), this relativity of perspectives. The forms do not refer to (metaphysical) reality, (their
objects are not images of reality), they organize experience. Metaphysical reality becomes "a mere
X"!395 "The more its metaphysical unity as a 'thing in itself' is asserted, the more it evades all
possibility of knowledge, until at last it is relegated entirely to the sphere of the unknowable and
becomes a396 mere 'X'", [my emphasis].397 It is the realm of phenomena, "the true sphere of the
knowable with its enduring multiplicity, finiteness and relativity", on which we stand. It is the
(multiplicitous and relativized) organization of phenomena, not reference to a metaphysical origin,
which lies at the basis of knowledge.
"And to this rigid metaphysical absolute is juxtaposed the realm of phenomena, the true
sphere of the knowable398 with its enduring multiplicity, finiteness and relativity.399
But this reorientation does not destroy the either the unity or the coherence of knowledge.
394 ibid 395 compare this with the discussion of Chapter 3 396 (Kantian) 397 ibid 398 see Chapter 3 399 ibid
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"But upon closer scrutiny the fundamental postulate of unity is not discredited by this
irreducible diversity, [my emphasis], of the methods and objects of knowledge; it merely
assumes a new form. True, the unity of knowledge can no longer be made certain and
secure by referring knowledge in all its forms to a 'simple' common object which is related
to all these forms as the transcendent prototype to the empirical copies." [my emphasis]400
(This latter demand is, of course, the rationale of the Naturalist claim of reference.)
"But instead, a new task arises: to gather the various branches of science with their diverse
methodologies - with all their recognized specificity and independence - into one system,
whose separate parts precisely through their necessary diversity will complement and
further one another. This postulate of a purely functional unity replaces the postulate of a
unity of substance and origin, which lay at the core of the ancient concept of being."401
Cassirer conceives his "symbolic forms" functionally, (and serially), i.e. in terms of the
"mathematical concept of function".
"And this creates a new task for the philosophical critique of knowledge. It must follow the
special sciences and survey them as a whole. It must ask whether the intellectual symbols
by means of which the specialized disciplines reflect on and describe reality exist merely
side by side or whether they are not diverse manifestations of the same basic human
400 ibid 401 ibid
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function. And if the latter hypothesis should be confirmed, a philosophical critique must
formulate the universal conditions of this function and define the principle underlying it.402
Instead of dogmatic metaphysics, "which seeks absolute unity in a substance to which all
the particulars of existence are reducible", he seeks after "a rule governing the concrete diversity
of the functions of cognition, a rule which, without negating and destroying them, will gather them
into a unity of deed, the unity of a self-contained human endeavor."403 [my emphasis]404
Perhaps the most succinct overall statement of Cassirer's thesis is found in his "Einstein's
Theory of Relativity".405 Each of the perspectives of scientific knowledge: physics, chemistry,
biology, ... (the "cognitive forms"), - and ultimately myth, religion and art, ... (the "cultural
forms"),406 are taken as alternative and equipotent (organizational) perspectives on the phenomena.
"Each of the original directions of knowledge, each interpretation, which it makes of
phenomena to combine them into the unity of a theoretical connection or into a definite
unity of meaning, involves a special understanding and formulation of the concept of
reality."407
402 ibid p.77, my emphasis 403 ibid 404 Cassirer extends his theory of symbolic forms beyond "nature", (i.e. beyond the sciences), into the "cultural forms":
art, myth, religion, etc. -i.e. beyond cognition itself. I will deal with this aspect of his thesis presently, taking a neutral perspective, but first I would like to extend and modify this, his core and scientifically grounded position somewhat.
405 Cassirer 1953 406 I will question the eventual scope of his vision presently 407 ibid, P.446, my emphasis
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Ordinary Naturalism confuses a particular organization, (mathematical physics), with the
phenomena which are organized. That is the basis of its assertion of reference -and "scientific
realism"408. "The "objects", (the organizational primitives -i.e. "images"), of one particular form
are assumed, (incorrectly), to reference ontology -to relate to "an ultimate metaphysical unity".
"Where there exist such diversities in fundamental direction of consideration, the results of
consideration cannot be directly compared and measured with each other. The naive
realism of the ordinary view of the world, like the realism of dogmatic metaphysics, falls
into this error, ever again. It separates out of the totality of possible concepts of reality a
single one and sets it up as a norm and pattern for all the others. Thus certain necessary
formal points of view, from which we seek to judge and understand the world of
phenomena, are made into things, into absolute beings.[my emphasis]"409 410
What these "formal points of view" do, instead, is organize phenomena. What is consistent
under all forms, however, are the phenomena themselves. Naturalism confuses a particular "frame
of reference", i.e. form, (and assumes that there is only one comprehensive frame possible411), with
the invariant relationality of experience in the abstract, (i.e. under all consistent frames)412 It
confuses a specific organization, (and a specific characterization), of experience with the
408 another misnomer 409 ibid, p.447 410 Naturalism, at whatever level of sophistication, clearly falls under this injunction. 411 i.e. Naturalism 412 compare Van Fraassen's "co-ordinate-free descriptions". "Quantum Mechanics: an Empiricist's View"
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experience itself413 which is organized. It results, (and I repeat myself), in an (improper)
assignment of (unique) metaphysical reference rather than a (legitimate) judgement of empirical,
(i.e. experiential), adequacy for the primitives of its theories.
"Only when we resist the temptation to compress the totality of forms, which here result,
into an ultimate metaphysical unity, into the unity and simplicity of an absolute 'world
ground' and to deduce it from the latter, do we grasp its true concrete import and fullness.
No individual form can indeed claim to grasp absolute 'reality' as such and to give it
complete and adequate expression.[my emphasis]"414
Cassirer's denial of "completeness" and "adequacy", however, is not the same as denying
that any individual form can grasp the whole of the phenomena comprehensively! Nor does it
speak definitively on the issue of reduction! I will address both of these issues shortly.415
"It is the task of systematic philosophy, which extends far beyond the theory of knowledge,
to free the idea of the world from this one-sidedness. It has to grasp the whole system of
symbolic forms, the application of which produces for us the concept of an ordered reality,
and by virtue of which subject and object, ego and world are separated and opposed to each
other in definite form, and it must refer each individual in this totality to its fixed place. If
we assume this problem solved, then the rights would be assured, and the limits fixed, of
413 to include scientific experiment as an extension of ordinary experience 414 ibid, p.446 415 If a given form were, in fact, capable of reducing all other theories, and no other could, it would obviously cut
against equipotency and "relativization" -i.e. against the whole sense of his thesis! This is the current rationale for dogmatic Naturalism as grounded, (problematically, I believe), in mathematical physics.)
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each of the particular forms of the concept and of knowledge as well of the general forms
of the theoretical, ethical, aesthetic and religious understanding of the world. Each
particular form would be 'relativized' with regard to the others, but since this
'relativization' is throughout reciprocal and since no single form but only the systematic
totality can serve as the expression of 'truth' and 'reality', [my emphasis], the limit that
results appears as a thoroughly immanent limit, as one that is removed as soon as we again
relate the individual to the system of the whole." 416
Cassirer's is not a capricious relativism; it is a relativism as rigorous in concept as is
Einstein's. Just as Einstein characterized his theory as having removed "the last remainder of
physical objectivity from space and time", Cassirer's conclusion removes the last remainder of
metaphysical, (i.e. absolute), reference from knowledge. It is based in the essential methodology
of science: in its (Hertzian) theorizing function! It is the nature of science to construct a form,
complete and interdependent between symbols, ("images"), and calculus which acts as a whole.417
Under all the forms, (of "nature", at least), Cassirer maintains that what must be maintained
are the "invariants" -i.e. that which must be preserved under any consistent form. These are not
"things" or "images", but rather, (mathematically), that which remains constant under all legitimate
forms. In the sense which I will expand the notion, I argue that it corresponds to my prior
(relativized) definition of "experience".
416 ibid, p.447 417 cf. the "training seminar" of Chapter 1
164
"But above all it is the general form of natural law which we have to recognize as the real
invariant and thus as the real logical framework of nature in general......No sort of things
are truly invariant, but always only certain fundamental relations and functional
dependencies retained in the symbolic language of our mathematics and physics, in certain
equations." 418
I will postpone my critique of Cassirer's thesis for a little. Though I think there are
problems and questions which need to be resolved, I would like to make the connection to my own
thesis before going into those. In its essence, i.e. the essential relativism of knowledge, and his
case against reference, I think the argument is very strong and very fundamental. There are very
strong questions and delimitations that I will raise when I return to Cassirer's broader thesis later.
They will not, however, question this, his core position.
The solution to the dilemma:
Nowhere does Cassirer question the profound effectiveness of modern science, however.
His orientation is wholly and profoundly scientific. Rather, he preserves the various sciences as
perspectives, as organizations of phenomena. He has, moreover, provided the tools necessary to
resolve the epistemological dilemma created by the combination of my first and second theses.
I therefore propose a fundamental, (and final), "Copernican Revolution" -a profound
change in perspective- contrary to that, (i.e. the Naturalist perspective), which I conditionally
418 Cassirer, 1923, pps. 374-379, my emphasis
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adopted419 at the end of Chapter 2, (and to the stance I now ultimately proclaim), which "reduces"
the materialist position itself to organization and not to reference. I argue against ordinary
Naturalism, and for a more sophisticated realism, (essentially a Kantian -and Cassirerian- one),420
consistent with the results of the first two theses. By this, (once again), I do not mean to say that
the relationality of Naturalism, (or Naturalist science), is faulty, but that its metaphysical reference
as reference is faulty. My thesis, though built with Naturalist "bricks", does not therefore entail the
(further and unnecessary) Naturalist "foundation" of reference. Though it assumes the validity of
the Naturalist organization, (at least on the human scale), it does not assume the metaphysical
reality of Naturalism's primitives. In questioning our actual, (referential), cognition of
metaphysical reality, it is not, therefore, innately self-contradictory! Though stated in Naturalist
terms, my thesis can legitimately question the actual (metaphysical) existence, (or even the
possibility of knowledge), of the referents of those terms.
Ordinary Naturalism, though it will not say so, is through and through grounded in a
specifically metaphysical dogma, i.e. absolute reference, (however sophisticated), to absolute,
(rather than relativized), "material" == "substance". This is the "material" in "materialism",421 and
was the specific target of Kant's and Cassirer's profound arguments.
As realists, contrariwise, (and I speak to no one else), we must posit the existence of an
absolute, external reality. It is, I have argued, an axiom of realist reason. But, I further argue
419 but with perfect legitimacy, I now maintain -as a relative stance 420 Kant's thesis is profoundly difficult to accept admittedly, both intellectually and intuitively -but so was Einstein's.
Where Einstein relativized the physical world, Kant sought to relativize the epistemological one. His lapses can be assigned to his deprivation of the examples of modern mathematics and modern science -which subjects were always his primary focus -and which could have corrected him. That he was two hundred years before his time is surely not an argument against his credibility.
421 as usually conceived -i.e. not in a Cassirerian sense
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based on Kant, on Cassirer, on the advances of modern physics, on Maturana's penetrating analysis
and on the results, (and natural concordance), of my first two theses, that human cognition does not
know, and can not know that absolute reality. I argue we cannot know that metaphysical world in
itself, even in "sophisticated" reference! I propose that we stand, even at the human scale,422 in the
same relation to ontology that current physics does, (at least as I understand, let's say, Bohr's or
Heisenberg's position to be.) I propose that our human scale cognitive world is as much -and as
solely- a pure algorithm as is the worldview of quantum physics. It is utilitarian and not
referential. But it is an organic, "tactile" algorithm, (a "GUI"), that evolution constructed.423 This
sentence, however, is no longer paradoxical. It must itself now be understood in my larger context,
as the very "evolution" in it is itself relativized, (i.e. it is a relative assertion within the (particular)
Naturalist form).
The results of my first two theses are therefore consistent under this epistemological
rationale. The resolution lies in the scientifically and mathematically, (but most certainly not
arbitrarily), conceived relativization of knowledge itself. Relational implications, predictive
systems, (to include scientific theories), are not, (with Quine), epistemologically determinate.
Rather, their essence, (which is their predictivity), can be isolated, (following Cassirer), as
relational invariants, (in a mathematical sense), over the field of consistent hypotheses in a sense
parallel to that in which Einstein's equations of special relativity were isolated as invariants from
the "ether" in which they were originally grounded by Lorentz. Or, rather, relational implications
422 more properly "domain" than "scale", as I do not think this is a size issue. I will expand this momentarily. 423 This is the implication of my footnote early in Chapter 1. Let me repeat it here: Ideally instrumentation and control
would unify in the same "object". We would manipulate "the object" of the display itself and it would be the control device. Think about this in relation to our ordinary "objects of perception" -in relation to the sensory-motor coordination of the brain and the problem of naive realism! We do not use our biological algorithm, we live in it!
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are invariant, but predictive organizations, (i.e. theories), even comprehensive ones, are not! They
are the (better or worse), "SUPERB" or "MISGUIDED"424 "forms" which organize those
implications.
Whence Cassirer's Thesis:
There is, interestingly, a very real similarity of intent at least, (if not in scope or rationale),
between Bas Van Fraassen's "co-ordinate free" and "semantic" approach to modern physics and
Cassirer's "symbolic forms".
"To formulate a view on the aim of science, I gave a partial answer to the question of what
a scientific theory is. ... It does not follow that a theory is something essentially linguistic.
That we cannot convey information, or say what a theory entails, without using language
does not imply that -after all, we cannot say what anything is without using language. We
are here at another parting of the ways in philosophy of science. Again I shall advocate one
particular view, the semantic view of theories. Despite its name, it is the view which de-
emphasizes language."425
"Words are like coordinates. If I present a theory in English, there is a transformation
which produces an equivalent description in German. There are also transformations which
produce distinct but equivalent English descriptions. This would be easiest to see if I were
so conscientious as to present the theory in axiomatic form; for then it could be rewritten so
424 cf Penrose "The Emperor's New Mind" (his CAPS!). cf Appendix D 425 Van Fraassen, 1991, pps.4-5
168
that the body of theorems remains the same, but a different subset of those theorems is
designated as the axioms, from which all the rest follow. Translation is thus analogous to
coordinate transformation -is there a coordinate-free", [invariant?] "format as well?' [my
emphasis] The answer is yes (though the banal point that I can describe it only in words
obviously remains)."426
Though Van Fraassen ultimately rejects axiomatics, and confines himself to the domain of
physical science, his position has a very definite resemblance to that of Cassirer, at least insofar as
the latter is confined to "nature". Each is epistemologically relativistic,427 and each is grounded in
invariants. Van Fraassen rejects axiomatics, (which I believe is the most cogent formulation of the
problem), however, on the basis of a need for meaning and interpretation, i.e. reference. He goes
on:
"To show this, we should look back a little for contrast. Around the turn of the century,
foundations of mathematics progressed by increased formalization. Hilbert found many
gaps in Euclid's axiomatization of geometry because he rewrote the proofs in a way that did
not rely at all on the meaning of the terms (point, line, plane,...). This presented
philosophers with the ideal: a pure theory is written in a language devoid of meaning (a
426 ibid 427 "There are a number of reasons why I advocate an alternative to scientific realism ... One concerns the difference
between acceptance and belief; reasons for acceptance include many which ceteris paribus, detract from the likelihood of truth. This point was made very graphically by William James; it is part of the legacy of pragmatism. The reason is that, in constructing and evaluating theories, we follow our desires for information as well as our desire for truth. We want theories with great powers of empirical prediction. For belief itself, however, all but the desire for truth must be 'ulterior motives'." (ibid p.3) Please note the connection to the essential Hertzian perspective. "Information" is concerned with predicting future events; "truth" is something else altogether.
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pure syntax) plus something that imparts meaning and so connects it with our real
concerns."428
My thesis of the "schematic object", however is directed precisely to that point. It is
precisely my point that "meaning" be taken in its mathematical sense for such a system. A
mathematician understands the meaning of a term to be precisely that which is implied by the
syntax, i.e. it is a virtual term "ordering" the system in which it is defined. If the mind and
perception specifically, (the phenomena), is taken in this sense, ordering process- if it is taken as an
organization, and its terms as metaphors of process then there is no longer the metaphysical
question of meaning or of reference. The terms mean precisely what the syntax implies -i.e. they
are virtual terms only! I maintain these are our real concerns! The real problem is the one that
Cassirer defined: that of "experience" itself and how theoretical science relates to it,429 -and that
involves a total reevaluation of the problem of reference.
Cassirer's epistemology, of course, is firmly grounded in axiomatics. Discussing Hilbert,
Cassirer says:
428 ibid 429 Theory, (seen as a Hertzian, free construct -as developed in this chapter), must match, (in some sense), the
"topology" of temporal and spatial consequence in experience. As stated thus far, this idea is, of course, Kantian. Russell however, (in his "Foundations of Geometry"), argued to extend the Kantian frame to projective geometry. I feel it must be broadened again past that -past even topology and into the mathematics of abstract transformations. What is required is that the predicted results of the theoretical system (through some transformation!) must match the results of naive (?) experience, -and conversely! I.e. that the results of naive experience -through some (mathematical) transformation - should match the retrodictive predictions of the theory. But this transformation, (since it is past topology), need not preserve objects, and therefore, not reference! What it must preserve is the web of relationality in its most abstract sense.
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"The procedure of mathematics here", (implicit definition), "points to the analogous
procedure of theoretical natural science, for which it contains the key and justification."430
Contra Cassirer: (What are the real parameters?)
Though I accept, (and argue), Cassirer's core position of epistemological relativism, (I
believe it is absolutely warranted on the very pure and very strong phenomenological grounds
wherein he evolved it), I will now question its scope and its applicability. What are the legitimate
forms?
Cassirer's thesis goes beyond "cognition" and science, ("nature") into a symmetry of
cultural forms, (to include science as a special case), as well. Van Fraassen does not, nor did Kant,
(who remained entirely within "nature"), but this is a question of scope. There is also a question of
the identification of the legitimate (primitive) forms -even within "nature" itself.
Before addressing these questions, however, let me first complete my examination of the
broadest formulation of Cassirer's thesis. Going beyond the "natural forms", (physics, biology,
chemistry, etc), he extends his thesis into ground which I must at least question. He proposes that
the forms of "nature", of "cognition", are only part of the innate symmetry of perspectives across
the phenomena. They, (the natural forms), represent those forms which relate phenomena directly
to a metaphysical, (cognitive), framework. Phenomena can however, (he asserts), be organized on
other grounds: art, myth, religion, etc., but they achieve this universal validity by methods entirely
different from the logical concept and logical law.
430 ibid p.94
171
But again our perspectives widen, [i.e. beyond "nature" and into the purely cultural
forms], if we consider that cognition, [itself], however universally and comprehensively we
may define it, is only one of the many forms in which the mind can apprehend and interpret
being. In giving form to multiplicity it is governed by a specific, hence sharply delimited
principle. All cognition, much as it may vary in method and orientation, aims ultimately to
subject the multiplicity of phenomena to the unity of a 'fundamental proposition.' The
particular must not be left to stand alone, but must be made to take its place in a context,
where it appears as part of a logical structure, whether of a teleological, logical, or causal
character. Essentially cognition is always oriented toward this essential aim, the
articulation of the particular into a universal law and order.431
(I disagree with his distinction -so too do the "cultural forms" embody law. The difference,
I believe, is in the orientation -i.e. to cognition -to "externality" as world-ground. Any form, even
the "cultural forms", will have, (by definition), its own sense of law and logical structure. It is a
question of the meaning of "logical structure".)
"But beside this intellectual synthesis, which operates and expresses itself within a system
of scientific concepts, the life of the human spirit as a whole knows other forms. They too
can be designated as modes of 'objectivization': i.e., as means of raising the particular to
the level of the universally valid; but they achieve this universal validity by methods
entirely different from the logical concept and logical law. Every authentic function of the
human spirit has this decisive characteristic in common with cognition: it does not merely
431 Cassirer, 1953, p.77
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copy but rather embodies an original, formative power. It does not express passively the
mere fact that something is present but contains an independent energy of the human spirit
through which the simple presence of the phenomenon assumes a definite 'meaning', a
particular ideational content."432
But please note carefully that all of Cassirer's "functions of the human spirit" -even his
"cultural forms" specifically articulate phenomena -i.e. they are not free, "idealistic" constructs!
("...an independent energy of the human spirit through which the simple presence of the
phenomenon assumes a definite 'meaning', a particular ideational content.")
"This is as true of art as it is of cognition; it is as true of myth as of religion. All live in
particular image-worlds, which do not merely reflect the empirically given, but which
rather produce it in accordance with an independent principle. Each of these functions
creates its own symbolic forms which, if not similar to the intellectual symbols, enjoy equal
rank as products of the human spirit. None of these forms can simply be reduced to, or
derived from, the others; each of them designates a particular approach, in which and
through which it constitutes its own aspect of 'reality'. They are not different modes in
which an independent reality manifests itself to the human spirit, but roads by which the
spirit proceeds towards its objectivization, i.e. its self-revelation."433
432 ibid. pps. 77-78, my emphasis 433 ibid, my emphasis
173
(That "none of these forms can simply be reduced to, or derived from, the others" seems to
provide an essential argument to dogmatic Naturalism. Conversely, I will argue that it suggests
and delimits a more correct extension of Cassirer's solution to the overall problem. I will address
these very large problems shortly. His meaning must be examined very closely.)
"If we consider art and language, myth and cognition in this light, they present a common
problem which opens up new access to a universal philosophy of the cultural sciences.434
"The 'revolution in method' which Kant brought to theoretical philosophy rests on the
fundamental idea that the relation between cognition and its object, generally accepted until
then, must be radically modified. Instead of starting from the object", [my emphasis]," as
the known and given, we must begin with the law of cognition, which alone is truly
accessible and certain in a primary sense; instead of defining the universal qualities of
being, like ontological metaphysics, we must, by an analysis of reason, ascertain the
fundamental form of judgement and define it in all its numerous ramifications; only if this
is done, can objectivity become conceivable. According to Kant, only such an analysis can
disclose the conditions on which all knowledge of being and the pure concept of being
depend. But the object which transcendental analytics thus places before us is the correlate
of the synthetic unity of the understanding, an object determined by purely logical
attributes. Hence it does not characterize all objectivity as such, but only that form of
434 ibid
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objective necessity which can be apprehended by the basic concepts of science, particularly
the concepts and principles of mathematical physics. ..."435
Cassirer asserts an absolute "spiritual" relativism, (but always articulating the phenomena),
-i.e. an absolute symmetry across the whole of the "cultural forms", (the "spirit"), of man.
"There result here not only the characteristic differences of meaning in the objects of
science, the distinction of the 'mathematical' object from the 'physical' object, the 'physical'
from the 'chemical', the 'chemical' from the 'biological', but there occur also, over against
the whole of theoretical scientific knowledge, other forms and meanings of independent
type and laws, such as the ethical, the aesthetic 'form'. It appears as the task of a truly
universal criticism of knowledge not to level this manifold, this wealth and variety of forms
of knowledge and understanding of the world and compress them into a purely abstract
unity, but to leave them standing as such."436
Though starting from very stable ground, I think that Cassirer ended up in a somewhat
ambiguous position. He, like Kant, used words with great precision,437 so he must be read very
carefully -even technically. "Nature", and "the forms of nature", for Cassirer, are technical words.
He defines the "forms of nature" for us -e.g. physics, biology, chemistry. These are some
of the "values" of his specific function, (his "purely functional unity"), of the human spirit, (here
435 ibid 436 Cassirer, 1923, p.446 437 I think it is a necessary concomitant of the very abstract nature of their ideas
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specifically the cognitive forms). A philosophical critique "must formulate the universal
conditions of this function and define the principle underlying it."
We must place this passage in the context of Cassirer's redefinition of the formal concept
however. We must see it in the context of "the mathematical concept of function" to understand it.
The various forms are functional "values" -in a technical mathematical sense -of a definite, and, for
Cassirer, serial ordering, (and principle). They are the alternative orderings of the phenomena,
(defined by a serial function), -and constitute a series of series. The phenomena, however, remain
always the orientation -the focus -of all the forms, (even the "cultural forms"). There is in this no
assertion of comprehensiveness, (and even a seeming denial of it), for any given form however.
He seems to argue against reduction,438 (and therefore comprehensiveness), as well -but against
"reduction" and "comprehensiveness" in what senses?
Compare: (1) "none of these forms can simply be reduced to, or derived from, the
others",439 (2) "no individual form can indeed claim to grasp absolute 'reality' as such and to give it
complete and adequate expression."440, and (3) "each particular form would be 'relativized' with
regard to the others, but since this 'relativization' is throughout reciprocal and since no single form
but only the systematic totality can serve as the expression of 'truth' and 'reality', the limit that
results appears as a thoroughly immanent limit, as one that is removed as soon as we again relate
the individual to the system of the whole."441
438 "None of these forms can simply be reduced to, or derived from, the others" 439 ibid, my emphasis 440 ibid, p.446 441 ibid, p.447
176
What is the sense of Cassirer's "cannot be simply reduced to or derived from"? That no
individual form can give "complete and adequate expression to reality" and that no form can be
"simply reduced" does not necessarily imply that reduction, (i.e. translation), in a non-simple sense,
or that comprehensiveness, (as a complete accounting for phenomena), is impossible. (3),
moreover, seems to contradict (1) and (2).
Consider, moreover, his "invariants of nature": though "no sort of things [his emphasis] are
truly invariant, but [it is the]..fundamental relations and functional dependencies retained ... in
certain equations..[which are truly invariant]" He proposes these, (the functional invariants), as
"the real logical framework of nature in general" [my emphasis]. But "nature" is a pluralistic word
for Cassirer -the "natural forms" are all the forms of science!
We have, therefore, an assertion of invariance442 across all the forms of science -and cross-
reduction across the invariants. Indeed, this is the only sense in which "invariance" makes any
sense at all, (it is a "coordinate-free" perspective). "Invariance", therefore, means invariance across
different, (all the different), perspectives of nature -and epistemologic relativity. For what other
interpretation of the "relativization" of (3) is there except as alternative orientations of the same
phenomena?
Consider also his seeming denial of comprehensiveness. "The 'relativization' [of forms] is
throughout reciprocal". "No single form but only the systematic totality can serve as the
expression of 'truth' and 'reality'." What he is actually asserting, I argue, is that although multiple
forms are legitimate, no single one of them can describe the structure as abstracted from an
orientation! What Cassirer is portraying here is exactly a "coordinate free" perspective! It is not,
442 of functional dependency but not of "things"
177
therefore, a denial of comprehensiveness443 that he is arguing, but a denial of the (metaphysical)
adequacy of any particular orientation. It is only in their multiplicity that he believes that they
express "'truth' and 'reality'". "The limit that results appears as a thoroughly immanent limit, as one
that is removed as soon as we again relate the individual to the system of the whole."444
If these are "the real logical framework of nature", and they are invariant across all the forms
of nature, then all the forms of nature are, by implication, cross reductive and comprehensive!
That these forms cannot be "simply...reduced to, or derived from the others", does not mean,
therefore, that they cannot be reduced or derived at all!
It is cross-reduction and relativistic invariance which tie the forms together and it is only in
their totality that they express reality -and experience. The mathematical axiom system will serve
to illustrate the case again. That any (adequate) axiom system for a given discipline will be
443 Comprehensiveness is, of course, a highly pertinent issue because of the very definite, (and very powerful), claim by
ordinary Naturalism for just such an (ultimate) comprehensiveness for mathematical physics . (I will address this issue presently). This is a very strong claim, and one I think we all actually do accept -at least in principle. However, if one particular form, (e.g. Naturalism), is actually capable of such comprehensiveness, (even in principle), and no other is, then this would constitute a very definite objection to his thesis.
Cassirer believed that the only salvation for the symmetry and relativism he envisaged lay in his extension across the cultural forms:
"As long as philosophical thought limits itself to analysis of pure cognition, [his emphasis], the naive-realistic view of the world cannot be wholly discredited, [I will disagree with this],. The object of cognition is no doubt determined and formed in some way by cognition and through its original law -but it must nevertheless, so it would seem, also be present and given as something independent outside of this relation to the fundamental categories of knowledge.** If, however, we take as our starting point not the general concept of the world, but rather the general concept of culture, the question assumes a different form. For the content of the concept of culture cannot be detached from the fundamental forms and directions of human activity: here 'being can be apprehended only in 'action'."
I believe the actual salvation of his thesis and the guide to its extension lies in the idea of converse -i.e. mutual reduction. If his basic conception is right, and I think it is, (on phenomenological grounds), then multiple cross-reductions and a true relativism will be possible. The possibility is founded in the conception of alternative axiom systems, (and orientations), in formal mathematics and in my extension of Cassirer's reformulation of the formal logical concept.
444 ibid, p.447
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comprehensive is, of course, clear by definition. But to confuse the discipline itself with one
particular, (of many possible), adequate axiom systems, is incorrect. Peano's system is not the
same as the positive integers. (A more specific and perhaps a more elegant tool for illustrating this
conception lies the mathematical notion of “ideals” in abstract algebra. I have discussed this in
detail in the Lakoff/Edelman appendix. cf: Afterward: Lakoff – Edelman)
Cassirer is asserting alternative functional orientations across the phenomena in his thesis
of "Symbolic Forms". Each draws different functional, (and serial), perspectives, "diverse
manifestations of the same basic human function".445 This is an explicit invocation of his
"mathematical concept of function". I suggest, instead, an extension of it: that the objects of
knowledge are constituted in different, (and alternative), "axiom systems"446 which "crystallize"
the phenomena, (under the "concept of implicit definition"). (This is certainly consistent with the
Hertzian perspective, more so, I believe, than even Cassirer's interpretation.) I suggest that it is the
phenomena themselves which are the actual invariants!447 It is a solution based, not in the
mathematics of functions but, as Cassirer suggested often as the true focus of modern thought, -in
that of the manifold itself. What results is a true epistemological relativity, (in a mathematical
sense), and the possibility of multiple, each-truly-comprehensive and cross-reductive independent
perspectives.448
445 Also: "A philosophical critique must formulate the universal conditions of this function and define the principle
underlying it." 446 Alternatively, “generators of an Ideal” –cf Afterword 447 Are the phenomena themselves, then, invariant equations? No, they are what the equations embody. 448 See the discussion of mathematical “ideals” in the “Afterword: Lakoff, Edelman,…” for a further elaboration of
these ideas.
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I will leave the problem of the definition of the actual (valid) forms without reaching a definite
conclusion. Cassirer's solution is seductive, to be sure -and may very well be correct, but it is
outside of the needs for my thesis. What is unquestionable, I think, is his "coordinate-free"
orientation to phenomena. Such a perspective on physics alone would stand sufficient to my
requirements and my interests here, and Cassirer's Hertzian stance, narrowed to Van Fraassen's
smaller physical perspective, will adequately serve my case. I do, nonetheless, think that the case
for the "forms of nature" has definite merit as well,449 but, as Cassirer himself explicitly states,
beyond that we leave the arena of "cognition" altogether. But cognition is precisely our area of
interest here. Our context here is precisely that of cognition and metaphysics!
[Important Note 6-20-1999: a modification of my conclusions]
In reflection, I have altered my conception of this. I have concluded that an extension of
the necessary forms to biology is a necessary component of my thesis. See the footnote to the
Afterward: Lakoff - Edelman regarding his "embodied logic" and biology as a pure "form".
(Hyperlink to Lakoff Appendix, relevant section)***]
If my area of interest were to change -if I chose to look at "the phenomena" artistically, let's
say, then this would no longer be my orientation, and his broader case might be argued. But then,
conversely, I would no longer be able to express it in a cognitive context!450
449 Note 6-20-1999: In reflection, I have altered my conception of this. I have concluded that an extension to biology
is a necessary component of my thesis. See the footnote to the Afterward: Lakoff - Edelman discussing "embodied logic" and biology as a pure "form". (Hyperlink to Lakoff appendix, relevant section)***
450 An interesting and important point comes up here, however. If his broader thesis is correct, and my extension of it as well -i.e. mutual cross-reductions and comprehensiveness - then the "invariants", (if there should be such), of those other forms will be (reductively) retained as invariants even in the sciences! Thus, if there be absolutes, (invariants), in art, in music, in religion, then they will be retained as invariants even in the sciences, (in psychology, for instance). I consider this a very significant scientific conclusion, and running contrary to current social
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Cassirer's is a profoundly beautiful and elegant conception, to be sure. I am not sure that I
can accept the broadest symmetry that Cassirer asserts however, a symmetry, (and a still further
Copernican Revolution), that extends beyond cognition and science itself into the cultural forms:
language, religion, myth.2 But I believe the symmetry within cognition and science itself is wholly
justified.
The Power of Naturalism
Naturalism, however, is a profoundly comprehensive theory! Not only mathematical
physics, but its reductive incorporation of the other disciplines, from biology and chemistry
through (proposedly) psychology, philosophy, ethics, religion,451 presents a purportedly complete
(comprehensive) theory of all the phenomena. Quine demonstrates, however, that there are always
other interpretations of the phenomena, no matter the level of detail. Can there be other
comprehensive forms then? I think the answer is necessarily yes! Need they be physical forms?
The possibility of alternative, and comprehensive, physical forms, certainly seems quite believable.
Heisenberg vs. Schroedinger illustrates the plausibility. Whether Cassirer's other "natural forms":
biology, chemistry, etc. are capable of such a legitimate extension to comprehensiveness452 is
another issue, however.
Cassirer wrote in another era,453 but this does not, in itself, invalidate his conclusions or
their possible extension to a broader relativism. On the subject of biology, for instance, he dealt
relativism. There may be an ultimate scientific decision possible between, let's say, John Cage and Beethoven! -Or between Zoroaster and Jesus!
451 The primitives of some of these forms are distributed and derivative under the reduction, however. 452 with equivalent distributions and derivativeness of primitives 453 though not that long ago!
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with the issues of vitalism. In modern times, however, there is a very strong case made on much
more rigorous grounds which supports the same, independent case for biology. It is that of
Maturana and Varela.1 To appreciate it, it is necessary, of course, to effect the same "Copernican
Revolution" which Cassirer suggested. Maturana and Varela's case is made on very pure
phenomenological grounds. The biology they propound is not grounded upon mathematical
physics. Its primitives are not those of the latter, but rather, physics, (and human knowledge) is
derived as a function of linguistic coupling, (third order structural coupling) -i.e. it is contained as a
(non-centralized) theoretical derivative of biology's own primitives:
"It is by languaging that the act of knowing, in the behavioral coordination which is
language, brings forth a world. ...We find ourselves in this co-ontogenic coupling, not as a
preexisting reference nor in reference to an origin, [my emphasis], but as an ongoing
transformation in the becoming of the linguistic world that we build with other human
beings."454
Maturana and Varela's thesis does not find its epistemological roots in substance, but drives
past its materialist beginnings to find its new epistemological center in "autopoietic unities" and
"structural coupling". It ends up questioning the very physical ground from which it began. In
many ways it represents the "Heisenberg" case of biology. It represents an alternative theoretical
perspective on experience and on science. It works because of the purity of its phenomenology.
Can other "natural forms" be asserted in this same sense?455 Could chemistry, for instance, be
454 op.cit Pps.234-244, my emphasis 455 Maturana and Varela reveal such an alternative orientation in "structural coupling" and "autopoietic unities". That
these other "symbolic forms" must encompass the whole of experience, (i.e. the whole of past and future experience -
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stated with the phenomenological purity with which Maturana and Varela stated biology? That is
the only real issue. This is Hertz' problem, after all, pure and simple. It is also the case I made for
the training seminar in Chapter 1.
I will not profess an absolute conclusion on these questions other than in the case of
physics, where I conclude, (on Quinean grounds), that there must be, indeed, multiple possible
comprehensive forms. The case for biology seems more than plausible and leads to me to accept
the broader case for the "natural forms", though I will not insist on it.
But my conclusion in its essence, and beyond Cassirer's, is a fully relativistic one. The
truly fundamental forms are (necessarily) comprehensive forms -i.e. they are fully functional
"axiom systems"456 capable of exhausting the phenomena. (Alternatively, "the phenomena" is that
which remains constant -i.e. invariant- under all such exhaustive perspectives.) They "slice" the
phenomena, (all the phenomena), from different perspectives. To be fully relativistic, each form
must be complete. Though Cassirer seemed to drive towards this complete relativism, he didn't
ever complete it.457
But must not a comprehensive organization be categorical, i.e. must there not be only one?
(If we could achieve the Laplacean ideal, would it not be unique?)458 Or, rather, might there not be
to include scientific experiment), I think is incontrovertible. But they need not encompass it in the same way as does physics, for example. They need not encompass it as the primitive and hierarchical ground of their science, but may weave and distribute its relationality into a much less central, (i.e. removed from "axiomatic" status), much less concentrated position in its theoretical structure. They need not adopt the primitives of another orientation as their own primitives -those may become "theorems"!
456 Cf Afterword: Lakoff and Edelman on mathematical "ideals"
457 I believe because of the limitation in his formal concept 458 The Laplacean ideal is not realist by definition.
"In the introduction to his "Theorie analytique des probabilites" Laplace envisages an all-embracing spirit possessing complete knowledge of the state of the universe at a given moment, for whom the whole universe in every detail of
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alternative yet still comprehensive predictive organizations with different perspectives and different
utilities? Under the Aristotelian logic, and assuming comprehensiveness, (i.e. assuming the
possibility of a single and complete accounting of all phenomena), there is a linear reduction of all
true theories to a single substratum of primitives.459
Hierarchy, (set-theoretic, type ordered inclusion), is an essential component of the existing
Naturalist perspective: i.e. that there is a necessary hierarchy of spatial scale. It argues that that
hierarchy is mirrored in the process of the reduction of scientific theories: e.g. biology is a subset
of chemistry, and chemistry of physics. (Thus psychology and all the phenomena of experience, of
knowledge, and of the "spirit" as well, are embedded in that hierarchical ordering -as biological
subsets.) It presumes that our naive world, (or at least most of it), is hierarchically mirrored in the
primitives of any true theory, (i.e. that the objects of naive realism are objects of that true theory as
well). It presumes that they can be represented as legitimate and necessary groupings of those
primitives. Thus our ordinary objects and the ordinary things they do are, in fact, real and
its existence and development would thus be completely determined. Such a spirit, knowing all forces operative in nature and exact positions of all the particles that make up the universe, would only have to subject these data to mathematical analysis in order to arrive at a cosmic formula that would incorporate the movements both of the largest bodies and of the lightest atoms. Nothing would be uncertain for it; future and past would lie before its gaze with the same clarity. ...Du Bois-Reymond elevated scientific knowledge far above all accidental, merely empirical bounds...If it were possible for human understanding to raise itself to the ideal of the Laplacean spirit, the universe in every single detail past and future would be completely transparent. 'For such a spirit the hairs on our head would be numbered and no sparrow would fall to the ground without his knowledge. He would be a prophet facing forward and backward for whom the universe would be a single fact, one great truth'." Cassirer, "Determinism and Indeterminism in Modern Physics", pps.3-4
Under a functional logic, (i.e. one not based in the generic concept), there is the possibility of alternative "axiom systems", (organizational perspectives), exposing alternative utilities, (e.g. biology, psychology, etc. -or alternative physical theories). The Laplacean ideal does not, therefore, presuppose a unique theory, (Newtonian, for instance), and reference.
If we were, in fact, to achieve a science, (theory), such that "the hairs on our head would be numbered and no sparrow would fall to the ground without his [our] knowledge", i.e., comprehensiveness, I maintain that it still not need be unique. The Laplacean ideal is not tied necessarily to Newtonian or any other particular theory, but constitutes the basis of determinism and could apply to raw empiricism as well. (ibid)
459 See Afterword: Lakoff and Edelman for a further discussion of classical logic and science
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necessary metaphysical objects and happenings. This argument is crucial to the strength of
Naturalism and its metaphysical claim!
But scale is not a priori inherent or the only way to preserve the phenomena, i.e. it need not
necessarily "cut reality at the joints". 1 If other organizations, more effective, (i.e. other schematic
organizations), are found, then they are legitimate as well. Our naive objects, as objects, are not
necessarily metaphysical objects.
Science, until very recently has supported such a spatial, (and theoretical), hierarchy -from the
macro to the human scale to the micro to the atomic, (which, of course, theoretical reduction
generally supports -i.e. biology -> chemistry -> physics), -or from cosmology right down
through the human scale to the atomic.
At the smallest level of scale, of course, (and at the largest scale as well -EPR), the case for
hierarchy has broken down in this century. As an example, let me cite Penrose's "most optimistic"
view of quantum mechanics, (most optimistic for scientific realism, that is):
"I shall follow the more positive line which attributes objective physical reality to the
quantum description: the quantum state. .
"I have been taking the view that the 'objectively real' state of an individual particle is
indeed described by its wavefunction psi. It seems that many people find this a difficult
position to adhere to in a serious way. One reason for this appears to be that it involves our
regarding individual particles being spread out spatially, rather than always being
concentrated at single points. For a momentum state, this spread is at its most extreme,
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since psi is distributed equally all over the whole of space, (my emphasis),...It would seem
that we must indeed come to terms with this picture of a particle which can be spread out
over large regions of space, and which is likely to remain spread out until the next position
measurement is carried out...."
The particle -this smallest part of our "object"- is not included, (spatially, reductively), within the
spatiality of the atom or within the molecule -or even within the human scale object of which it is
the theoretical (and supposed material) foundation. Naturalism can no longer support, therefore, a
consistent hierarchy of scale! At the human level, of course, it is a very useful tool, and that is just
what I propose it is -constructed by evolution! Schematism, (and "Symbolic Forms" as well),
suggests other, non-scaled and non-hierarchical organizations -i.e. they support any other
efficacious organization. It is a simple matter of utility.
Naturalism's primitive substratum, (the primitives of mathematical physics), is deemed
unique and "true of" == "refers (isomorphically) to" ontology. It is Naturalism's epistemological
basis for a claim of reference.460 But under a functional logic, (i.e. a logic not based in the generic
concept), there is the possibility of alternative "axiom systems", (different functional logical
concepts/theories, -not as class abstractions from phenomena or as hierarchical spatial perspectives
into the phenomena, but as lines drawn across phenomena -as connective functional rules), and a
different sort of "reduction", (i.e. translation), exposing alternative utilities, (e.g. biology,
psychology, etc. -or alternative purely physical conceptions). So may we consider the new
possibility that the relationality of experience, (and experiment), can be entirely preserved under
varying (comprehensive) functional perspectives, no one of which stands as the canonical
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revelation of ontology/experience. The assertion of comprehensiveness for a given reducing
theory would not then imply that it would necessarily, therefore, be the sole and unique
organizational primitive -i.e. that would be the only one.
This is the sense of my extension of Cassirer's "symbolic forms". I argue, with Cassirer, for a
relativism of forms which organize the phenomena, but against reference. I do not argue for his
particular specification, (choices), of these forms, nor do I assert my own alternatives to these
forms, but I do argue for his general conclusion.
It is in Cassirer's sense of the organizational, rather than the referential relevance of theories
that I propose that the relations of ordinary Naturalism -and my own thesis as well- can be, (must
be), retained in a deeper realism. "Experience", our true primitive, (and, I have argued, the other
axiom of reason), is not the same as any particular organization of it. It is not identical with its
(legitimate but particular) characterization as "sense impressions" under the Naturalist form, for
instance. I have argued a (broadest -and truly relativistic) definition of "experience" as that which
remains invariant under all consistent and comprehensive worldviews.461
What must be preserved is the web of implication of experience in our world, but hierarchy
as such need not be maintained. A comprehensive theory, ("form"), e.g. Naturalism, stands as an
"axiom system" to generate the field of experience. But if other theories, (forms), and other
"axiom systems" are found, (and Quine definitely implies their existence), also comprehensive,
460 cf. Appendix E 461 But does "experience" itself absolutely, (i.e. metaphysically), refer to something else? My thesis proposes that it
does not. I propose, rather, that it is an organization of atomic, (and indeterminate), process. It is, therefore, real and ontic, but irreducible and non-referential.
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then the preference is no longer epistemological but utilitarian. Each, however, must fully preserve
"experience" -to include the whole body of past (and future) scientific experiment.462
I have proposed that our ordinary perceptual world -our innate and functional organic naive
realism- is such an organization itself, constructed by evolution, (as stated in relative -but
legitimate- Naturalist terms), for efficient viability. At the human scale, Naturalism is an extension
of that existing organization -i.e. of that which evolution has given us. But there is clearly no
paradox remaining in these statements in light of the prior discussion. My thesis is, therefore, self-
consistent and the epistemological dilemma is resolved.
462 This is the point on which I question, (but do not necessarily deny), Cassirer's suggestions of the particular
comprehensive "symbolic forms" -i.e. in that I believe that they must each embody the whole as past and future scientific experiment. In defense of his choice, however, that relationality of experiment need not necessarily be maintained as "central" to the organization of a particular form. That is, it need not lie close to its "axiomatic" base, but need only be maintained somewhere and somehow within the form as a whole. Thus biology could stand as such a "form" in Maturana's conception, for instance, wherein the experimental results of science would be maintained within third order structural coupling, for example. But how would science be retained in a mythical form, for instance? Or language? And yet he has touched something very powerful in both of these. That I am, as yet, unable to see the specific relevance of these suggestions does not convince me that they are, therefore, wrong! In the specific case of religion, for instance, however, I believe that Cassirer has misconstrued the problem. Let me make a counter suggestion: that religion, identified not with its ordinary practice, but with its incarnations in the religious mystics - exhibits an alternative biological form corresponding to the rational form suggested by Quine, i.e., one in which "ordinary objects" are no longer the organizing rationale. (cf. William James "Varieties of Religious Experience").
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My thesis is, I believe however, more than consistent. Even from a purely Naturalistic
perspective, I maintain that it is the only complete and consistent explanation yet offered of what it
is we have set out to understand -i.e. the whole of cognition! The problem of the "Cartesian
theatre", (sentiency), for instance, has heretofore either been trivialized and eliminated by ordinary
Naturalism, (leading to a sort of linguistic or materialistic "idealism"), or it has been referred, for
instance, to epiphenomenalism or emergence. But the latter are little more than an invocation of
magic, (they do not vivify the ghosts they summon).
On its own grounds, I believe my scientific thesis stands well vis a vis its competition -it is
biologically, psychologically, logically and teleologically cogent. It is, moreover, far more
compatible with the epistemology of modern physics than is any other alternative -it speaks the
same language. It "covers the territory", (of mind and mind-brain), for the first time and assumes
no "magic", (also for the first time).
But our "ordinary objects", (the objects of naive realism), need not be, (and in fact, are
not), preserved as metaphysical primitives -i.e. as necessary unities. Quine acknowledged the
possibility:
Quine Speaks to my Proposal
"One could even end up, though we ourselves shall not, by finding that the
smoothest and most adequate overall account of the world does not after all accord
existence to ordinary physical things.....Such eventual departures from Johnsonian
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usage463 could partake of the spirit of science and even of the evolutionary spirit of
ordinary language itself."464
This is exactly the case I have made. I argue that the "smoothest and most adequate overall
account of the world" does not, indeed, accord existence to ordinary physical things. My departure
from Johnsonian usage does "partake of the spirit of science and the evolutionary spirit of ordinary
language itself".
This concludes the epistemological argument. In the next chapter, I will complete my
solution of the mind-body problem with a statement of my third thesis which will supply the
"what", the "matter of mind". All the hard work has already been done, however, so the chapter
will be brief. The problem is not so hard; it was our presuppositions which made it seem so.
463 Johnson demonstrated the reality of a stone by kicking it! 464 W. V.O. Quine 1960, pps. 3-4
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Preface to Chapter 5, (the Final Step)
So where have we got to with our realism? Realism must accept or propose two basic
postulates as metaphysical, ontological postulates: the actual metaphysical/ontological existence of
externality and also the real metaphysical/ontological existence of experience. But for these two
postulates to have any meaning, there is a presupposition: the existence in that same sense –i.e. the
real metaphysical/ontological existence of some connection between the two. This is the existence
that Kant did not mention, but which is implicit in his writings. That interconnection, that
relationship between the two, is what I will call “interface”. That that particular existence, (of the
interface), must be described in context-free465 terms -that we cannot describe it from a particular
perspective -is the lesson of chapter 4. It is that abstract, that invariant concept of interface whose
existence we must also metaphysically posit as realists. Assuming, moreover, that it were
structured in the way that I have proposed under the concept of implicit definition, (and this is my
third hypothesis), then it supplies the actual reality and the metaphysical/ontological existence of
mind.
This is an abstract thesis, but it is necessarily abstract. It is the conclusion that I believe
realism must come to.
465 cf Van Fraassen
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Chapter 5: What? The Substance of Mind
"We can still distinguish science from scientism, a view in which science, which allows
us so admirably to find our way around in the world, is elevated (?) to the status of
metaphysics. By metaphysics I mean here a position, reaching far beyond the ken of even
possible experience, on what there is, or on what the world is really like. Scientism is also
essentially negative; it denies reality to what it does not countenance. Its world is as chock-
full as an egg; it has room for nothing else. Commitment to the scientific enterprise does
not require this. If anyone adopts such a belief, he or she does it as a leap of faith. To
make such a leap does not make us ipso facto irrational; but we should be able to live in the
light of day, where our decisions are acknowledged and avowed as our own, and not
disguised as the compulsion of reason."466
Though I have argued against the "material" and the "substance" of Naturalism as
metaphysical existences, there is a deeper -and truly metaphysical- sense of substance that I do
wish to maintain. It is embodied in our, (and Kant's), minimal realist assumptions -in the axioms
of externality and of experience.
Though Cassirer argues for a broad range of symbolic forms, there is another form implicit
in his thesis, (roughly equivalent to the whole of the natural forms), -and innate in Kant's as well.
It is the metaphysical form, i.e. the whole of the metaphysical context of the problem itself. (It was
466 Bas Van Fraassen, Quantum Mechanics, p.17
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as a "Prolegomena to any Future Metaphysics" that Kant himself characterized his work, after all.)
This metaphysical form is the proper context for any conception of cognition, (and realism), but,
precisely because of Kant, it is necessarily severely restricted and analytic.
Inside of the form of metaphysics, (wherein we are now framing the problem), we are
constrained by Kantian parameters -i.e. the fundamental, (rather than the historically limited),
parameters discussed in chapter 3. These abstract limits, the axioms of externality, and of
experience, and the relativity of perception to the (human) instrument whereby it is effected,
dictate a general, relativized and abstract solution to the problem.
Always implicit in Kant, however, was the assumption of some connection between our
cognition, and the reality which is perceived, (metaphysical reality), -and that connection was
assumed to be reflected in experience, ("intuition"). Always implicit in Kant is the relationship
between the absolute external existence which he affirms and the modifying, coupling relationship
of cognition itself. Kant's is very much a modern mathematical conception. He argues that we
cannot separate the facts of our "instrument", (our cognition), from that which it "measures",
(cognates). The relationship between that cognating entity and its object, however, is understood
in a very profound and sophisticated sense -very much in the sense of modern algebra. His
concept of intuition, (experience), is a relativistic one. The connection is seen as a limit concept -
as the most abstract possibility- conceived relativistically to "the X" of metaphysical reality.
Alternatively, we might today characterize this connection as the most abstract reinterpretation of
Maturana and Varela's "structural coupling", but removed from its strict Naturalistic
(metaphysical) formulation. I think the most natural characterization of it is, simply and abstractly,
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re.
"interface"! This interface, this connectivity, between cognator and that which is cognated, is
assumed, in fact, in any realist conception of reality, (most definitely to include Kant's itself). It is
implicit in materialism, in dualism ...; it is implicit in behaviorism, and identicism ..., in "memes"
and in neural process. I mean it to be the minimum intersection, (the limit), of all of these realist,
(i.e. non-idealist), possibilities. This minimum conception of interface is then, (by definition),
necessary and apodictic to any realist position. Realistically, it does, therefore, metaphysically
exist! This is the metaphysical reality that Kant does not name, but which is implicit in his, and
any other realist position. As a realist, I claim it therefore to truly metaphysically exist, and I call it
"substance". This is not, however, the "substance" of materialism, but an analytic conception -i.e.
it is exactly the metaphysically minimal necessity of realist cognition.467
That there is something more, some other "substance", some externality other than the
interface,468 is also apodictic to realism -it is presumed in the axiom of externality -and I confirm it
as well. Kant has stripped the latter of all knowable determinate form, (but not of existence),469
but it is the former with which I wish to concern myself he
467 There is an understandable demand here for a more precise definition, a more concrete characterization of this
"interface". But I think the demand, truly considered, is really for a metaphysical characterization of precisely the kind that Kant and Cassirer obviated. It is the essential and invariant -i.e. the relativistic and "context-free" component of all realist philosophies that I wish to isolate, and that is approached, legitimately and solely, as a limit concept. Mathematicians will best understand my meaning. It is the analytic and limiting essence, (i.e. invariant), of the connectivity of cognition in general that I define as "interface" and that I propose as apodictic to all realist philosophies and as itself metaphysically real.
468 Though real, matter, (external substance), itself is, for Kant, "substantia phaenomenon". 469 Cassirer's "Symbolic Forms" is an extension of the Kantian position, and relativizes experience. Or rather, it
relativizes the interpretation of experience. Experience itself is a primitive. We can describe it in various ways under the differing "forms", (e.g. sensuous impressions" under Naturalism), but ultimately it is a limit concept. (See Kant "limits" vs. "bounds"), -it is what remains invariant under all consistent interpretations, (forms). "Objects" are implicitly defined within the variant forms. Are there ontic objects, then, (i.e. ontic localizations)? We will never know!
Consider Kant:
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The Last Hurdle
There remains one last difficulty with my (Naturalist) hypothesis of Chapter 2. From the
standpoint of my original claim of a complete solution to the mind-body problem, "mind", (at the
stage of chapter 2 -and even at the stage of Chapter 4), remains conceivable only in a reductively
materialist, (alternatively: an organizational), sense. It remains only process and without
"awareness" except as the latter is itself considered reductively.
What is "mind" and where is it? How could it be? The answer is that it is! It must "be".
For it is the (apodictic and metaphysical) "substance" of the interface itself that I propose is the
substance of mind. The reality, the metaphysical presence of this interface is the immediate and
necessary consequence of the synthesis of our two realist fundamentals: externality and experience.
It is the relativistic equation between a cognitive entity and externality. This necessary
presumption of connective "substance" supplies the last remaining element for the complete
solution of the mind-body problem.
"Now, if I go farther and, for weighty reason, rank as mere appearances the remaining qualities of bodies also, which
are called primary (such as extension, place, and, in general, space, with all that which belongs to it (impenetrability or materiality), shape, etc.) -no one in the least can adduce the reason of its being inadmissible. As little as the man who admits colors not to be properties of the object in itself, but only as modifications of the sense of sight, should on that account be called an idealist, so little can my thesis be named idealistic merely because I find that more, nay, all the properties which constitute the intuition of a body [object] belong merely to its appearance." Kant, Prolegomena, P.37, his emphasis.
He goes on: "The existence of the thing”, (my emphasis), “that appears is thereby not destroyed, as in genuine idealism, but it is only shown that we cannot possibly know it”, (my emphasis), “by the senses as it is in itself."
I would modify Kant's last sentence to delete "of the thing". [To: "The existence that appears is thereby not destroyed, as in genuine idealism, but it is only shown that we cannot possibly know it by the senses as it is in itself."] If extension, place, space, impenetrability, materiality, shape are brought into question, (even cardinality in QM), then objects, as objects are also questioned. What remains are my two axioms: the Axiom of Externality and the Axiom of Experience. But these are limit concepts in a strict mathematical, (and Kantian), sense.
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The Third Hypothesis: a formal statement:
Given that the interface, (as just defined), metaphysically exists470 and given further that it
is structured as postulated in my first and second hypotheses, (and this is my third hypothesis), then
it internally and necessarily defines our objects and what they do -and they too exist! And, as
demonstrated by my arguments in Chapter 2, it knows them! All the problems of structure, all the
problems of logic have been dealt with in the previous hypotheses, and a plausible Naturalist
rationale is in place. All that remained was existence. It is the metaphysical existence of the
interface itself which supplies the reality, (the existence), of sentiency! Mind is the unified
concept,471 (the rule), of this interface. Under the combination of my three hypotheses, then, mind
becomes quickened, becomes aware, becomes "live". We do know, we are aware, we are real.472
What we are sentient and aware about however, is not metaphysical externality. Rather, it is the
metaphorical organization of primitive process with which we deal.
470 which I have demonstrated that we must, as realists, assume
471 i.e. the unified constitutive concept 472 There is a wonderful, (and I think very relevant), passage in Cassirer's "Spirit and Life" that I ran across many years
ago:
"For man it follows that he must traverse his appointed orbit, in order at the end of his road to find his way back again to its beginning. That is the fate imposed by our 'circular world'. 'Paradise is bolted fast, and the cherub far behind us; we must travel around the world and see whether perchance an entrance can be found somewhere from the rear.'" "Spirit and Life", P.858 in "The Philosophy of Ernst Cassirer", Tudor, 1958
Let me paraphrase it: Man has been expelled from the eastern gate of Eden, (from simplistic connection to his naive world), by his acquisition of knowledge, (and its innate skepticism). The gate is now guarded by an angel with a flaming sword, (the consequence of reason), preventing his return. Forced to face the harsh and bitter world outside, he has embarked to walk clear round the world, (in his acquisition of knowledge), and hopes to find a gate unguarded on the other side so that he may re-enter paradise!" Man was shut off from simple contact with reality when he first questioned that contact. Cassirer asserts that the whole of the human project of knowledge was to return to the simplicity, (in the good sense of the word), from whence we came! I feel we are very close to that gate. Rationality and perception, mind and reality are no longer antithetical. (Cassirer's quotation is from Kleist's "The Marionette Theatre".)
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The problem was that the "egg" of Naturalist metaphysics, (as characterized by Van
Fraassen), was just too full and left no room for anything else. Or, rather, we were ignoring the
shell!
The difficulty of the substance of mind was the result of an illegitimate metaphysical
dogmatism, (presumed, incorrectly, as innate to Naturalism) -by its asserting more than we can
ever know. It asserted relative organizations -i.e. its "material objects" as absolute referents to
absolute material reality and thereby claimed completeness, (and exhaustion), of reference.
Nowhere in that domain, however, could specifically sentient mind exist. It excluded the very
possibility of "mind" in our ordinary sense of it.
The problem is resolved, however, by reducing our metaphysical presumptions to the
minimal -and legitimate- basis possible. That basis is the minimal and universal assumption of
ontic interface, (conceived in its most abstract mathematical sense), which proves to supply the
"matter" of mind sufficient in itself.473
Philosophical Implications
I think my thesis opens a new perspective on the classical dilemma of idealism versus
materialism, i.e., the question of the primacy of the mind versus the primacy of the physical world.
My metaphysical answer comes down, therefore, on the side of the mind, relativizing Naturalism.
In that sense my answer is "idealistic". But, (big "but"), "mind", as I redefine and reduce it, (in a
very real sense of the word "reduction"), is specifically a metaphysical interface. This interface is
real, that is to say, "substantive" (=="physical"). I do not say, (nor do I believe), that it is all that is
473 It is curious to me that materialists always seem to be deriding metaphysics. They are its strongest proponents.
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real but rather that it is innately impossible to know the unmediated nature of that something more.
This latter, of course, is just a restatement of Kant's essential conclusion.
That interface, as I propose it, is not the ephemeral and capricious "mind" of classical
speculation. It is not "spirit" as opposed to "material". It is specifically and scientifically interface.
Mind is purely "physical" in that sense -i.e., it is a metaphysical thing and no more. It is part of the
world -it is real, but it is not separate or "purely personal". This is what we know exists. That
more exists, we must also accept as realists. But, once again, specifically as realists we must
accept the interface as well. The interface is the only assumption needed for mind, and that is all, I
propose, that mind is.
Given the reality of a system of axiomatic relationality in the sense of my first two theses,
then "mind" becomes "live" in all the senses we normally demand of it. The mind-body problem is
solved in all its aspects. I think I have "cracked the code" of mind and brain.1 It is a strange and
disturbing one, I admit, but I believe it is, overall, the most plausible alternative on the table.
This concludes the presentation of the core of my overall thesis. The next chapter is a brief
statement of conclusions and consequences, and the last chapter serves as an epilogue. Appendix F
will deal briefly with Dennett's "color phi" and briefly foreshadow a future extension of my model.
Dennett supplies the clue. (The "Afterward: Lakoff / Edelman" is a restatement and further
clarification of the logical problem.)
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Chapter 6: Conclusions and Opinions
Scientific Conclusions:
I consider my most important result, (though you may think this strange), the Naturalist
one: i.e. that "mind" is the (reduced) "concept" of the brain!474 I hold that it is both legitimate and
important within the (reinterpreted) Naturalist framework and leads to definite and practical
empiric lines of research. That Naturalism is itself thereby relativized detracts neither from its
utility nor from its importance -no more than did the introduction of relativity or indeterminacy
into modern physics lessen its viability or importance. Rather, it produced profound and
immediate practical results. Naive realism is a biological and behavioral algorithm superb for
normal life, and Naturalism, its natural extrapolation, is valuable beyond measure -as well it should
be under my hypotheses. It is to the ultimate empirical results, (or not), of my thesis, however and
finally, that I will equate its ultimate value.
Devil's Advocate:
Though I have argued against our knowledge of externality, and for a schematic
organization of process, could not our external, metaphysical world still be like the objects of our
cognition. Of course it could! The possibility is suggested in my conception of interface. Since it
implicitly defines our objects within, conceivably it might, as well, define the "objects" of external
reality without! But this is a profession of extreme faith, and not of science.475
474 Alternatively, it is the brain's rule of ontogenic coupling 475 It is a question of bounds and limits again. Or, more simply, of the distinction between an upper bound and a least
upper bound. Reality clearly sets definite upper bounds to (evolutionary) development, but does it convey to the
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"If anyone adopts such a belief, he or she does it as a leap of faith. To make such a leap
does not make us ipso facto irrational; but we should be able to live in the light of day,
where our decisions are acknowledged and avowed as our own, and not disguised as the
compulsion of reason."476
I, however, do not choose to, (nor do I have to), make such a leap of faith. I propose that
what we have is a viable, (and truly real!), working model that simply "does the job", i.e. it is at
least compatible, and probably beneficial477 vis a vis absolute externality.
Come, isn't it the height of arrogance to presume, (under the Naturalist presumption), that
this race of apes, barely able to scribble for a mere few thousand years, has been able to divine the
nature of absolute reality? How much more probable is it not, (changing the metaphor), that we
are merely constructing "a hive"?478
organism a least upper bound, (which would be defining)? The former encompasses (raw) "structural coupling", but the latter would be necessary for "congruent structural coupling". It is an assumption equivalent to the "parallel postulate", you see!
476 Bas Van Fraassen, Quantum Mechanics, p.17 477 "beneficial" is itself a synthetic a priori perspective 478 Why do we think we know even the boundaries of all the possible solutions to all of the problems of reality?
Whence comes our arrogance that we feel we have solved the ultimate problems of the universe and of our existence in it?
Is it not more believable, (under the very Naturalist assumption), that we have merely expressed our own particular mode of existence, -that human civilization, like a swarm of bees, has simply built a hive? What is this logic we are so sure of? Ultimately, biologically, it is an expression of the "structural coupling" of the race with its environment. But the invariants of that coupling are derived from the structure of the uniquely human brain. Other brains, other modes of coupling almost certainly would embody another protologic. Ordinary logic, (i.e. "associationist" logic -after Dreyfus' term), denies its biological roots. It believes it has touched eternity and verity. How? Why? What teleological mystery does it hide? When we thought that man was created by God in his image and that God gave us this open channel to truth, then there was a meaningful rationale for such a view. But when man became, purely and simply, a material animal, derived mechanistically and randomly by material combination, then this mechanistic process lost all justification as correlating with anything other than its own mechanical necessities. But it works! How and why? Perhaps that is itself the answer. It is an operative process that works in the world in which it lives! This provides no guarantee of its ontological posits at all however -it is an operative process that works -and that's all!
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So Why Bother?
But if this is the ultimate answer, if this "ontic indeterminism" is the conclusion we must
reach, what is the point of it all? Near the conclusion of Chapter 2, I admitted the (intuitive)
difficulties of my thesis. But modern physics has much the same difficulty -its picture of reality,
though intensely beautiful and exotic, offends those same normal sensibilities. The (why bother)
answer for physics is that that very picture produces desirable, powerful, and practical results right
at the human, (naive), scale, and which we cannot deny. The transistor, nuclear power, working
telephones and radios, ... are necessary and practical consequences of that very theory -and they
would be impossible without it. I propose that this will be very much the case for my conception.
Though admittedly offensive to our (naive) realist sensibilities, if it is correct479 it will lay the
theoretical ground necessary for the quantum advances in neuroscience, for instance, which will
finally and specifically, (rather than generally and destructively), cure the terrible aberrations of
mental illness. But the mind-brain puzzle has far larger implications than that. It deals with the
problem of man in all its aspects. It deals with all his social, ethical and artistic parts.480 The final
implications must not be underestimated.
This is the "why bother". Even offensive theories can yield useful and powerful results,
necessary to man! The final test, the final judgment therefore, must be made on results. But,
before results can be obtained, it is necessary, first, to entertain the possibility.
479 and I do not dogmatically assert that it is. The future of science must answer this question. 480 I think it would be a real mistake to discount the possibility of real, purely physical implications from my thesis. In
the transition beyond "objects", wholly new degrees of freedom may be possible for physics itself.
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My reconception of fundamentals, though radical, is absolutely consistent with the historical
progress of science -of physics, biology, mathematics and logic. It solves the biological and the
philosophical problems inherent in the mind-body problem, and exorcises the "homunculus" once
and for all. It provides an Archimedean fulcrum to overturn our naive realistic presuppositions,
(inherited by "scientific realism"), and let us get on to the serious business of creating a science of
mind and brain. It provides a viable context in which I believe workable theories are now, finally,
possible.
No substantial progress will ever be made in dealing with "mind", or in the treatment of its
terrible, destructive aberrations, (both individual and societal), -until the mind-body problem itself
is solved and workable tools are developed. To deal with the mind, we must deal with its "objects"
and the relations between them. To deal with the brain, we must deal with its process. To
constructively and specifically481 affect the processes of mind482 via the brain, the relationship
between the two must be understood!
The simplistic orientations of naive realism, ("though grown up and sporting a beard" -to
steal a phrase), just will not stand any longer. Great issues, to include the most profound social,
ethical and spiritual aspirations of the race, depend upon the resolution of this problem -and upon
its consequent, the establishment of a mature and viable neuroscience. There is too much pain in
our world, and too much need, -dependant upon real solutions to these problems, to cling to the
playgrounds of our intellectual youth.
481 i.e. at the "fine-grained" level of mind 482 or to gain reflective insights on them
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How do we live?
So, (given my thesis), what is the point? Do we exist, therefore merely contemplating our
navels, lost in the "ontic indeterminism" of metaphysics? No. I, for one, rarely even think about
metaphysics, but love and feel pain, pay attention to passing cars, and generally live my life as you,
(or any dogmatic Naturalist), would. I practice Descartes' interim life strategy of normalcy, (by
necessity), and pretty much live my life as I always have.1 I speak the language of Naturalism
because it is good language and because it is, well ..."natural"!
When I choose to consider the connection however, I know that by following my inbuilt
model, (and extending it), I am in harmony with that nameless externality. I do not use my model,
you see, I live in it!
My "Act of Faith":
But what do I, personally and as my act of faith, believe? (I, after all, get to have beliefs as
well!) Though I do not believe in the necessity of spatially and temporally separate metaphysical
objects, (consistent, certainly, with the views of modern physics), nor in the metaphysical "aether"
in which they are still conceived(!), I, (personally), believe in the metaphysical existence of other
minds!483 (That there is still more, -an absolute externality, "phaenomena substantia"- I also
believe.) But those other minds, specifically as minds, (as per my second thesis), are all precisely
products of implicit definition, variations on, (values of), a single universal function. They are, I
believe therefore, continuous variations of me. We are all, I believe consequently, more than
brothers, but "states" of the same being. "You" are "me" in a different "place", (state) -there is no
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necessary spatial or temporal separation between us, i.e. there is no necessary metaphysical
"aether" between us!
But somebody already said all that, didn't they?
"'I tell you the truth, whatever you did for one of the least of these brothers of mine, you did
for me. ... whatever you did not do for one of the least of these, you did not do for me.'"
(Mat. 25:40-45)
483 I also believe in a continuity of sentiency, at least with the higher animals -for reasons which should be perfectly
obvious by now. Just where the "cutoff point" may be, I would not be presumptuous enough to speculate.
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Chapter 7: Epilogue
How do you convince a bird, living in a dying tree, to leave its accustomed perch, its
familiar nest, and go to inhabit another. You may praise the new view, and describe fantastic
horizons invisible to the old. You may catalogue the prospects of juicy worms, temperate climes,
and soaring flights through inestimable thermals. But the bird, clutching stubbornly to its worn
branch, may only envision the loss of its well-defined routines. The path to an easy patch of straw
for its nest or a worm-rich meadow might become convoluted or even impossible because of
distance or predators! It cannot even envision the possibilities of the new place unless it is willing
to chance an exploratory flight. Its world is simple and uncomplicated -or at least the
complications are well known. This has been my problem here. I believe the mind-body problem
is the most difficult in the history of the human intellect. It hinges on the problem of cognition -
and that is the problem of everything! Its solution, I feel, involves a brand new "roost" -a new
intellectual perspective with horizons different but incomparably broader than before.
Admittedly however, though it proffers "sunsets of unmatched vividness", and "new and
fertile meadows", it involves a definite risk as well. It may turn out, after all, that the "nest" I
propose lies over fallow fields and iron-hard soil where no "worms" might survive! You are right,
therefore, to be conservative and cautious in the selection of your ultimate habitat, but you are
wrong if you are timid in your survey -your future may depend on it. I invite you to conquer your
fear of vertigo and try your wings in an exploratory flight to this very different tree of knowledge.
"Safe (that is, probable) hypotheses are a dime a dozen, and the safest are
logical truths. If what science is seeking is primarily a body of certain truths, it
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should stick to spinning out logical theorems. The trouble with such safety,
however, is that it doesn't get us anywhere."484
There are really just two schools of thought on the mind-body problem. One holds that the
relationship between the mind and the brain is inherently unsolvable. It holds that the natures of
mind and brain are (1) either absolutely incommensurate, (are of different kinds), or (2) the
problem is beyond intrinsic limitations on human understanding. The other school holds that the
relationship is perfectly direct and unproblematic, albeit totally one-sided and exceedingly
complex. The first offers no practical hope whatsoever for the dysfunctions of the human mind,
but the latter destroys the reason for caring in the first place. It's solution is that we are all
automatons, "zombies"! Mind, in its ordinary sense, is a fantasy, a "figment" of the imagination!
What, then, does it matter whether another automaton makes "pain" noises rather than "happy"
noises? Less delicately, what possible objection could there be to the Dachau "fetus series" or to
the atrocities in Bosnia? The solutions offered by both schools, moreover, are counterintuitive,
limit the scope of empirical investigation and involve significant logical difficulties. I have offered
a new alternative capable of resolving the whole of the problem and commensurate with the whole
of the human spirit.
My thesis opens the further and distinct possibility of an actual "physics", i.e. a
mathematical and scientific mechanics of mind and brain, as it defines, for the first time, an
appropriate context in which it could be formulated. Just as the SUPERB485 486 theories of
Newton, Maxwell, and Einstein were literally unthinkable in the cosmological context of Ptolemy
or in the physical (and gravitational) context of Aristotle, neither can the SUPERB theories which
must eventually encompass the mind and the brain arise without the context -and the continuum -
which will make them possible.
I believe the mind-body problem is the most important problem in the history of our
(human) species. Subsuming both science and ethics, it will ultimately determine our future as a
civilization. Though this sounds overly dramatic and even downright pompous, reflection shows
that it is not. Answers to what we are, and why we are will determine what we can do and what we
will do.487 Profound belief determines actual practice! The bounds of future civilization will be
set by our ultimate understanding of our own being. This problem demands, therefore, the greate
latitude and the greatest tolerance to radical ideas. It is too important to be treated otherwise.
It has been said of scientists, (and it certainly applies to philosophers of mind as well), that
they live, alternately, in two disjoint worlds. They do not take their reality home with them. The
reality they believe as professionals is not the reality they believe when they dodge cars on the
freeway or make love. None will put out a saucer of milk for Schrödinger’s cat.
Is Dennett prepared during his self-stimulating monologue, (whilst sitting in his rocker and
listening to Vivaldi), to accept himself solely as a "center of narrative gravity", solely as the
cumulative product of temporally and spatially separate and discrete processes, (the "Final Edition"
published on his "Demonic Press"), lacking "figment" or "qualia"? I, personally, am perhaps
willing to accept him as such, but I am certainly not willing to accept me as such.
487 Consider Nazism, as just one recent example.
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Like Dennett, I have been wrestling with this problem for over 35 years. I came to it not
from philosophical curiosity or "epistemic hunger", but as a result of personal tragedy -the loss of a
loved one, (my mother), to the maw of mental illness. Frustration -and anger- at the inability of
science to help her and a survey of the dismal "mythological",488 (Freudian and quasi-Freudian),
state of then-current thinking on the subject489 caused me to begin a personal and private search, of
necessity based in logical and abstract theoretical criteria -but aimed at an empiric goal.490
Emerging from my "cave", (of contemplation), just a few years ago, I was surprised and
fascinated by the illuminating and brilliant bonfires which had been lit on the plains of biology and
philosophy. Since then, with more than a little trepidation, I have been scouting each of the major
encampments so lit. I have concluded that I have something still new and novel to say. I think that
my torch, crafted as much by art as by science, carries a unique Promethean flame. I think I have
solved the essence of the problem of mind-brain. Now I, like Benjamin Franklin, Rousseau's
"backwoods philosopher", stand before the sophisticates of Paris in my bearskin cap.491
Though my thesis admittedly opens new and fundamental problems -more, perhaps, even
than it solves, that very fact unlocks whole new worlds of possibility for scientific advance and in
itself constitutes an argument for serious consideration. If, in fact, we have already "arrived", if
you are satisfied that we do, in fact, already possess in rough form a valid picture of the whole of
488 echoing Einstein's characterization of Freudianism 489 and their damnable and blatant arrogance about it! 490 Since then, my perspectives have widened. I have come to believe that the tragedies of mental illness are echoed in
the tragedies of the human social condition -the wars, the hatred, the arrogance, the exploitation of man by his fellow man, these are other aspects of the same basic problem. Under the perspective of dogmatic Naturalism, these are normal, and therefore necessary. I do not believe they are.
491 Van Doren, 1938
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our reality, then the very poverty of that reality as regards the human condition must make you
very sad -and kindle the hope that something more is possible. I think it is!
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Appendix A, (Information and Representation)
(The Odds Against Representation)
(This appendix is an integral part of the discussion of Chapter 1, but I felt it was too long
for a footnote, and would otherwise have interrupted the flow.)
"Information", (and "representation" in whatever form), as a rationale for the evolution of
the brain, just isn't a viable hypothesis. The brain, I argue, is an organ of (ontogenic) process -of
response, not of "information".
A Little Combinatorial Argument:
A measure of the complexity of the reality with which an organism must deal is the organism's
context of information about it. But information is grounded in context. Consider an individual
(informational) sensor. It is not enough for a genetic accident simply to provide that sensor.
Somehow it must furnish evolutionary advantage and differentially link that sensor to response
through its functioning. To be useful as "information", (and retained under the evolutionary
process), it must usable over the range of its possibilities. It must provide differential response
over that range.
Each sensor, (as an "informational" sensor), must be minimally binary by definition. To be useful
as information, (and retained on evolutionary grounds), it must have been utilized or at least
connected in both of its possible states. Two sensors -as information, it seems- would have to have
been utilized in all four of their possible combined states. But is this true? No, perhaps they might
have been used or connected individually, (and retained). But then they would not yield combined
information-i.e. they would not be mutually relevant. Even so, each individual sensor is an
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evolutionary mutation and each had to be connected to two paths. The evolutionary "work"
performed for the two would be 4 units!
Alternatively, suppose evolution simply proliferated sensors hugely and then sampled the
combined array under a "Monte Carlo" strategy. Would this work? I think it might, but it would
not be "information". It would be response instead! Information necessarily embodies context.
When we sample a voting population, for instance, we know what it is we are dealing with, (i.e. the
context of the sample). It is a predictable population: Democrat, Republican, Independent, No vote
cast. Organisms, or at least primitive organisms, contrarily cannot know the context of their
sample beforehand. To be just a little bit cute, organisms are not capable of a "Monte Carlo"
strategy. The only comparable strategy of which they are capable would be a "Russian Roulette"
strategy492 -not a particularly good tactic.
The only context, (the possible sensory array states),493 in which reality could have meaning as
information for human organisms is of the magnitude: 2 to the power of 107, the latter being
Maturana's estimate of total human sensory receptors. 494 Taking each of the 10,000,000 human
sensory cells as a minimally binary input device, their informational potential -the context within
which information would be received- would be 210,000,000 . Converting the base, this is:
=103,010,290
492 e.g. sticking pseudopods into flames -"Monte-Carlo-ing" its way through life! Note: The “monte carlo” strategy
was suggested as an answer to the dilemma I propose. 493 the set of all combinations of value input from the receptors 494 Maturana, 1987, estimates that there are 107 human sensory cells.
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This is a staggering number! The number of all the subatomic particles in the entire known
universe,495 multiplied by the number of seconds in the 4 billion years of evolutionary history is,
by comparison, far less than 10102. But the latter number, contrarily, may be considered as a gross
upper bound to evolutionary possibility!
A Simple Limiting Argument:
Maximal, (limiting), assumptions:
a. From the beginning of evolutionary history there were always less organisms
than subatomic particles in the known universe496 (i.e. less than 1084)497
b. Every organism mutated once every second for this four billion years498 ( 4
billion times 365 times 24 times 60 times 60 = 4 x 109 x 3.1536000 x 107 < 1.3
x 1016 < 1017
495 T-7 , (1084) is far greater "than there are subatomic particles in the entire known universe"! Asimov, 1977, P.58 496 Instead of trying to approximate the possible organisms at any given time, (I started with a Fibonacci series, but
abandoned it to a simpler procedure), it suffices to substitute a number greater than the total number of subatomic particles in the universe -surely greater than the required number- for every term. This generates a (gross) upper limit for the series.
497 Asimov, 1977 498498 If you won't accept this assumption of the mutations per second, multiply it by a few thousands, -or millions, -or
even trillions; you are only adding to the final exponent -at most a few tens. You could actually raise it to 1010,188 times per second without affecting even the literal statement of my conclusions. I suspect that long before you got to this huge number, however, that you would be stopped by the ghosts of Planck and Heisenberg! Surely complementarity suggests that there is a lower limit to the relationship between causality, mass, space and time which can have measurable effects -i.e. "information"!
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c. Every single mutation was beneficial
d. Not even a single (beneficial) mutation was lost
e. All mutations were ultimately (somehow) summed into one organism
Computation:
1084 x 1017 = 10101
Conclusion: the number of total (beneficial) mutations for the organism named in "e" is less
than
10102 499
The Argument:
Assuming a standard bitwise, (i.e. digital), theory of information, this simple argument
demonstrates a discrepancy of more than "just a few" (!) orders-of-magnitude between
informational possibility and evolution's ability to incrementally embody any significant portion of
it in an internal representative model. Even if every single mutation were model defining, it is a 3
To get an idea of the scale involved here, listen to Asimov on the disparity in size between a
proton and the whole universe: "We find that the number of protons it takes to fill the observable
universe is 4.6 X 10124. " 500 That is, the ratio of the volume of a proton to the volume of the
whole universe is 1 / 4.6 X 10124 ! (disparity > 1 / 10124 ) But this is a lesser disparity, (much
lesser), than evolution's capacity to flesh out humanity's supposed informational capacity. The
huge difference in Asimov's striking example isn't even sufficient to so much as dent the three
millions exponent.501
Why so great a gap between theory and pragmatic potential? How could "representation" be
effected?
Think about simple digital models. Consider just the three "idiot lights" on the dashboard of
my decrepit old truck as a primitive instance. All eight of its possible states are relevant to
response and, considered as an "information model", it must account for each of them. OFF-OFF-
OFF is significant -and allows me carefree driving- only in a context of possibility. In fact one of
them, (the oil light), is non-functional and not "information" at all. This simple system, in
consequence, does not qualify as a representative model. That part of it that does qualify as
information, (insofar as it is "information"), requires an accounting for its context of possibility.
500 Asimov, 1977 p.226 501 Envision a celestial turreted microscope. The lowest power is only capable of resolving objects as big as the whole
universe. Progressively, the next objective lens is capable of resolving objects as small as a proton. On this "God's-eye" microscope, there would have to be 24,276 objective lenses on the turret, each with an increase in resolution comparable to that between the first two!
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The hypothesis of an internal representative model as the rationale for the sensory system
presumes an incremental evolutionary correlation to its context of possibility. Evolution would
have had the problem of progressively correlating a model with each, (or some significant portion),
of the possibilities of the sensory array -and with potential response as well.
But evolution had less than 10102 502 chances to achieve this correlation. The most optimistic
correlation is 10102 instances,503 and the ratio of model correlation to possible sensory states is
10102 / 103,010,298 < 1 / 103,000,000 !
Even if the model itself were taken as an edifice of (107) actual internal binary bits, (paralleling the
sensory array), this would only regress the problem. Evolution still would have the problem of
incrementally correlating alternative model states with potential response and the numbers would
still stand. The odds of a "designed", or even a connected response would still be less than 1 /
103,000,000 -which is as close to zero as I care to consider!504 It is less, (much less), than the ratio of
the size of a proton to the size of the entire universe. Its utilization as "information" would still
require an accounting for -and an incremental evolutionary correlation to- its context of possibility.
Contrarily, taking my two proposed, (and grossly exaggerated), upper bounds for mutational
possibility, 10102 and 1010290 respectively, the same informational possibility could be embodied in
just 339 or 34,162 binary receptors respectively!505 Why so many sensory possibilities?
502 alternatively, 1010,290 503 alternatively, 1010,290 504 Alternatively, we would have to assume that individual evolutionary mutations could each (accidentally) correlate
information to model at a scale of ten to the power of three millions! 505 2339 = 10102 and 234,162 = 1010,290
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The argument applies equally to the possibility of even an isomorphic parallelism of response,
("congruent structural coupling"), as Maturana and Varela have proposed moreover, (as
distinguished from the case of an internal, representative model). That assumption still requires a
correlation to sensory input! (This is the only "trigger" that anyone has postulated.) The
(maximum) ratio of "designed" response, (and parallelism), to possible sensory input is less than 1
/ 103,000,000!
In short, we simply have too many sensors to support the "information" scenario -way too many!
There are "10" -with three million zeros after it(!) -times-too-many sensory possibilities for
evolution to have done anything with in the entire history of the universe! Conversely it is quite
clear that the entire future of the universe, (assuming a finite model), would be insufficient to dent
it either. Shall we talk "parsimony"? Objective reality is a bound to the evolution of organisms, it
is not a limit which can be matched or paralleled.
Paul Churchland has argued that if each synapse is capable of just 10 distinct states, then the brain
is capable of 10 to the power of one hundred trillion, (=10100,000,000,000,000), distinct states. This
number is impressive and considerably larger than the one I am considering, it is true, but it does
not refer to the possibility of acquisition of information, (specifically as information), from the
environment nor to the possibility of evolutionary correlation to beneficial action -i.e. utilization.
Churchland's number, therefore, only amplifies the discrepancy and the argument I have made!
It is evolutionarily plausible, certainly, to consider 10,000,000 sensory inputs as triggers of
process. But it is not evolutionarily plausible to think of them as environmentally determinate -i.e.
as inputs of information- as this immediately escalates the evolutionary problem exponentially -i.e.
to 210,000,000, (minimally)! Exponents are awesome things.
216
"Information" and "representation" in whatever form just isn't a viable rationale for the evolution
of the brain. I argue that the brain is an organ of ontogenic process. It is an organ of response, not
of "information". The function of that organ is to organize primitive biologic process; it is not to
represent its surroundings. Its job is adequate response, not knowingful information. Between
knowing and adequacy is a wide gulf. Evolution demands that an organisms' performance be
adequate. Nowhere in the physical or evolutionary rationale is there a place for "knowing" save by
"miracle".
Objective reality is a bound to the evolution of organisms; it is not a limit which can be
matched or paralleled.506 [View a simple graphic] [Return to Chapter 1]
506 An objection was made to this argument, (Appendix A), by a mathematician, (an anonymous referee), who
invoked a "monte carlo" perspective. An extremely limited random sampling, he argued, is sufficient to sample a huge field of data. The problem I see with his argument is that it presumes a pre-existing context within which to orient and evaluate such a sampling. It is the preexistence of that context which allows such a sampling to be meaningful. But how did evolution acquire such a context -the context of information? It is the definition of the context itself which is exponential and to which my argument is entirely relevant.
We, as organisms, do not begin with a given, a priori context within which to plan and take advantage of such a "monte carlo" strategy at the level of my argument. It is the assumption of that context itself which, I argue, is petitio principii.
217
Appendix B, (Isomorphism and Representation)
(An amplification of the discussion of Chapter 3) 507
Early on in their book, Maturana and Varela508 emphasize a seemingly trite but profoundly
pertinent point: "everything said is said by someone".509 There is an important and deeper
corollary: any discussion will always take place inside of a model, i.e. a context. For the mind-
body problem that model may be "physical", "mental", "behavioral", "linguistic" or some new
alternative, but there will always be some model. We are locked, i.e. closed, inside a "magic
circle", to use Cassirer's term.
When we demand a correlation between objective reality and the brain, what we are really
asking for is a correlation between "the brain", as an entity within our human model, and our
"objects" and their system of law as further entities of that same model!510 Within this context
however, "isomorphism" is a legitimate demand -founded on needs of internal consistency of the
model. There must, therefore, be some isomorphism, (i.e. an automorphism), between the brain
and the rest of our (human) model of reality. "Isomorphism", however, is a broader concept than
Naturalists' use of it.
Technically, two domains are "isomorphic" to each other if a one-to-one correspondence
can be specified between them which preserves some (possibly different) operation or operations
507 This discussion really belongs in the body of the discussion from which you were referred. Its necessary length,
however, would have disturbed the flow of argument, and a four page footnote would have been unconscionable, so I have placed it here.
508 Maturana and Varela, 1987 509 This is an assertion of closure.
510 I will discuss an ontic correlation presently.
218
internal to each of them.511 But the mathematical concept is more general than the isomorphism
between integral domains, (e.g. the whole numbers), or between ordered fields, (e.g. the rational
numbers), for example. This kind of isomorphism supplies the model for the Naturalist
conception, relating "points" to "points", "betweens" to "betweens" or "things" to "things". It
provides the rationale of hierarchical reduction as well. The mathematical concept has more
profound possibilities, however, residing in its group-theoretic usage. This "isomorphism" can
relate entirely different contexts!
Consider the isomorphism between J3, the additive group of integers modulo 3, and the
group of rigid rotations512 of an equilateral triangle onto itself as a simple example. This is a
correlation between the "objects", ['0', '1', '2'], and a group of transformations, each of the latter
mapping an infinite domain onto itself. It relates, in strict isomorphism, a domain of "things" to a
domain of continuous mathematical functions!513 It illustrates a very different and, I propose, a
more appropriate model for the kind of correspondence between "the brain" and "objective reality".
Consider further, and beyond this primitive example, correspondences between "things" of
this sort and projective transformations, or topological ones. Finally, consider correspondences
between "things" and transformations that go beyond topology and onto abstract sets -i.e. consider
transformations in their most abstract sense:
511 By definition, if, given a set of "objects" "O", (o1,o2,o3...), with an operation "*" between them, and a set of "objects"
"Z", (z1,z2,z3...), with an operation "#" between them, there exists a one-to-one correspondence "&" between the "o's" and the "z's" which preserves their operationality, (i.e. such that &[oi * oj] = &[oi] # &[oj] ), then they are said to be isomorphic under & as regards * and #.
512 the rotational symmetries 513 This is not strictly true. In this example, the latter have, of course, three points of discontinuity.
219
"Generally speaking, those one-one transformations of any set of elements which preserve
any given property or properties", [phenomenal invariants?], "of these elements form a
group. Felix Klein (Erlanger program, 1872) has eloquently described how the different
branches of geometry can be regarded as the study of those properties of suitable spaces
which are preserved under appropriate groups of transformations. Thus Euclidean
geometry deals with those properties of space preserved under all isometries, and topology
with those which are preserved under all homeomorphisms. Similarly, 'projective' and
affine' geometry deals with the properties which are preserved under the 'projective' and
affine' groups..." (Birkhoff and Mac Lane, "Modern Algebra", p. 125)
But the case of transformations is larger than "spaces":
"The algebra of symmetry can be extended to one-one transformations of any set of
elements whatever. Although it is often suggestive to think of the set as a 'space' ... and of
its elements as 'points', this picture does not affect the formal algebra." (ibid P.119, my
emphasis).
Certainly the brain is a transformation when considered either on the level of behavioral
response, (input-output), or on the level of fine-grained neural process. I suggest that the "objects"
of the brain, (mind), are transformations coordinating distributed response. I suggest that these are
the "objects of effective action"514 named by Maturana and Varela and that they are (group-
514 i.e. the only "objects" they will allow for the brain
220
theoretic) isomorphic to the other, (i.e. "objective") "objects" of our self-same human model! I
suggest that it is in this sense of "isomorphism" that they map to the "objective world", (of our
model).
The specifically metaphysical question, (as opposed to the question of the internal
relationality of the model itself), is another issue. "Structural coupling", (Maturana, 1987) -
appropriate relationality- provides the key. It requires that the relationship of an organism to its
environment is one of (beneficial) process and not of information. Though that correlation is
certainly opportunistic and necessary, it is a long "logical leap" from this to being sufficient, -to
capture. It does not, therefore, imply a functional parallelism, (i.e. an isomorphism), but a causal
indeterminacy. Though this conclusion enormously complicates our conceptions of "physical" or,
more correctly, of ontic- reality, I will argue that it provides the last link in the actual explication of
the mind-body problem.
There is a categorical difference between metaphysical reference and the internal,
model/model automorphisms of our logically closed human cognitive world. It is the latter which
constitute the problem of science. Here I have suggested a particular kind of automorphism
between the brain and its world.
221
Appendix C, (Mind-Body and Artificial Intelligence: Hubert Dreyfus)
The subject -and the problem- of artificial intelligence, (AI), has an obvious relevance to
my discussion. Here pragmatic demands of technology have forced a clarification of fundamental
issues -issues common to both the mind-machine and the mind-body problems.
Hubert Dreyfus carried on a running war with the adherents of artificial intelligence for
many years. While I differ with many of his conclusions, he has clarified several fundamental
problems and has exerted a meaningful influence on its subsequent development. In his book:
"What Computers Still Can't Do",515 he maintains that the continuing optimism by AI researchers,
(despite what he describes as their forty years pattern “of early successes and consistent long-term
failures”516), for the possibility of machine intelligence is based on their deep-seated conviction
that the human brain functions like a "general-purpose symbol-manipulating device", (a digital
computer). If this is true then, they presume, their ultimate success is assured.517 Dreyfus
maintains, however, that their conviction is based on four very questionable assumptions which he
asserts they have improperly accepted as axioms. These assumptions are relevant to the mind-
body problem as well. They limit the scope of imagination.
515 Dreyfus 1992
516 He makes a very strong case in the third edition.
517 If a biological machine can do it, so, presumably, can a silicon one!
222
(1) the biological assumption:
"A biological assumption that on some level of operation -usually supposed to be
that of neurons -the brain processes information in discrete operations by way of
some biological equivalent of on/off switches"518
(2) the psychological assumption:
"A psychological assumption that the mind can be viewed as a device operating on bits
of information according to formal rules. Thus, in psychology, the computer serves as a
model of the mind as conceived of by empiricists such as Hume (with the bits as atomic
impressions) and idealists such as Kant (with the program providing the rules). Both
empiricists and idealists have prepared the ground for this model of thinking as data
processing -a third-person process in which the involvement of the 'processor' plays no
essential role."519
(3) the epistemological assumption:
"An epistemological assumption that all knowledge can be formalized, that is, that
whatever can be understood can be expressed in terms of logical relations, more exactly in
518 op cit P.156
519 ibid
223
terms of Boolean functions, the logical calculus which governs the way the bits are related
according to rules."520
and,
(4) the ontological assumption:
"Finally, since all information fed into digital computers must be in bits, the computer
model of the mind presupposes that all relevant information about the world, everything
essential to the production of intelligent behavior, must in principle be analyzable as a set
of situation-free determinate elements. This is the ontological assumption that what there
is, is a set of facts each logically independent of all the others.521”
Dreyfus raises serious doubts about the first assumption, based on the results of current
neurophysiology -neurons are no longer understood as simple binary switches, for instance. He
concludes a broader inquiry more strongly: "In fact, the difference between the 'strongly
interactive' nature of brain organization and the noninteractive character of machine organization
suggests that insofar as arguments from biology are relevant, the (biological) evidence is against,
(my emphasis), the possibility of using digital computers to produce intelligence".522
He makes substantial arguments against the second assumption based on a survey of
research in Psychology and Cognitive Simulation and comes to the same conclusion I reached in
520 ibid
521 ibid
522 ibid P.162
224
chapter 1: "the assumption of an information-processing level is by no means so self-evident as the
cognitive simulators seem to think; ... there are good reasons to doubt that there is any information
processing going on"!523
The third and fourth assumptions involve more fundamental issues:
"But this still leaves open another ground for optimism: although human performance
might not be explainable by supposing that people are actually following heuristic rules in
a sequence of unconscious operations, intelligent behavior may still be formalizable in
terms of such rules and thus reproduced by a machine. This is the epistemological
assumption."524
He argues that human behavior, (understood as the input and output of physical signals),
though presumably completely lawful in the sense that "formalists" require, does not support the
epistemological assumption as made by Turing and Minsky. They do not simply claim that man is
a physical system describable by natural law, (as are boats and planes), they claim that man is a
Turing machine.
"...When Minsky or Turing claims that man can be understood as a Turing machine, they
must mean that a digital computer can reproduce human behavior ... by processing data
representing facts about the world using logical operations that can be reduced to
matching, classifying, and Boolean operations ... All AI research is dedicated to using
523 ibid P.163, my emphasis 524 ibid P.189
225
logical operations to manipulate data representing the world, not to solving physical
equations describing physical objects ... (however) considerations from physics show only
that inputs of energy, and the neurological activity involved in transforming them, can in
principle be described and manipulated in digital form".525
But even the weaker form of the assumption -the use of the laws of physics to calculate in
detail the function of human bodies, (and brains)- may be physically impossible. There are
theoretical limits to processing density! Therefore "the enormous calculations necessary may be
precluded by the very laws of physics and information theory such calculations presuppose."526
Nor, Dreyfus argues, does research in language translation and semantics support Turing's or
Minsky's interpretation. It raises, instead, insurmountable problems of context and heuristics. This
empirical objection is not sufficient to dismiss the assumption, however. Its supporters can "offer
the platonic retort ... that we have not fully understood this behavior, we have not yet found the
rules.. "527
He bases his central argument on Wittgenstein's. Wittgenstein provisionally assumed "that
all non-arbitrary behavior must be rule like, and then reduce[d] this assumption to absurdity by
asking for the rules which we use in applying the rules, and so forth."528
525 ibid p. 196 526 ibid p. 197 527 ibid p.202-203 528 ibid P.203 He elaborates: "It is a question of whether there can be rules even describing what speakers in fact do. ...
one must ..have further rules which would enable a person or a machine to recognize the context in which the rules must be applied. Thus there must be rules for recognizing the situation, the intentions of the speakers, and so forth. But if the theory then requires further rules in order to explain how these rules are applied, as the pure intellectualist viewpoint would suggest, we are in an infinite regress." (ibid P. 203). Wittgenstein resolved the problem in terms of the "practical demands of the situation". For the computer, however, this is not possible. "The computer is not in a situation." (my emphasis)!
226
"For the computer people the regress ... stops with an interpretation which is self-evident,
but this interpretation has nothing to do with the demands of the situation. It cannot, for the
computer... generates no local context. The computer theorist's solution is to build a
machine to respond to ultimate bits of context-free, completely determinate data", (my
emphasis), "which require no further interpretation in order to be understood. Once the
data are in the machine, all processing must be rulelike, but in reading in the data there is a
direct response to determinate features of the machine's environment... so on this ultimate
level the machine does not need rules for applying its rules. ...So human behavior, if it is
to completely understood and computerized, must be understood as if triggered by specific
features of the environment."529
The third assumption is thus logically dependent upon the fourth:
"A full refutation of the epistemological assumption would require an argument that the
world cannot be analyzed in terms of context-free data. Then, since the assumption that
there are basic unambiguous elements is the only way to save the epistemological
assumption from the regress of rules, the formalist, caught between the impossibility of
always having rules for the application of rules and the impossibility of finding ultimate
unambiguous data, would have to abandon the epistemological assumption altogether. This
assumption that the world can be exhaustively analyzed in terms of context-free data or
529 ibid P. 204
227
atomic facts", (my emphasis), "is the deepest assumption underlying work in AI and the
whole philosophical tradition. we shall call it the ontological assumption..."530
The ontological assumption is the profoundest presupposition of AI researchers. It is a
fundamental assumption of western philosophical and scientific thought in general:
"As in the case of the epistemological assumption, we shall see that this conviction
concerning the indubitability of what in fact is only an hypothesis reflects two thousand
years of philosophical tradition reinforced by a misinterpretation of the success of the
physical sciences."531
Computers are characterized, (even by the proponents of AI), as accepting a "task
environment" defined in terms of discrete objects which are organized into the data structure
"which makes up the computer's representation of the world." "Every program for a digital
computer must receive its data in this discrete form. ... When one asks what this knowledge of the
world is, the answer comes back that it must be a great mass of discrete facts."532
"the data with which the computer must operate if it is to perceive, speak, and in general
behave intelligently, must be discrete, explicit, and determinate; otherwise it will not be the
sort of information which can be given to the computer so as to be processed by rule. Yet
530 ibid P.205 531 ibid P. 207 532 ibid P. 208
228
there is no reason to suppose that such data about the human world are available to the
computer and several reasons to suggest that no such data exist"533, (my emphasis).
He cites Minsky's attempt to specify the magnitude of the mass of knowledge necessary for
humanoid intelligence. Minsky estimates the number of facts required as on the order of one
hundred thousand for reasonable behavior in ordinary situations, a million for a very great
intelligence. If this doesn't satisfy us, we are to multiply this figure by ten!534 But this immediately
leads to the "large database problem" -how could one find the information required in a reasonable
amount of time?
"When one assumes that our knowledge of the world is knowledge of millions of discrete
facts, the problem of artificial intelligence becomes the problem of storing and accessing a
large data base ...and ... little progress has been made toward solving the large data base
problem."535
The same problem arises when he considers the problem of disambiguation, (and
"context"), in linguistics:
"... finally, human activity itself is only a subclass of some even broader situation -call it
the human life-world- which it would have to include even those situations where no
human beings were directly involved. But what facts would be relevant to recognizing this
533 ibid P. 206 534 Dreyfus argues that the "facts" required may well be infinite! 535 ibid P. 209
229
broadest situation? ... Well then, why not make explicit the significant features of the
human form of life from within it? Indeed, this deus ex machina solution has been the
implicit goal of philosophers for two thousand years, and it should be no surprise that
nothing short of a formalization of the human form of life could give us artificial
intelligence. But how are we to proceed? ... Without some particular interest, without
some particular inquiry to help us select and interpret, we are back confronting the infinity
of meaningless facts we were trying to avoid."536
He comes to the conclusion that the only way out of the dilemma is to conceive of "facts"
as "a product of the situation".
"There must be some (other) way of avoiding the self-contradictory regress of contexts, or
the incomprehensible notion of recognizing an ultimate context, as the only way of giving
significance to independent, neutral facts....then the only alternative way of denying the
separation of fact and situation is to give up the independence of the facts and understand
them as a product of the situation."537
His final judgement is severe. Artificial Intelligence research has revealed fundamental
flaws in the assumptions we make about mind, brain, and, I propose in consequence, -about our
access to the world itself:
536 ibid P. 221-222 537 ibid P.224
230
"Recent work in artificial intelligence (is) a crucial experiment disconfirming the
traditional assumption that human reason can be analyzed into rule-governed operations on
situation-free discrete elements -the most important disconfirmation of this metaphysical
demand that has ever been produced."538
Dreyfus' is quite convincing in many respects. I specifically disagree with the scope of his
objection to the third (epistemological) assumption, however. In the particular form in which he
stated it, though, it is unobjectionable:
"that all knowledge can be formalized, that is, that whatever can be understood can be
expressed in terms of ... Boolean functions, the logical calculus which governs the way the
bits are related according to rules."
Neither Boolean functions nor "atomic bits", (context-free "facts"), will suffice -as his
arguments ably demonstrate. But Dreyfus extends his legitimate objections to this form of the
assumption to an argument against the general platonic case "that whatever can be understood can
be expressed in terms of logical relations". But Boolean functions and atomic facts do not exhaust
the possibilities either for "understanding" or for "logical relations"! In Chapter 2, (The Problem of
Logic), I argued an alternative formal concept, Cassirer's "functional concept of mathematics" and
the alternative logic which is its consequence. Aristotelian (and Boolean) logic is the harvest of
the Aristotelian (generic) concept! Classical logic -and its modern extensions- consist in the
abstraction and manipulation of ultimate, context-free "atomic bits"! They are the calculus-of-
538 op cit Pps. 303-304
231
abstraction of "marks". They are themselves purely digital, (i.e. discrete), processes, and therefore
valid heirs to all the arguments Dreyfus makes against mind, (and thought), in a digital computer.
They are not the logic of mind, nor, I argue, of the brain!
Dreyfus' arguments have nothing to do with silicone or copper.539 His arguments are
arguments against discrete logic itself, and applicable to any instantiation of the mind-body
relationship grounded in it, even a physiological one! The large database problem, the heuristics
problem, the context problem, (and the digital computer itself), are all, as problems, products of
classical digital, (i.e. discrete), logic, and, ultimately I argue, of its formal concept.
Dreyfus characterized the fourth (ontological) assumption as presupposing that : "all
relevant information about the world, everything essential to the production of intelligent behavior,
must in principle be analyzable as a set of situation-free determinate elements ... -that what there is,
is a set of facts each logically independent of all the others." I would extend his characterization,
however. The fundamental presupposition is that "the world" itself consists of such situation-free
determinate elements! Dreyfus argues against analysis, I argue against reference.
Finally, I strongly disagree with Dreyfus' "finesse" of perceptual and physical
phenomenology into distinct and mutually disjoint domains:
"(This) is not to deny that physical energy bombards our physical organism and that the
result is our experience of the world. It is simply to assert that the physical processing of
the physical energy is not a psychological process, and does not take place in terms of
sorting and storing human-sized facts about tables and chairs. Rather, the human world is
539 He never even mentions them in any significant way!
232
the result of this energy processing and the human world does not need another mechanical
repetition of the same process in order to be perceived and understood."540
He quotes Neisser:
"There is certainly a real world of trees and people and cars and even books. ... However,
we have no direct, immediate access to the world, nor to any of its properties."541
but argues contrarily:
"Here... the damage is already done. There is indeed a world to which we have no
immediate access. We do not directly perceive the world of atoms and electromagnetic
waves (if it even makes sense to speak of perceiving them) -but the world of cars and books
is just the world we do directly experience. ... 'the human world is the brain's response to
the physical world.' Thus there is no point in saying it is 'in the mind,' and no point in
inventing a third world -between the physical and the human world -which is an arbitrarily
impoverished version of the world in which we live, out of which the human world has to
be built up again."542
His evisceration of the problem, (the exact parallel of the eliminative materialist's, for
instance), fails to answer important questions: "How perception?", "How mind?" "How is the
human world 'the brain's response to the physical world?'" The answer, (on both sides), is that both
540 ibid P. 268, my emphasis 541 ibid
233
the problem and the question are the result of semantic confusions. I don't think they are. I believe
the platonic ideal can be achieved. The explication of both the mind and the physical world can
be encompassed in a comprehensive set of rules, but not by the sort of rules, (or logic), currently
envisaged. The dream of one comprehensive knowledge is attainable, but it need not be simple -
this book supplies my answer.
"If there could be an autonomous theory of performance, it would have to be an entirely
new kind of theory, a theory for a local context which described this context entirely in
universal yet nonphysical terms. Neither physics nor linguistics offers any precedent for
such a theory, nor any comforting assurance that such a theory can be found."543
My hypothesis of "implicit definition, (Chapter 2), coupled with the "schematic object" ,
(Chapter 1), supplies the formal beginnings of such a theory. It is an autonomous theory of
performance, "a theory for a local context (describing) this context entirely in universal yet
nonphysical terms."!
542 ibid Pps. 269-270 543 ibid P.202
234
Appendix D: (Roger Penrose)
Roger Penrose categorized scientific theories based on a number of criteria. To the extent
that they satisfy these criteria, he classified them all the way from, (his caps), SUPERB down to
MISGUIDED, (SUPERB, USEFUL, TENATIVE, MISGUIDED):
1. Scope: -range and variety of phenomena explained, and hitherto unexplained. The scope of
the theories Penrose classifies as "SUPERB" is, of course, well known. They explain the whole
range of facts of our scientific view of reality: “the actions of the mold on a piece of bread, the
dynamics of a violin, the workings of a transistor, and the explosions of supernovas.”
Newton's theory, Maxwell's, the special and general relativities, and quantum mechanics
explained vast ranges of phenomena. Their fecundity was startling.
2. Consistency: "Always constrained by logical argument and known facts." (P.422) This is, of
course, fundamental. An inconsistent logical system proves, (trivially), both everything and
nothing. A theory incompatible with known facts, of course, has no relevancy as a theory of
reality.
3. Accuracy: Need not be perfect, but extremely accurate over many orders of magnitude!
(Degree of accuracy is a value criterion, however, and is a decision factor in deciding between
theories.) The degree of accuracy of the "SUPERB" theories is astounding:
A. Euclidean geometry: "Over a meter's range, deviations from Euclidean
flatness are tiny indeed, errors in treating the geometry as Euclidean amounting to
less than the diameter of an atom of hydrogen!" (P. 152)
B. Galilean and Newtonian dynamics: "As applied to the motions of planets
and moons, the observed accuracy of this theory is phenomenal -better than one
235
part in ten million. "The same Newtonian scheme applies here on earth -and out
among the stars and galaxies -to some comparable accuracy". (P.152)
C. Maxwell's theory: "Maxwells theory, likewise is accurately valid over an
extraordinary range, reaching inwards to the tiny scale of atoms and subatomic
particles, and outwards, also, to that of galaxies, some million million million
million million million times larger!" (P.152)
D. Special relativity: "Gives a wonderfully accurate description of phenomena
in which the speeds of objects are allowed to come close to that of light -speeds at
which Newton's descriptions at last begin to falter." (P.153)
E. General relativity: "Einstein's supremely beautiful and original theory
...generalizes Newton's dynamical theory (of gravity) and improves upon its
accuracy, inheriting all the remarkable precision of that theory...In addition, it
explains various detailed observational facts which are incompatible with the older
Newtonian scheme. One of these (the 'binary pulsar'..) shows Einstein's theory to
be accurate to about one part in 10 to the 14th power." (P.153)
F. Quantum mechanics: Explains "hitherto inexplicable phenomena...The laws
of chemistry, the stability of atoms, the sharpness of spectral lines...the curious
phenomenon of superconductivity.. and the behavior of lasers are just a few
amongst these." (P.153) "No observational discrepancies" (at all) "with that theory
are known."
236
4. Mathematical elegance:
"Both relativity theories -the second of which subsumes the first -must indeed
be classified as SUPERB (for reasons of their mathematical elegance almost as
much as of their accuracy)." (Page 153) (This relates both to easy utility and to
aesthetics!) Again: "It is remarkable that all the SUPERB theories of nature have
proved to be extraordinarily fertile as sources of mathematical ideas. There is a
deep and beautiful mystery in this fact: that these superbly accurate theories are
also extraordinarily fruitful simply as mathematics." (P. 174)
5. Experimental support: -to establish the unique relevance of a theory to reality -to establish
correlation to experience.
6. Substantial advance to understanding: -- i.e., it must be a "conceptual organizer". This
criterion relates to the mathematical elegance of criterion 4, to future applicability, -and to overall
world-view.
7. Simplicity:
"Ptolemaic theory of planetary motion became more and over-complicated as
greater accuracy was needed" (P.155). Copernican theory simplified the data of
astronomy. "'Tidiness' -quark and lepton theories "are, for various reasons, rather
more untidy than one would wish". (P.154) (This criterion is cross-related, clearly,
to #'s 9, 8, and probably to #6.)
237
8. Provides a predictive scheme:
"Kepler's and Mendeleev's theories, while accurate, did not provide a predictive
scheme and later were subsumed into Newtonian dynamics and quantum theory
respectively!" (P.155) It is a criterion of usefulness.
9. Aesthetics:
"A beautiful idea has a much greater chance of being a correct idea than an ugly
one"..."...The importance of aesthetic criteria applies ...to the much more frequent
judgments that we make all the time in mathematical (or scientific) work."
("Always constrained by logical argument and known facts.") (P.421) Also, see
his comment on the Relativities. This criterion is transparently a purely artistic one.
#'s 1, 4, 6, and 8, (at least), clearly have artistic components as well
Any physical theory satisfying these definitive criteria qualifies as "SUPERB". I believe
that the satisfaction of these criteria constitutes a necessary and sufficient definition of a viable
"theory of reality" in the general sense as well -i.e for world-views! The adequacy of their
fulfillment, taken as a balanced whole, constitutes the actual basis of choice between theories of
reality, and, ultimately, between world-views.
Nowhere are these criteria themselves based in a particular conceptual scheme of reality or
in specific metaphysical assumptions, however! Any conceptual system of whatever nature
actually meeting these criteria, (to include correlation = #3, redundantly), qualifies that system as
"SUPERB"! But all these criteria involve solely "relational" aspects of a theory -its internal
structural relationality and its relationality to the perceptual model, (and the phenomena). The
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ranking of a particular theory, -and its believability-, derives from the extent of their fulfillment
alone.
Though I dearly love the book, I do not value the "Emperor's New Mind" as a theory of
mind-brain. I value it as a wonderful and succinct synopsis of the state of modern physics and as
what I believe is a meaningful formulation of the actual criteria by which we evaluate theories -all
theories. To paraphrase one of his reviewers: even if Penrose's ideas are correct, they don't explain
consciousness, only how the brain works!544 Penrose's is a theory of physics -and specifically a
theory of the physics of brain function. The problem of self-reference, (sometimes referred to as
"the mind's I”), which both he and Hofstadter, for instance, treat in terms of Gödel’s Theorem is
not the most important part of the problem of mind. Though they may well be correct in their
resolution of the difficulty, my opinion is that the problem itself, and their proposed solution is an
internal one only, i.e. it is an internal, model-model complication of the calculus. I believe it is a
problem of ordinary logic, ("associationist logic" in Dreyfus' terminology –or “objectivist logic” in
Lakoff’s), rather than of the constitutive logic of implicit definition. That ordinary logic, I believe,
stands to our constitutive logic in the same role that Diophantine, (integer), arithmetic stands to
continuous arithmetic. I believe it is a limited and partial, (though valid), calculus; it is not the
continuous and universal logic of mind. Its very concepts are built on the special, limiting case of
abstraction, not on (Cassirer's) functional rule of connection, for instance, nor would they
countenance my own Concept of Implicit Definition. (Cf. Chapter 2) -i.e. they represent the limit
case of a general function and inherit the difficulties of that genealogy.
544 This, in my opinion, succinctly sums up the case for Edelman’s hypothesis as well.
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Appendix E: Dogmatic Materialism and Reality
At the basis of ordinary Naturalism are two fundamental assumptions: that perception
(somehow) embodies externality, and that rational thought can utilize the "facts" of perception to
discover the actual nature and ground of that externality. It is seriously committed to only one
possibility for that ground, moreover, and it is "substance".
I argued the error of the first assumption in my first two chapters. I argued that perception
does not embody externality; that its objects are schematic artifacts, embodying the relationality of
brain response only. But the brain does not embody metaphysical externality either! It is,
following Maturana and Varela, only in "structural coupling" with it. Lacking a metaphysically
simple referent for our perceptions, however, (metaphysical) "substance" is no longer an obvious
or immediate hypothesis.545 And yet no one can seriously question either the validity or the utility
of science!
Why do we believe the things we do? Why, specifically, do we believe in "matter", or
"objects" -as absolutes? What else could science, (and physics specifically), concern?
Naturalism, in its modern essence, assumes that the reduction of the whole of reality into
biology, chemistry, and physics will be successful. It further presumes that biology and chemistry
themselves will reduce, finally, to just physics. History in general supports these conclusions, and
this is taken as a conclusive substantiation of the materialist hypothesis.
There are two profound weaknesses in this argument, however. The first is its assumption
that physics itself is capable of a further reduction to "substance" -which is certainly not confirmed
545 Its actual enticement was always sensory anyway: the world had to be "solid"!
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in recent science but rather contravened.546 The second weakness is its tacit incorporation of a
limited logical possibility -i.e. that reduction/replacement is inherently an asymmetrical process!
This limited conception of relational possibility, implicit in Naturalism's reductionist argument and
leading to the "material" conclusion, is, from a mathematical standpoint, profoundly naive! From
the standpoint of abstract algebra, for instance, it is simplistic. Mathematical disciplines are
constantly, (and almost at the whim of the author), regrounded, reoriented, and recast. Theorems
become axioms and axioms theorems. And yet the discipline retains its integrity!
That one system of relationality, (theory), is capable of embodiment in another is not
therefore a convincing argument that converse, -or other transformations, equally viable- are not
possible or significant.547 It would be considered mathematically naive to presume that, because of
the existence of one orientation, that other "reductions", (transformations), are consequently, (or
even probably), impossible, less important or irrelevant!548
But materialism makes exactly that assumption. It assumes that, since the whole of our
cultural world is reducing, historically, to biology, chemistry, and physics, that this is a necessarily
asymmetric reduction, and that the essence of reality is therefore physical,- and presumably
material. From the broadened perspective of the "schematic artifact", however, it is an unnatural
and unjustified assumption. The structural coupling of the brain is the embodiment of response -it
is the whole of the relationality between "perturbation" and action. Its very "objects" are not
546 In the twin-slit experiment, for instance. 547 Quine's argument is absolutely conclusive here. 548 If we assume that Maturana and Varela's arguments for ontogenic coupling and structural drift are viable, for
instance, then the whole of the physical world co-reduces to biology -and to its ontogenic hypothesis specifically! Behaviorism then becomes a "Quinean ladder".
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metaphysical, (nor "substantial"), but procedural549 -nor are they referential! What is important is
not a particular organization, a particular perspective on that structure, but its relationality as a
whole!
Theories, as orientations of "data", (and pictorial perceptual "theories" as well), are
organizational structures. They are, I believe, transformations mapping the "perceptual space",
(the schematic perceptual model), back onto itself.550 As such, following Quine, they are always
amenable to profound translation and reorientation -no matter the precision of experimental
correlation! What is unique and permanent are the invariants of the system of possible
transformations, (including even those which might redistribute the objects themselves) -which
embody its relationality as a whole. (See the discussion of hierarchy and mathematical ideals in
the “Afterward: Lakoff, Edelman and Hierarchy.
Materialism is profoundly committed to a physical theory of reality.551 It is thereby
committed to the best picture that actual physical theory, (not its experimental data), can present -
to a succession of theoretical approximations552 refining closer and closer to a picture of its
presumed actual objective physical -and material- reality.
"We have only to look about us to witness the extraordinary power that our
understandings of nature have helped us to obtain. The technology of the modern world
549 Nor is a simple correspondence with externality implicit in them. 550 They map historical experience/experiment onto future experience/experiment. 551 -and to the conclusive evidence of its technology as well! This is materialism's strongest coherent argument. 552 This is not to say that successive physical theories refine a particular approximation of the object, but rather that
successive theories are believed to be in closer and closer overall correlation to reality- i.e. that successive theories better approximate reality.
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has derived, in good measure, from a great wealth of empirical experience. However, it is
physical theory that underlies our technology in a much more fundamental way..."
(Penrose, 1989, P.150)
But what sense do materialism's metaphysical assumptions of "object" or "substance" make
to modern physical theory? What sense do they make in the relativistic universe, or in the quantum
theoretical one? What is "the object" to modern science? What does "matter", conceived non-
reductively as "substance", have to do with modern physics? Physics, as a discipline, has always
been ready to question its presuppositions!
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Appendix F: "Dennett and the Color Phi"
(Towards a Working Model of Real Minds: Dennett, Helmholtz and Cassirer)
I really like Daniel Dennett's "Consciousness Explained"553. It is not because I can
agree with his conclusions, (except in a certain sense), that I like it, but because it is a brutally
candid and forthright exposition of the Naturalist position, proceeding with compelling logic,
and without hedging. It is, moreover, a phenomenologically pure position. I think it is,
(agreeing with his own parenthetical question), really "Consciousness Explained Away"
however, rather than "Consciousness Explained" because, at the end, "we are all zombies".554
There is one crucial argument he makes against the existence of mental states, (i.e. "figment"),
however, in which I think he has correctly identified a profound antinomy -and, I believe, a
necessary and major modification to our ordinary conception of mind. He has argued it from
"the color phi".
"The color phi" names an actual experiment, suggested by Nelson Goodman, wherein
two spots of light are projected in succession, (at different locations), on a darkened screen for
150 msec intervals with a 50 msec interval between them. The first spot, however, is of a
different color, (red, say), than the second, (green). Just as in the case of motion pictures, (the
"phi phenomenon"), subjects report seeing the continuous motion of a single spot, but
interestingly, they report that it changes color, (from red to green), midway between the two
553 Dennett, 1991 554 I know, I know! I must, in threat of disingenuousness, quote his footnote to this comment: "it would be an act of
the utmost intellectual dishonesty to quote this statement out of context."
But the context he demands is 470 pages of careful redefinition and argument against all the normal senses of mental function and existence -qualia, figment, the "substance of mind". The upshot is that it is O.K., (i.e. socially correct), to be a zombie! But the sense in which his statement would normally be understood out of context is essentially what it still means. He attempts to make any objection, (or any comment on its own prima facie unintuitiveness), unraisable. There is another cult, (besides the Feenomanists!), in the jungle, you see! :-)
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termini!555 Dennett bases a very interesting, (and, I feel a very important), argument against the
very possibility of a "Cartesian Theatre", against a unity, (and "figment" = substance), of
consciousness on this well documented and reproducible experiment. Dennett's argument, in
brief, is this:
Mental states, the "Cartesian Theatre", if they exist, are subject to the laws of causality,
of time precedence. For one event to affect another, it must occur before it. Let me, for
discussion's sake, label the events described. Let E1 be the ("heterophenomenological"556),
perception, (hereinafter to be called by me "h-perception"), of the first, (red), spot. Let E2 be
the h-perception of the red-changing-to-green, and let E3 be the h-perception of the final green
spot.
Dennett argues, based on the principle of causality, that E2 cannot occur until after E3.
Since there were only two actual, (physical), events, (the first and second projected spots), he
argues that the h-perceived midpoint, (the "mental event", i.e. red-changing-to-green), cannot
occur until after the reception of the second actual event, (green projection), as it was that which
provided the very sensory data necessary to the h-perception of change. Other than a (mystical)
hypothesis of "projection backward in time", there remain for Dennett just two possibilities for
an internal, "Cartesian Theatre" consistent with the experiment: the "Stalinesque" and the
"Orwellian" hypotheses.
The first involves the creation of a "show trial" staged by a subterranean "central
committee", (after the fact of both real events, of course, and involving a "delay loop"), wherein
the complete, (and partially fabricated), sequence, (red ->red-changing-to-green -> green), is
555 and not, for instance, that it is red all the way till its terminus, with a final and sudden change-to-green. 556 Dennett introduces the criterion "heterophenomenological" to describe "mental events", which he does not
believe in, to describe whatever-it-is that is named by them, i.e. to talk about them as they are (linguistically) used by real bodies and brains, (which he does believe in), but with a neutral metaphysical commitment.
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"projected", (i.e achieves sentiency). Under this hypothesis, the whole of our sentiency, our
consciousness, occurs "after the fact". The second possibility, the "Orwellian" hypothesis, is
that the actual events are received by our sentient faculty as is, but that our memory then
rewrites history, (just as the thought police of Orwell's "1984" did), so that we remember not
two disjoint and separate events, but the connected, and pragmatically more probable sequence
red -> red-changing-to-green -> green.
Dennett argues that ultimately neither theory is decidable -that either is consistent with
whatever level and kind of experimental detail science may ultimately supply, and that,
therefore, the only pragmatic distinction between them is purely linguistic, and therefore trivial.
He argues that there is no "great divide", no actual moment, (nor existence), of sentiency, but
only the underlying brain process, (which all theories must countenance), itself. Based on the
"spatial and temporal smearing of the observer's point of view", he expounds his thesis of
"multiple drafts" wherein there is no "theatre", only brain process -and its various "speakings",
(drafts).
And yet the observer himself has absolutely no problem with these events! His
perspective is very clear: E1 -> E2 -> E3. It is our interpretation, (and rationale), for this
sequence that causes the problem.
I think Dennett has a very strong argument, but I want to refocus it. Nondecidability is
all very well and good, but it is a much weaker line than the one he started out with- on the
possibility of synchronization! In a very real sense, I feel it is very similar in intent and
consequence to Einstein's "train" argument against simultaneity.
Consider, (with Einstein), an imaginary train moving (very fast)557 down a track, with
an observer standing midway on top of the moving train and observing two (hypothetically
557 nearing the speed of light
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instantaneous) flashbulbs going off at either end of the train. The train goes by another
(stationary) observer standing (hypothetically infinitely) close by the track as the bulbs go off.
Suppose that the moving observer, (OT), reports both flashes as simultaneous. He argues that
since both photon pulses reach him simultaneously, (granted for all frames on the local,
infinitesimal scale, and thus agreed on (?) by both observers who are assumed infinitely close -
i.e. side by side), that therefore the pulse from the rear of the train, having to "catch" him, must
have left its source sooner than the pulse from the front which added his velocity to its own and
so must have left later. Relative to OS, (stationary observer), however, the two sources travel
the same distance to a stationary target, (himself). Since OT and OS are momentarily adjacent
to each other, (i.e. within a local frame), they should be able to agree that the two pulses arrive
there simultaneously. What they cannot agree on, however, (in that instance), is whether the
events, (the flashes), occurred simultaneously -nor that the other could have thought, (i.e. could
have observed), them so! Time, in Dennett's words, is "smeared"!558 We could, of course and
significantly559, vary the parameters to make either event "earlier" and the other "later".
The argument is that from the standpoint of one observer, he must maintain that the
other cannot see them as simultaneous, and vice versa! Thus from OS's standpoint, if he sees
them as simultaneous, then, since he is stationary, they occurred simultaneously. But if they
occurred simultaneously, and since OT is moving, then OT cannot, (OS argues), see them as
simultaneous, (and conversely). And yet both observers pass through an infinitesimal local
frame of reference, (side-by-side). Time is "smeared"!
Just as Einstein's two observers, near the limits of physical possibility, cannot agree
whether the two lights were simultaneously flashed at the ends of the train or not, (i.e. cannot
558 Are the observers, (and the experimental apparatus), then "heterophenomenological"? 559 i.e. -relative to Dennett's problem
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establish a common temporal frame of reference), nor that the other could observe them locally
as such, neither, given Dennett's pointed argument, can we establish a common temporal frame
of reference for "the world" and "the mind" at the limits of cognition.560
I agree with Dennett that "the color phi" identifies a legitimate and critical aspect of the
mind-body problem. The spatial and temporal "smearing" of the percept and the non-explicit
reference of qualia that he demonstrates forces a profound extension to our traditional
conception of the "theatre". But his dimensional "smearing" actually fits very well561 with the
model I am proposing. I submit that it is more plausible in terms of the "focus" and "function"
of an operational object than in terms of his "multiple drafts", "demons" and "memes" in the
"real world". His objections to the ordinary "Cartesian theatre" are admittedly valid, but so
were those of Cassirer and Helmholtz before him:
"For example, if we conceive the different perceptual images, which we receive
from one and the same 'object' according to our distance from it and according to
changing illumination, as comprehended in a series of perceptual images, then from the
standpoint of immediate psychological experience, no property can be indicated at first
by which any of these varying images should have preeminence over any other. Only
the totality of these data of perception constitutes what we call empirical knowledge of
the object; and in this totality no single element is absolutely superfluous. No one of the
successive perspective aspects can claim to be the only valid, absolute expression of the
560 For macroscopic science, these limits are at the scale of the speed of light. For atomic physics, they are at the
scale of Planck's constant. And for the brain, I suggest, they are at the scale of minimal biological response times, i.e. in the 100 msec. range.
561 when taken "heterophenomenologically" -i.e. with a neutral ontic commitment. Heterophenomenology works both ways!
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'object itself;' rather all the cognitive value of any particular perception belongs to it
only in connection with other contents, with which it combines into an empirical whole.
...In this sense, the presentation of the stereometric form plays 'the role of a
concept'", (my emphasis), "'compounded from a great series of sense perceptions,
which, however, could not necessarily be construed in verbally expressible definitions,
such as the geometrician uses, but only through the living presentation of the law,
according to which the perspective images follow each other.' This ordering by a
concept means, however, that the various elements do not lie alongside of each other
like the parts of an aggregate, but that we estimate each of them according to its
systematic significance...." (Cassirer, 1923, pp. 288-289, citing Helmholtz)
But Cassirer's reformulation of the formal concept itself must be considered for an
understanding of his meaning here. The concept, for Cassirer, is a function. It is "the form of a
series", independent and distinct from what it orders. This is the "systematic significance"
which he purports. I urge, extending Cassirer's insight and in the sense of my conclusions of
Chapter 2, that the stereometric form itself, the percept,562 then plays the role of, (is), a function.
From the standpoint of (relativized) Naturalism,563 if we take the mind to be schematic,
but specifically a "predictive" and "intentional" schematic model, (which extension I will
suggest shortly), rather than a static and "representative" one564, then the temporal and spatial
"smearing" of the percept do not have the implications against the "theatre" per se that Dennett
attributes to them. I have argued that the percept itself is conceptual, (albeit specialized,
562 This, the percept as concept, is clearly at odds with, but, (I have argued), a legitimate extension of, Cassirer's
ideas. He did not have the perspective of the schematic object. 563 cf. Chapter 4
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invariant and constitutive), and therefore, following Cassirer, functional. It is an entity of order
and process -and it is "smeared". That is the normal nature of functions -they are smeared!
What Dennett explains by "multiple drafts", (and the "demonic" process he envisions beneath
them), I explain by "focus". We focus the percept, (via implicit definition) according to
operational need.
An Extension of the Schematic Model: A Brief Sketch
Let me frame the following in the language of ordinary Naturalism, (this will be a short
appendix). I want to sketch a very large canvas very quickly.565 In "the color phi", I think that
Dennett has identified a very important difficulty in our ordinary conception of mind. It
suggests an enlargement and a more sophisticated perspective on the schematism I have argued
heretofore. Though I think I have successfully laid the solid foundation, let me now sketch the
design of the cathedral itself, i.e. the design of real minds!
I have dealt, previously, with the schematic object. I argued that the object of
perception is a schematic artifact of reactive brain process, specifically "designed" to optimize a
simple and efficient "calculus" of response. But the converse side to that argument is that an
actual calculus was enabled! What are the (Naturalistic) implications of that calculus, and of
the schematic model?
Follow me in a thought experiment! Keeping your eyes fixed to the front, you perceive,
(in your perceptual model), this paper in front of you, the wall behind it, and, perhaps, the
564 i.e. vis-à-vis current process 565 I could, of course, try to footnote every misconception and every possible claim of inconsistency, but we have
already done that, haven't we? I think I have paid my dues. "Predictivity", "intentionality", et al are, under my thesis, perfectly valid conceptions within the Naturalist "form" - and I may consistently use them as such without self-contradiction! Within the context of my larger perspective, they are model-model correlations, synthetic a priori "slices" across the phenomena.
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pictures of your family. There may be pens and pencils, books. You may hear music from the
stereo next to you, (and perhaps still in peripheral vision). There may be a window, and the
lights of the neighbor's house beyond it. But there is no wall behind you! There is no car in the
driveway outside of your house -indeed, there is no "house" at all. There is no city, no taxes, no
friends. The sun does not exist in this model. There is no government, no "universe", -no
tomorrow! The (purely) perceptual model is incomplete as a model of "reality" and it is,
(Naturally!), inadequate even to keep you alive! There is something else necessary for
completeness of the model detailed in this book, i.e. a new perspective on it. It is an intentional
aspect. It is necessary to supply the object behind your back and the reality "over the hill"! It
supplies the connection to "tomorrow" and "yesterday". It supplies "causality". It is necessary
for the completeness of a model of "the world". It is necessary, (specifically following
Dennett!), even for the individual "objects" of perception itself, (E1 and E3 for instance). This
model, I suggest, is where E2, (the object of Dennett's perplexity), lives. It cohabits there very
comfortably with E1 and E3 which, I argue, are also predictive and schematic objects. There is
a seamless integration, (above the scale of 100 ms, let us say), of what we normally think of as
our pure percepts and the intentional fabric within which they are woven.566 This model, I
566 But let us turn Dennett's argument around. Dennett argues strongly and convincingly that "figment", (mental
states), are logically inconsistent with our, (his), ordinary (naïve) views of cognition and reality. If, instead of accepting his conclusion however, we choose to accept the reality of that figment -E1, E3, and E2, -if we believe that E2 is actually perceived, (whatever it may be), then his argument takes on a different import and works against the very ground in which it was framed: i.e. his ordinary view of cognition and the Naturalism, ("objectivism"), in which he embedded it. The "color phi", he says himself, embodies a precise and reproducible experiment -you and I would both expect to "see" it!
I consider the "phi phenomenon" itself more interesting than the "color phi", however. The credibility and intentional depth of a series of oversized, rapidly sequenced still pictures, (a movie), is quite suggestive. Its potential for an uncanny parallelism with our ordinary experience suggests that the latter, (i.e. ordinary experience), is itself a predictive and integrative phenomenon grounded in a schematic, intentional model in precisely the same manner as I propose the "color phi" to be.
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believe, is the actual "home" of mind, and the legitimate purview of a truly scientific
psychiatry.567
"Now what is a phenomenal space? Is it a physical space inside the brain? Is it the
onstage space in a theater of consciousness located in the brain? Not literally. But
metaphorically? In the previous chapter we saw a way of making sense of such
metaphorical spaces, in the example of the 'mental images' that Shakey, [a robot],
manipulated. In a strict but metaphorical sense, Shakey drew shapes in space, paid
attention to particular points in that space, based conclusions on what he found at those
points in space. But the space was only a logical space. It was like the space of
Sherlock Holmes's London, a space of a fictional world, but a fictional world
systematically anchored to actual physical events going on in the ordinary space in
Shakey's 'brain'. If we took Shakey's utterances as expressions of his 'beliefs', then we
could say that it was a space Shakey believed in, but that did not make it real, any more
than someone's belief in Feenoman would make Feenoman real. Both are merely
intentional objects.... So we do have a way of making sense of the ideas of phenomenal
space -as a logical space." Dennett, 1991, pps.130-131, my emphasis.
But this is my exact conclusion of Chapter 2. Dennett and I are not so very far apart
after all -save in our metaphysics, (wherein we are very different). Mind is a logical entity -i.e.
its "space" is a logical space. But Dennett's "mind" is based in associationist logic (after
Dreyfus' usage568), and dead, and mine is based in a functional logic, (the constitutive logic of
Kant), and live. We are not zombies!
567 Consider the world-views implicit in paranoia or schizophrenia, for instance, or in bipolar orientations 568 Or "objectivist" logic after Lakoff's
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On the issue of metaphysics, on the other hand, Dennett specifically argues that "nature
does not build epistemic engines."569 Why, then, does he think that he, either as a physical
engine of process, (and the "demons" of process), or as a linguistic engine of "memes", -is
epistemic, (i.e. metaphysically so)?570 I don't think that he, or I, are. This was my exact
conclusion of Chapter 4.
569 Dennett, 1991, P.382 570 Or that his book is so?
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Appendix G: An Outline of the Semantic Argument, (For Philosophers)
This appendix is the logical outline and synopsis of my argument I promised in the
Introduction. Though the line it traces is complex, I think it reflects the actual complexity of the
mind-brain problem itself and defines a plausible solution for the first time.
Outline of Argument:
1. Chapter 1, (the presentation of my first hypothesis), is not, in itself, primarily
argumentative in form. It is, rather, the constructive exhibition of what I believe is a more
plausible evolutionary alternative, (and a specific counterproposal), to the representative model
of cognition. This, the schematic operative model, is my hypothesis about the origins and the
organization of the brain. I propose that "cognition" and human reality, (viewed from a
contemporary Naturalist perspective), is a purely schematic, (i.e. internally organizational
rather than representational), artifact of (reactive) evolutionary process. The plausibility of this
first thesis is argued on the basis of innate design constraints for the control of specifically -and
especially- complex and dangerous processes. This, I propose, was exactly the "engineering
problem" that evolution was faced with in the design of control systems for complex
metacellular organisms. The primary argument for this model, and against representation,
(even behavior isomorphism/representation), is made elsewhere -at the conclusion of chapter 2,
in chapter 3 and appendices A and B. The only argumentative, (per se), aspect of this chapter
lies in what I believe is its stronger evolutionary plausibility vis a vis representation.
2. Chapter 2 approaches the mind-brain problem from the other side, (i.e. mind-brain
|div|571 mind). It presents my hypothesis for the origin and the organization of the mind. This
chapter too is primarily constructive, (rather than argumentative), and constitutes a totally
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independent line of investigation from that of chapter 1. It investigates the nature of logic and
specifically of the formal logical concept, (/category). It expands Cassirer's insight that the
logical concept, (category), is a "new form of consciousness" profoundly distinct and
independent from those of perception and abstraction. I expand on Cassirer's highly original
and mathematically oriented, (and generally overlooked), logical results,572 plausibly extending
them in terms of (one of) Hilbert's pivotal and purely mathematical revelation(s), i.e. "implicit
definition"573, to conclude that mind itself is a single (higher order and, like Cassirer's, a rule-
based) concept, the (constitutive) "concept of implicit definition". This, I argue, is the only
"form of consciousness", subsuming all the others. But this concept, like the axiom systems of
abstract mathematics, internally, (rather than referentially or oppositionally574), resolves its very
objects. Nor are they local, but global. It supplies thereby, for the first time, a plausible
rationale for the "Cartesian theatre", i.e. awareness. For how, in Leibniz' formulation, could the
many be expressed in the one? How could this part of even a "mental substance" know that
part? This is a purely logical problem -the problem of the "homunculus".
Implicit definition575 permits knowing, (as a whole -i.e. "the one"), what are, in some
real sense, our distinct and separate parts, ("the many"). This is because those parts, (objects),
are in fact non-localized and virtual (logical) expressions of the whole, (the rule). It opens a
genuine possibility, therefore, for the resolution of this essential requirement of "naive"
consciousness.
571 i.e divided by or, "seen from the perspective of" 572 Throughout his later writings, Cassirer constantly refers back to "Substance and Function" wherein he developed
the logical ideas which are their basis. cf, e.g. "Einstein's Theory of Relativity", "Symbolic Forms", "Determinism and Indeterminism", etc.
573 as strongly distinguished from Hilbert’s “formalism” which was specifically a theory of proof and quite distinct
574 i.e. as opposed to presentation vs. attention/abstraction 575 and the concept of implicit definition
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"Implicit definition" takes on a new significance in light of Cassirer's reinterpretation of
the formal logical concept, and a new, (and very different) application to the mind-brain
problem in view of my first thesis. If the function of mind and brain is primally
organizational rather than referential, then "interpretation" as an assignment of meaning -
and reference- is no longer the crucial issue -other than as it applies internally to the model
itself. (Chapter 4 deals specifically with the problem of reference. Appendix B is also
directed to this issue.)
3. Combining the conclusions of the second chapter with that of the first, I conclude
that if we identify the mind as the single (higher order and constitutive) “concept” defined by
the primitive logical, (i.e. logically behavioral), rule of the brain, (legitimized under the new
formal concept), then a perfectly natural and plausible physical definition of "mind" is possible:
i.e. that the mind is the concept576 of the brain! But here both "concept" and "logic" are
themselves interpreted reductively -biologically and operationally, (i.e. materially). This, I
propose, is the physical, (i.e. Naturalist), answer to the mind-body problem.577 But the
combination of the first two hypotheses creates a staggering epistemological problem, and
involves moreover, (so it seems), an obvious self-contradiction. If both our perceptual and
intellectual objects are solely artifacts of biological coordination, then on what ground can
knowledge, (and my own argument), stand? If the very language, (to include the very
"biological coordination" and "evolution" of my argument), in which I describe the problem,
(being part of that self-same human reality), is only internally organizational and not referential,
then what is it that am I describing? How can I even discuss the problem itself? Doesn't my
theory contradict itself? How, then, could there be science at all?
576 alternatively, the behavioral rule 577 Please note that I am not just saying that we can have a conception of the mind, but rather that mind itself is a
single (functional) concept (== rule) of a "higher dimension".
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4. Chapter 3 makes the first thrust towards the resolution of this epistemological
problem, (created by the combination of the first two theses). It also lays the groundwork for a
solution of the metaphysical problem of existence -i.e. "Where could a mind exist?". Framing
my argument in the context of Maturana and Varela's "Tree of Knowledge", (and specifically in
their concept of "structural coupling"), I argue an initial Kantian conclusion of "substantia
phaenomenon" confirming what I consider to be the two minimal and necessary (Kantian578)
realist assumptions: the "axiom of externality" and the "axiom of experience". (These will also
lay the foundation for my solution of the problem of existence.)
5. Building on the groundwork of chapter 3, chapter 4 tackles the epistemological
difficulty head-on. Building on -and delimiting- Cassirer's thesis of "symbolic forms", (itself
rigorously based in actual scientific methodology), I argue that knowledge is not referential, but
organizational. With Cassirer, I argue that the essential flaw in the referential conception of
knowledge, ("scientific realism"), lies in its confusion of a particular "frame of reference", i.e.
"symbolic form", (and its assumption that there is only one comprehensive frame possible579),
with the invariant relationality of experience in the abstract, (i.e. under all consistent frames).
This, we argue, is the heart of the issue. It results in a confusion of a specific organization of
experience with the experience itself,580 which is organized. It results in an (improper)
assignment of (unique) metaphysical reference rather than a (legitimate) judgement of
empirical, (i.e. experiential), adequacy for the primitives of the theory. I believe that Cassirer
was, in fact, very much a modern "antirealist"581, (though I question the ultimate scope of his
conception), and argue that his essential solution is, in Van Fraassen's terminology, "coordinate-
578 who, I argue, was very much a realist! 579 i.e. Naturalism 580 to include scientific experiment as an extension of ordinary experience 581 a word I consider to be a total misnomer
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free". His reformulation of the formal logical concept, (/category), allows a new logical
possibility and an escape from the dilemma.
Just as Einstein relativized measurement and disembodied the ether, so did Cassirer
argue for a scientific relativization of knowledge, and a disembodiment of direct reference. But
Cassirer's is not a frivolous, laissez-faire relativism, (nor is it solipsism); it is an explicit and
technical -I might well say "mathematical" epistemological relativity rigorously grounded in the
phenomenology of science.582
I argue beyond Cassirer however that "experience" itself may be defined as precisely the
relativistic invariant under all consistent and comprehensive worldviews, (forms). The
relativism that I argue is a rigorous one grounded in the principles of science; its invariants are
experience. This conclusion, I maintain, resolves the epistemological problem created by my
first theses.
Nowhere does Cassirer, nor do I, question the profound effectiveness or the legitimacy
of modern science. His orientation is wholly and profoundly scientific. Rather, the various
sciences are preserved as perspectives, as organizations of phenomena. Cassirer has provided
the tools necessary to resolve the epistemological dilemma created by the combination of my
first and second theses.
For even though my thesis assumes the validity of the Naturalist organization, (at least
on the human scale), it does not assume the metaphysical reality of Naturalism's primitives
thereby. In questioning our actual, (referential), cognition of metaphysical reality, it is not,
therefore, innately self-contradictory! Though stated in Naturalist terms, (as a legitimate but
582 Why is Einstein not saying that any measurements, (at all!), are valid? Why is Einstein's itself not a
laissez-faire physical relativism? It is because there is a rigid structure at the core of his assertion -i.e. the specific, (and precise), invariant equations of relativity. It is the rigid and invariant "equations", (alternatively "the topology"), of experience that structure valid theories. These "equations", this "topology", must be retained as invariant(s) under all viable theories. This is why neither mine, nor Cassirer's, is an irenic relativism. Also see my discussion of the “ideals” of Abstract Algebra.
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relative organization -and its terms as "focal points" of that organization), my thesis can
consistently and legitimately question the actual (metaphysical) existence of, (and even the
possibility of knowledge of), absolute referents of those terms!
Repeating my conclusion of chapter 4: the results of my first two theses are therefore
consistent under this epistemological rationale. The resolution lies in the scientifically and
mathematically, (but most certainly not arbitrarily), conceived relativization of knowledge
itself. Relational implications, predictive systems, (to include scientific theories), are not, (with
Quine), epistemologically determinate. Rather, their essence, (which is their predictivity), can
be isolated, (following Cassirer), as relational invariants, (in a mathematical sense), over the
field of consistent hypotheses in a sense parallel to that in which Einstein's equations of special
relativity were isolated as invariants from the "ether" in which they were originally grounded by
Lorentz. Or, rather, relational implications are invariant, but predictive organizations, (i.e.
theories), even comprehensive ones, are not! They are the (better or worse), "SUPERB" or
"MISGUIDED"583 "forms" which organize those implications.
It is in Cassirer's sense of the organizational,584 rather than the referential relevance of
theories that I propose that the relations of ordinary Naturalism -and my own thesis as well- can
be, (must be), retained in a deeper realism.
6. Building on the results of chapters 3 and 4, chapter 5 proposes an actual solution to the
problem of the "substance", (the "figment" in Dennett's mocking characterization), of mind.
But the problem has now, (by virtue of the perspectives gained in chapters 3 and 4), been
considerably simplified.
583 cf Penrose "The Emperor's New Mind" (his CAPS!)
584 i.e. as organizations of phenomena
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nt!
I propose that the actual and metaphysical basis for mind is already presumed under any
and all realist, (i.e. not idealistic), conceptions of reality. And that presumption is that of the
interface itself -i.e. the connectivity necessarily, (a priori), presumed, (howsoever it may be
reduced/explanatorily-oriented under any particular conception), between a cognating entity and
the external reality in which it exists. It is that minimal interface itself, conceived in its most
abstract and minimal sense, (as a limit) -the intersection of necessity of all realist theories-
which I maintain, (as a realist), therefore metaphysically exists! It is apodictic, (by definition),
under all realist worldviews.
But I maintain furthermore that this minimal, (and analytically conceived), interface is
sufficient to the problem of the substance of mind as well. If it is assumed that this (minimal)
interface (metaphysically) exists,585 and if it is furthermore assumed that it is structured as
postulated in my first two hypotheses, then mind itself (metaphysically) exists! It fully and
internally defines -and knows586- its objects! This is my third hypothesis. I conclude that we,
as minds, are (metaphysically == truly) real! We do (metaphysically == actually) exist! We
are sentie
The problem of substance was caused, I argue, by Naturalism's overstrong metaphysical
presumptions which left no room for, and concealed the possibility for a (metaphysical) reality
of mind. To repeat myself, the problem was that (Van Fraassen's) "egg" of Naturalist
metaphysics was just too full and left no room for anything else. Or, rather, we were ignoring
the shell!
End of Outline.
585 which, as realists, we must 586 i.e. it does not just "account for" them
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In a serious, (and regrettable), way I suppose that the form and the order of my
argument is in itself confusing -it is certainly complex. But it is complex, necessarily I think,
because I am proposing a very different paradigm wherein even the simplest questions demand
new answers. On the most general level of organization, I argue backwards, (analytically).
rather than forwards, (synthetically), but I feel the nature of the subject, and the demands of
comprehension compel me to do so. Each of the three steps reorients and reevaluates, (and to
some extent invalidates), the one before it. They are each, as Kant calls such a move, a
"Copernican revolution", and this disorientation is in the very nature of such moves. There is
good precedent for such a plan, however. They have constituted the most effective and the
most critical strategies of our intellectual history and are the actual record of our scientific
advance. It is also the way we necessarily learned in school. Before we could adopt more
sophisticated perspectives, we were required to "learn our facts" in more simplistic settings.
Do not be confused. I have, for the most part, talked the language of ordinary
Naturalism -as I must and should. It is good language. We must accept the reality of the
experience which we necessarily (?) describe in Naturalist terms. But we needn't thereby accept
the absolute reference which Naturalists demand. I argue, ultimately, that our naive, human-
scale world stands to the ultimate reality beyond it in the same relationship that modern physics
does, i.e. that of ontic indeterminism.
8. I equate the ultimate worth of my theory with the practical and pragmatic results it
will, (or will not!), ultimately generate. Though I, (personally), feel it is innately beautiful, it is
certainly a large meal to swallow. But just as the (beautiful and esoteric) theories of modern
physics damage our naive psyche, so do they produce immediate, practical, and unarguable
results, impossible without them. So do I propose that my thesis will produce the immediate
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and pragmatic results vis a vis neuroscience, (amongst other things), that we so desperately
need. The mind-body problem is the key to the whole of human culture, and I believe that I
have supplied its first truly plausible solution.
Question: on what basis did we ever presume that the foundations of biology,
philosophy and psychology were necessarily more simplistic than those of modern physics? If
the solution to the mind-body problem were that easy, would it not be a long settled question?
9. Mine is a realist theory. It is not idealism, no more than was Kant's. Rather, (repeating
Kant's claim), it bridges the gap between realism and idealism and resolves their differences. It
resolves the mind-body problem and is eminently compatible with contemporary science.
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Appendix H : Extended Abstract
This book presents a tentative but comprehensive solution to the mind-body problem.
The approach is classical rather than merely technically innovative, and triangulates the answer
between three distinct but related theses: one biological and evolutionary, one logical, and one
epistemological. Though individually controversial, I argue that together they constitute the
first plausible and truly adequate answer to the mind-body problem.
1. My first hypothesis, (in agreement with Maturana and Varela, Freeman and Edelman, for
instance), asserts that the brains of organisms, (human or otherwise), do not embody
representations of their environment as realists generally assert. I propose further, however,
that the "objects" of those brains embody schematic and virtual organizations of reactive
biological process instead. I propose that their primary evolutionary purpose was to enable an
internal operational and calculational simplicity uniquely empowered by a virtual object. I
argue that this simplicity and its implicit efficiency was necessary for the adroit functioning of
profoundly complex metacellular beings in a hostile environment. This purpose, I argue
furthermore, was actually antithetical to a representative role. (The apparently self-defeating
epistemological implications are resolved in my third thesis.)
2. Contrary to Dennett, Hofstadter, Churchland, et al, my second hypothesis asserts that the
problems of sentiency –of consciousness: the "homunculus" problem, the "mind's eye", "the
Cartesian theatre",... are capable of solution, (and I have proposed an explicit one). Indeed they
must be if mind in our ordinary sense of the term is to exist at all. But they are not solvable
within the confines of classical Aristotelian logic or its modern embodiments. Current logic,
still based essentially in the Aristotelian, (i.e. "generic"), formal concept, is inadequate, I
maintain, for the specifically logical problems implicit in the mind-brain problem. Building on
Ernst Cassirer's innovative rule-based, (rather than property-based), reformulation of the
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classical concept itself, (his "functional concept of mathematics"), and a new application of
David Hilbert's brilliant logical reorientation of mathematics onto purely axiomatic grounds:
"implicit definition", (as strongly distinguished from his "Formalism"), I propose a further
extension of Cassirer's technical Concept, (and its subsequent logic), largely equivalent to the
complex rule of an axiom system. It is the “Concept of Implicit Definition”, (CID). Following
and extending Cassirer's cogent arguments, dualism and opposition, (innate in classical logic
and themselves the basis of the “homunculus”, I argue), are then no longer innate in this new
Concept. As Cassirer argued for his own “Functional Concept of Mathematics”, CID no longer
derives from presentation vs. attention and abstraction in cognition- which latter is generally
accepted as the theoretical basis of the classical Concept, but is unary and internally, (i.e.
logically), resolving of its objects in the sense of modern mathematics. The extended Concept,
(CID), is no longer confined to intellectual cognition, (i.e. logic and concepts), however, but is
adequate to perceptual cognition, (i.e. "objects"), as well. It is part of a constitutive logic in the
sense envisaged by Kant. In concert with the first hypothesis, (non-representation == "not
presentation"), it allows a solution of the logical problem by permitting cognition and "objects"
without presentation and the latter's implicit oppositional "cognator" -i.e. without a homonculus.
Reconceiving brain function as organization rather than representation allows mind and
cognition in our ordinary, unified sense.
A significant corollary of this hypothesis is that it allows mind to be productively
defined as the biologically logical, (i.e. operative), "concept", (as an expression of the
behavioral rule), of the brain. (But here "logical" itself and "concept" itself are taken in a
reductively materialist sense.) This is an important result since I have argued that it is only in
taking our objects as specifically logical objects that the homunculus problem can be solved,
and it shows the relevance of that conclusion to the biological problem. But the "logic" just
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mentioned is biological logic in the sense of the first hypothesis. It is the “calculus” of our
biological “schematic model”.
3. My third hypothesis is epistemological, an extension of Kant's, and ultimately of Cassirer's
epistemology. Its purpose is to reconcile the apparent self-contradictions of the first two
hypotheses and to supply, as well, a plausible answer to the "what" of mind. Expanding on,
(and modifying), another of Cassirer's original conceptions, his theory of "Symbolic Forms", it
resolves both the problem of reference raised by my prior theses and that of their seeming
inconsistency as well, (their being stated in the very language of reference). Arguing from
Hertzian grounds, Cassirer maintained that our knowledge is organizational, (as an organization
of the phenomena), rather than metaphysically referential. There is, he argued therefore, a
plurality of alternative and equipotent (symbolic) "forms", (and their concomitant "objects"),
corresponding to different possible organizations of the phenomena and different organizational
intents.587 It is the confusion of (the "objects" of) a particular form with the invariant
relationality of the phenomena which it organizes, he argued, which leads to an unwarranted
assertion of metaphysical reference for its objects. His is, as Swabey stated it, a genuine
"epistemological theory of relativity". I argue that it is "coordinate free", (and non-referential),
in Van Fraassen's sense as well. It allows my first and second hypotheses to stand as consistent,
though relativistic, organizations of the phenomena using the language of naturalism, but
without the latter’s commitment to reference. I further argue an essentially Kantian position
consistent with Cassirer's to reduce the de facto metaphysical presumptions of naturalism to
their legitimate and necessary minimum. This, surprisingly, leaves room for the actual
existence of a "substance" of mind for which I propose a specific and plausible answer.
587 This is clearly parallel in many respects to the function and intent of Lakoff’s “Idealized Cognitive Models”!
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There remain, of course, significant problems. The most obvious of which still remains
"reference". But I argue that there is a categorical difference between metaphysical reference
and the internal, model/model automorphisms of what I maintain is our logically closed human
cognitive world. (cf Quine). It is the latter which constitute the problem of science, and I have
suggested a particular kind of automorphism between the brain and the world. (See Appendix
B).
However totally "antirealistic" it may sound, I will argue that my thesis is more compatible
with contemporary science than any alternative currently proposed. It preserves science and
ordinary experience as well.
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Afterward: Lakoff, Edelman, and “Hierarchy”
As I mentioned in the Introduction, I had not seen George Lakoff’s “Women, Fire, and
Dangerous Things” nor Gerald Edelman’s “Bright Air, Brilliant Fire" until very recently. It was
remarkable to me, therefore, to see how closely Lakoff’s logical and epistemological
conclusions resembled those of Cassirer588, (considered as the combination of Cassirer’s dual
theses: his logical thesis of “the functional Concept of mathematics" and his epistemological
thesis of “Symbolic Forms”), and how closely Edelman’s biological and philosophical
answers, based in Lakoff’s and his own original work, resembled my own conclusions. There
is an uncanny parallelism of structure, (though not of consequence), between the paths we have
followed to arrive at our conclusions.
Our structural differences are differences of degree –but important differences. I believe
that Lakoff, (and Edelman), have gone too far in the case of logic, and not far enough in the
case of epistemology. They fail589, crucially thereby, to provide the grounds for an answer to
the ultimate problem: i.e. how can “mind” or “consciousness”, (normally taken) coexist with the
existence of the brain?
Lakoff:
Lakoff grounds his work in logical reflections of Wittgenstein590 which questioned the
adequacy of the classical logical Concept and in the work of Rosch and a host of modern
empirical researchers which further challenged that classical Concept by demonstrating
exceptions in actual human usage of language and concepts across cultures and even within
588 Of which Lakoff, apparently, was unaware 589 -innocently for Lakoff who never promised such an answer, but more pointedly for Edelman who did 590 E.g. Wittgenstein’s “family resemblances”
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e
our own legitimate contemporary usage. From these grounds and his own original work,
Lakoff drew strong conclusions about the nature of logic591 –and the human mind- itself.
The Classical Concept
The classical concept592 is defined “by necessary and sufficient conditions” -that is,
by set theoretic definitions on properties. It is an elementary theorem of logic that the whole
of the operations of sentential logic, for instance, may be grounded solely in the primitiv
operations of intersection and complement.593 More generally, logical sets and categories,
(concepts594), are defined on presumed “atomic properties” and are commensurable wholly
based on the set-theoretic possibilities of those sets –i.e. union, intersection, complement, etc.
Concept-sets, (within this classical perspective), express a hierarchical “container
schema” moreover, (using Lakoff’s language). Though Lakoff frames his discussion to the
same end slightly differently, by this I mean that whenever we classically specify a genus, we
do so by eliminating one or more of these atomic properties, (by intersection of the properties
of species), at the same time thereby specifying an expanded extension, (union) –i.e. the set of
“objects” which the genus concept encompasses. The delimitation, (by property
containment), of the genus category is contained within, (is a subset - an intersection of), that
of the species category while the extension of the species category, conversely, is contained
within, (is a subset of), the extension of the genus category. In specifying a species category
591 compare Cassirer: "... Every attempt to transform logic must concentrate above all upon this one point: all
criticism of formal logic is comprised in criticism of the general doctrine of the construction of concepts." –cited at the beginning of my Chapter 2.
592 Lakoff is concerned with primarily with categories, but the distinction is technical and not necessary to this discussion. Cassirer dealt specifically with concepts, but he covered essentially the same ground.
593 Or on other subsets of set operations as well
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on the other hand, we do so by adding one or more properties –ultimately “atomic properties”
to the properties of the genus concept and this species concept encompasses a diminished,
(intersectional), extension of the extension of the genus.595 This classical categorization
therefore expresses an absolute, rigid and nested hierarchy of levels and containment. In
Lakoff’s terms it expresses a hierarchical “container schema”.596
Ultimately, (because they are nested), at the limits these processes specify (1) a
largest concept: “something”, (defined by no atomic properties), whose extension is
“everything”, and (2) a smallest concept: a particular “object” in reality, (or possible reality),
defined by all its atomic properties597. Given the classical paradigm then, reason necessarily
begins with “something”, (the most general concept), and points, inexorably, to some ”thing”,
i.e. a specific object.598
But Lakoff plausibly argues that concepts599 in legitimate human usage are actually
determined by any rule, (to include the classical rules of set operations on properties as just
one special case of a rule), or even by no rule at all ! Thus metaphorically based categories,
such as the Japanese concept of “hon” are generated, (determined by), a metaphoric rule of
extension and metonymically based categories are generated by a rule of metonymy.
(Metonymy is the case where one instance of a category is made to stand for the category.)
“Don’t let El Salvador” become another Vietnam” is an example Lakoff uses of a
594 See prior footnote: categories vs. concepts 595 “Cross categorization”, the “other . . . classical … principle of organization for categories” refers to the various
possibilities at any stage of genus or species categorization – on the particular choices of which “atomic properties” are to be eliminated or added. Cf Lakoff pps. 166-167
596 ibid 597 to include spatio-temporal properties 598 or the exact converse –i.e. beginning with some specific object or objects in reality or possible reality and
ending with everything!
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metonymically based category.600 Here “Vietnam” stands for the concept of all hopeless,
unending …. wars.
In the case of “radial categories”, such as the concept of “mother”, (to include birth
mother, adoptive mother, foster mother, surrogate mother, etc.), or of “Balam”601 in the
Dyirbal aboriginal language in Australia, they are determined by simple historical accident –
they are not generated from the central model by general rules .. [but] .. must be learned one
by one.”602 (Extensions from the central model are not “random” however, but are
“motivated”, his emphasis, “by the central model plus certain general principles of
extension.”)603
He argues his case rigorously and scientifically by exhibiting myriad examples that
are not compliant with the classical Concept and analytically by demonstrating the
degradation of concepts in actual bi-cultural environments –i.e. where a culture and language
is being overrun by another, (“language death”), as is the case with the Dyirbal aboriginal
language in modern Australia.604 The degradation is characterized by the loss of blocks of
suborganizations, not of random individual elements.
599 he would say “categories” 600 P. 77. Actually I like his “ham sandwich” better, but it was pre-empted by Edelman! 601 The category which is the source of his title and includes, among other things, women, fire, and dangerous
things. 602 Lakoff, P.91 603 As I will repeat later, this discussion of Lakoff’s thesis is woefully inadequate, but it will have to do for the
purposes of this appendix. He states as the “main thesis of [his] book .. that we organize our knowledge by means of structures called idealized cognitive models, or ICMs, and that category structures and prototype effects are by-products of that organization.” Ibid, p.68
604 See Lakoff, pps. 96-102
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Lakoff’s logic is not trivialized by this “free formation” of concepts however, (as it
might seem it would be605- logic being [paraphrase] “mostly concerned with categories”), as
he bases logic and the relevance of concepts ultimately in a preconceptual context rather than
in the concepts themselves. Concepts, (categories), he argues, are not created in a vacuum,
but within preconceptual schemas: “idealized cognitive models”, (ICMs). The latter are
ultimately determined, (he argues), by the function of the body in the external world–all
describable from “body in the world”.
“There are at least two kinds of structure in our preconceptual experiences:
A. Basic-Level structure: Basic-level categories are defined by the convergence of our
gestalt perception, our capacity for bodily movement, and our ability to form rich
mental images.
B. Kinesthetic image-schematic structure: Image schemas are relatively simple
structures that constantly recur in our everyday bodily experience: CONTAINERS,
PATHS, LINKS, FORCES, BALANCE, and in various orientations and relations: UP-
These schemas, however, being at the basis of our reasoning607, are necessarily
mutually relativistic and equipotent and we utilize them on a “best fit” rationale. The
605 If, according to Lakoff, (1) legitimate concepts may be formed on any principle or no principle, and if, also
according to Lakoff, (2), most of the business of logic is concepts, (categories), then it would appear, (at first glance), that (3) logic could prove any conclusion. But if logic can prove anything, then it can prove nothing! Thus it would appear, on the face of it, that his purported impossibility of a rigorous, comprehensive structure for categories in general would imply the invalidation of logic in general.
606 Lakoff, p.267. 607 rather than categories
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concepts that arise within them need not be commensurate across them. Thus he arrives at a
relativism of logic and concepts.
Lakoff’s Concept/category in many ways resembles Cassirer’s608 and he rejects, (as does
Cassirer), the classical “necessary and sufficient conditions”, (as he phrases it), which
ground set theoretic abstraction and the Aristotelian generic Concept. His logical and
ultimately epistemological relativism, (in his “idealized cognitive models”), is also very
similar to, (though it is not as abstract and comprehensive as), Cassirer's “Symbolic Forms”
which is described in my Chapter 4.
Cassirer and Lakoff’s Logic
Cassirer rejected the logical sufficiency of classical categorization as does Lakoff, but
he did not reject the possibility of any absolute, comprehensive structure for categories, (which
Lakoff does). Instead Cassirer retained an overall formal structure for categorization in the
notion of a mathematical functional rule or series.
Cassirer did not question the legitimacy of the classical schema, but he did question its
necessity and sufficiency. (Which is pretty much where Lakoff and myself stand as well.) He
608 There is an uncanny parallelism of argument throughout between Lakoff’s and Cassirer’s treatment of logic.
Consider, as an example, the following:
“Category cue validity defined for such psychological (or interactional) attributes might correlate“, (his emphasis), “with basic-level categorization, but it would not pick out basic-level categories; they would already have to have been picked out in order to apply the definition of category of category cue validity so that there was such a correlation.” (Lakoff: P.54, my emphasis) This is almost an exact parallel to one aspect of Cassirer’s argument against the classical concept, and the “theory of attention”, (see my Chapter 2), –and for a “new form of consciousness”.
Discussing Erdman, Cassirer writes: “…instead of the community of ‘marks,’ the unification of elements in a concept is decided by their ‘connection by implication.’ And this criterion, here only introduced by way of supplement and as a secondary aspect, proves on closer analysis to be the real logical prius; “ (his emphasis), “for we have already seen that ‘abstraction’ remains aimless and unmeaning if it does not consider the elements from which it takes the concept to be from the first arranged and connected by a certain relation.” Cassirer, “Substance and Function”, p.24
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argued that it is, in fact, a special and limit case of the Concept and of the possibilities of logic.
Cassirer maintained that many concepts –and specifically the very concepts of mathematical
and physical science609 –demonstrate another mode of concept formation and specification than
the classical scheme, (this is the subject of my Chapter 2). Both concept formation upward,
(genera), and downward, (species), can obey another rule-based law, i.e. the properties of their
extensions can embody a series other than the specific series of identity. As a crude example,
one member of the extension of a concept, (using an example drawn from numeric sets), might
contain the numeral “2”, another the numeral “4”, another “8”, “16”… rather than the numeral
“2” being in all of them. Thus the concept would express, (and be formed on the principle of),
the series 2,4,8,16,… across its extension rather than being based in the series of identity: 2, 2,
2,…. , (the classical schema). The extension of a category, therefore, may be defined based
upon the possession of some property belonging to a series or function on properties rather than
on the possession of some identical property(ies). Concepts can be specified by a function
other than identity. 610
Cassirer has supplied a clear counterexample and an alternative to the classical
schema, (which I explained at length and further extended as the subject of Chapter 2).
Simplistically, (and as crude illustration), we may have three pieces of “metal” in front of us
for instance, wherein none of their properties are the same! The first is a one pound piece of
gold, (color: yellow, specific gravity: a.aaaa…., conductivity: b.bbbb…., etc.), the second a
two pound piece of lead, (color: gray, specific gravity: l.lll…, conductivity: m.mmm…., etc),
609 Cf Cassirer, “Substance and Function”, “Einstein’s Theory of Relativity”. Incidentally, the original title for
“Substance and Function” was “Substanzbegriff und Funktionsbegriff”, i.e. Substance Concepts and Function Concepts!
610 Cassirer's "series" could be ordered by radically variant principles, however: "according to equality", (which is the special case of the "generic concept"), "or inequality, number and magnitude, spatial and temporal relations, or causal dependence"610 -so long as the principle is definite and consistent. But please remember that these are principles of category construction rather than properties of categories. see my Chapter 2
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and the third a three pound piece of tin: (…, …., …., etc.) None of these properties need be
identical however. They are related as “metal”, (and are specified as “metal objects”),
because the color of each, (for instance), is a value of the function COL(x) ε {yellow, gray,
silver,…), the specific gravity of each is a value of the function SG(x) ε {lll…, ggg…, …},
and so on. These objects, (the objects called “metal objects”), can “cross party lines”, so to
speak –i.e. they are not the product of strict set-theoretic intersection of atomic properties. In
the illustration their intersection across these properties is null! The extension of scientific
and mathematical concepts, (specifically, Cassirer argues), need have no atomic properties in
common611 . Repeating a short citation from my Chapter 2:
"Lambert pointed out that it was the exclusive merit of mathematical 'general concepts'
not to cancel the determinations of the special cases, but in all strictness fully to retain
them. When a mathematician makes his formula more general, this means not only that
he is to retain all the more special cases, but also be able to deduce them from the
universal formula."612
But this possibility of deduction does not exist in the case of the scholastic,
(Aristotelian), concepts, "since these, according to the traditional formula, are formed by
neglecting the particular, and hence the reproduction of the particular moments of the concept
seems excluded."613
611 Compare Wittgenstein’s “family resemblances”. 612 Cassirer, “Substance and Function”, P.20-23 613 ibid P.20-23, my emphasis
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f
"The ideal of a scientific concept here appears in opposition to the schematic general
presentation which is expressed by a mere word. The genuine concept does not
disregard the peculiarities and particularities which it holds under it, but seeks to show
the necessity of the occurrence and connection of just these particularities. What it gives
is a universal rule for the connection of the particulars themselves.... Fixed properties
are replaced by universal rules that permit us to survey a total series of possible
determinations at a single glance."614
Consider “the ellipse as a simple mathematical example of a genus” for instance. Its
species are functionally related –and fully recoverable- in the defining equation of ellipses in
general.
Conversely in the specification of species and subspecies, (“downward”), the process
does not necessarily lie in the addition of (identical) atomic properties either, (the members of
the extension of a subspecies, which is also a category, need not contain (any) identical
atomic properties by the same reasoning), but can be accomplished instead in the
identification of the value of a sub-function whose possibility is implicit within the genus.615
Ultimately, (and recursively), the question proposes itself: need there be a lowest, “bottom”
level concept at all?616 Speciation is no longer necessarily intersection or containment,617 (it
is no longer necessarily nested), so there is always the possibility of another, further rule o
614 ibid P.20-23
615 Since we can build a genus without commonality, so can we build a super-genus. Turning our perspective around, then, we may speciate downward from that super-genus without the utilization of commonality!
616 The other pole is clearly impossible. There is clearly no Concept, (category), of all concepts under Cassirer’s vision as it would necessarily be defined on “the rule of all rules”. But some, (most), rules are obviously inconsistent with other rules –disallowing the concept.
617 Since there is no longer a necessary presumption of nesting, the implication that there must be a “least member” is no longer justified.
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assembly for a subspecies of any species –at any level!618 There is thus no longer a
necessary logical focus on an ultimate “thing”.
Cassirer argues that the ultimate “objects” , (the “theoretical objects”), of mathematics
and physical science are “implicitly defined” by, (and express), the fundamental laws of the
science itself. He argues that they are instances of complex speciation based in the general
functional rules, (the laws), of the sciences themselves and not objects “in reality”.
Some of Lakoff’s categories, it is true, are also rule based, (other than the classical
rule), but in the case of his “radial categories”, they may be formed by historical accident.
Lakoff concluded that categories may be formed by classical rules, other rules or “no rule at
all”! But this characterization divorces him from the possibility of any universally
comprehensive categorical structure.619 Cassirer includes this special latter case as an ad hoc
rule, (series), however, rather than as an example of “no rule”. It would correspond to the
special case in mathematical set theory wherein a set is defined by the explicit listing of its
members. Cassirer’s conception may be likened to a line segment bounded on one end by the
classical criterion of identity of properties across members, (a “unity”), with the central
section composed of any and all functional rules, (i.e. rules of series/regular functions on
those properties), and bounded at the other end by the rule of explicit listing, i.e. no other rule,
(a “zero”). This view reconciles the two conceptions, I think, and might be acceptable to
Lakoff.620 What it does besides, however, is reveal a comprehensive structure across the
whole of categories/concepts.
618 Remember that under Cassirer's Concept, we do not eliminate properties to speciate, but rather functions. 619 Cf: the discussion of the crucial role of comprehensiveness vis a vis mathematical ideals
near the end of this Afterword. 620 Compare Lakoff, p.146 : “in the classical theory, you have two choices for characterizing set membership: you
can predict the members (by precise necessary and sufficient conditions, or by rule), or you can arbitrarily list
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I have suggested a further extension beyond Cassirer’s “Functional Concept” and sets
of n-tuples however in my arguments of Chapter 2. Just why is the color of “gold-metal”
yellow instead of gray? Why is “gold” a particular n-tuple rather than some other mix of
possible place-values? Physical scientists will never agree with Lakoff, for instance, that it
could be just an (accidental) property of a “radial category”, nor, possibly even with Cassirer,
that it is simply an element in a multi-place series. They will insist that it must be a necessary
property determined by physical law. Cassirer apparently glimpsed this connection in his
conception of the “ideal objects” of the sciences, but he never fully exploited it. (I have
pursued it in my “Concept of Implicit Definition”.621)
Both Lakoff and Cassirer followed the paths of their logical conclusions to see the
essential flaw in “naïve realism”, (as Cassirer termed it), and “objectivism”, in Lakoff’s
words, (I have used the term “naturalism”). If the classical logical schema of strict
hierarchical containment were legitimate, and, more importantly, if it were necessary and
sufficient, then the only possibility of science, as the resolution of experience and reality with
logic, would lie in the absolute objective existence, (however reduced), of our ordinary
objects. If valid logic and conceptualization is broader than that, however, then the possibility
of reality is considerably enriched. Valid conceptual, (or utilitarian cognitive), “objects”
them, if there is a finite list. The only choices are predictability (using rules or necessary and sufficient conditions) and arbitrariness (giving a list). But in a theory of natural categorization, the concept of motivation”, (his emphasis), “is available. Cases that are fully motivated are predictable and those that are totally unmotivated are arbitrary. But most cases fall in between –they are partly motivated.”
Cassirer suggested another, (and more classical), “middle ground” wherein the principle of “necessary and sufficient” is not grounded in an identity of properties, but in a functional relationship between them. The relationship between their proposals is more complex than is possible to describe here, but as a thumbnail sketch of my opinion, the deficiencies in the classical category that Cassirer resolves in his “Functional Concept of Mathematics”, Lakoff attributes to his Cognitive Models whereas the deficiencies in classical metaphysics are resolved by both of them very similarly in the epistemological relativity of “Symbolic Forms” by Cassirer and of “ICM’s” by Lakoff. Cassirer’s is the more general of the two solutions to the latter problem, however, as it is not framed within a specific image of the world, but within the constraints only of abstract epistemology as Kant definitively iterated them.
621 Cf my Chapter 2
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need not then express “membranes” around spatio-temporally contiguous properties of
ontological, (i.e. metaphysical), objects or groups of such objects!622 They can “cross party
lines”!
Cassirer had no problems with such an implication. It was implicit, of course, in his
neo-Kantian origins. Lakoff did. In his laudable commitment to realism, he was forced to
consider the minimal necessary requirements of such a (scientific) realism.623
He lists Putnam’s requirements of “internal realism”624
as:
(1) “A commitment to the existence of a real world external to human beings
(2) a link between conceptual schemes and the world via real human experience;
experience is not purely internal, but is constrained at every instant by the real world of
which we are an inextricable part
(3) a concept of truth that is based not only on internal coherence and “rational
acceptability”, but, most important, on coherence with our constant real experience
(4) a commitment to the possibility of real human knowledge of the world.”625
He has extended and refined Putnam’s position somewhat from this basis, (his “basic
realism”), to be able to answer certain further questions that arise, but this is a reasonably
622 This discussion constitutes my answer to one of the more difficult objections to my first thesis wherein it is
objected that “schematism” is “just a level of abstraction”, (Richard Reiner, private communication). The discussion above shows why it need not be!
623 The criteria of Putnam’s, Lakoff’s and Edelman’s basic realism are, I have argued in my chapters 3 and 4, essentially the same ones definitively identified by Kant. Kant is grossly mischaracterized as an “idealist”. He was, in fact, the penultimate modern realist in just the sense demanded by these thinkers. See chapters 3 and 4.
624 Which he uses as the jumping off point for his own “experiential realism”. Edelman, incidentally, has adopted Putnam’s definition pretty much “as is”.
625 P.263
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concise rendition of his stance vis a vis realism. I have discussed his position, (as reiterated
by Edelman), briefly in the preface to my Chapter 2, wherein I agreed with (1) – (3), but
strongly qualified (4). I had argued the equivalent of his essential conclusions as the subjects
of my chapters 3 and 4, i.e. the (bare) “axiom of externality”, and the (bare) “axiom of
experience” respectively. Because of his conclusions, Lakoff was further forced into a
position of epistemological, (as well as logical), relativism –against what has been called a
“God-eye view of reality”.626
Lakoff’s relativism, necessary because of his logical conclusions but challenged in
his own mind, (admirably, I maintain, as I consider myself a strong realist as well), by his
fervent commitment to science and realism, is ill-defined however. Though he talks about
relativism at length, he never clearly defines it. He begins by noting the anathema which
“relativism” is considered by the scientific world, but argues that there are, in fact, many
different forms of relativism. (Neither he, nor I, advocate a “relativism of everything”.) The
most cogent interpretation I can give to it, (Whorf aside), is that he advocates a cognitive and
logical relativism based on bodily function, (in the world), which leads to a relativism of
contexts, (ICM’s), which employ different categorical, (conceptual), schemas. Within each of
these ICM’s, there does exist a structure consistent with rigor, however,627 but ultimately the
ICM’s themselves are relativistic.
I like what Lakoff has done, (hugely!), but his ICMs, the relativism in which he has
based them, and his epistemology are deficient insofar as they are all derived from, (grounded
in the concept of), the human body and the functions of that body in the world. This is his
626 cf my chapter 4 for a discussion of Cassirer’s arguments on the same subject and of my extension of them.
627 “The main thesis of this book is that we organize our knowledge by means of structures called idealized cognitive models, or ICM’s, and that category structures and prototype effects are by-products of that organization..” Lakoff, 1987, p.68, his emphasis.
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overview, and this is the context within which they are framed. That very body in the world is
conceived in the primary set theoretic sense, (he would call it the “container schema” ICM),
however! But if they all may be described within the container schema, (the body in the
world), then ultimately all of his ICMs and his epistemology are theoretically reducible to a
container schema! This is a contradiction of his own position against a “God’s eye” picture of
the world.628 It is the generality of Cassirer’s solutions629and of my extensions of them,
(founded ultimately in a neo-Kantian perspective), which allows the solution of the general
logical and ultimately of the epistemological problems.
Though Lakoff rejects the view that “anything goes” –that any conceptual system is as
good as any other, nowhere does he approach the possibility of a scientific, mathematical
relativism which would give rigor to his conceptions –save within a tacit objectivist context.
It is the possibility of a general and comprehensive structure of the Concept which
allows the true relativity of the essential forms/ICMs. I will argue shortly, in the context of
mathematical “ideals”, that the various “generators” of such an ideal must each be capable of
generating the whole of the “space” of that ideal –to include all possible alternative generators
as well. Thus each (legitimate) structure must be comprehensive to be translatable, (i.e. capable
of itself being generated by another set of generators). But its concepts/categories/objects may
be distributed in the translation.630 This is intelligible only outside of the classical conception
of logic, and is the essence of my conclusion of chapter 4. Lakoff’s “Concept” is certainly
broader than the classical concept, but he takes his arguments too far –against any rule of
concept formation.
628 I.e. all his arguments against it are reducible within it. I will have more to say on this subject shortly and will
suggest a way out of his dilemma.
629 and their origins in science and mathematics 630 cf my Chapter 4
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Please do not misunderstand me. I loved Lakoff’s book. It is brilliant, far reaching,
and, I believe, essentially valid. He develops and documents his arguments solidly, but I think
his strongest point is in his clear and cogent examples from our own normal usage631, (as well
as from extensive anthropological studies), which makes his essential case almost
unanswerable. His conception is considerably richer than it is possible to describe within the
confines of an appendix, nor is it as simplistic as I have characterized it. We have huge areas of
agreement and possible interaction, (his and Rosch’s “basic level categories” have a natural
correlate in my “schematic perceptual objects”, for instance.)
Lakoff’s ICMs are biologically based –on the human organism. Human cognition and
human reason consists, for Lakoff, in the application of the best fit of these inbuilt ICM’s, (and
their respective categories), to a given problem or situation. They constitute an “embodied
logic” deriving from the nature of the human organism itself. There is an obvious parallel
between Lakoff’s “embodied logic” and the more general case I have argued. I have argued
that logic is indeed embodied, but at the primitive level of cellular process! This more general
characterization allows the crucial epistemological move,632 (which Lakoff’s does not), beyond
the “God’s eye view” he disclaims.
The distinction is important because at the cellular level of phenomenology biology becomes a
pure form, (in Cassirer's sense and compatible with Cassirer's Hertzian premise). This is
especially transparent in Maturana and Varela's book, for instance, (see chapter 3), i.e. in its
explicit constructiveness and the subsequent purity of their phenomenology.
Citing a few pertinent examples quoted earlier in chapter 3:
631 Cassirer’s case was grounded primarily in scientific examples. 632 Through what Maturana and Varela call “structural coupling”
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"Our intention, therefore, is to proceed scientifically: if we cannot provide a list that
characterizes a living being, why not propose a system that generates all the phenomena
proper to a living being? The evidence that an autopoietic unity has exactly all these
features becomes evident in the light of what we know about the interdependence
between metabolism and cellular structure."
"Autopoietic unities specify biological phenomenology as the phenomenology proper of
those unities", (my emphasis), "with features distinct from physical phenomenology...
because the phenomena they generate in functioning as autopoietic unities depend on
their organization and the way this organization comes about, and not on the physical
nature of their components."
"Ontogeny is the history of structural changes in a particular living being. In this history
each living being begins with an initial structure. This structure conditions the course
of its interactions and restricts the structural changes that the interactions may trigger
in it", (my emphasis). "At the same time, it is born in a particular place, in a medium
that constitutes the ambience in which it emerges and in which it interacts. This
ambience appears to have a structural dynamics of its own, operationally distinct from
the living being. This is a crucial point. As observers, we have distinguished the living
system as a unity from its background and have characterized it as a definite
organization. We have thus distinguished two structures that are going to be considered
operationally independent of each other, (my emphasis), "living being and
environment."
These are purely constructive and operational definitions, (or capable of being made so
within "structural coupling"), in the precise sense of Hertz and Cassirer and clearly mesh with
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the substance of my chapter 4. They are Hertzian "images" with a definite, predictive logical
structure.
At the level of cellular biology therefore, biology becomes a pure form, and, as such, it,
(and the logic I posit within it), is capable of legitimate embodiment633 within the now viable
scientific epistemological relativism espoused by Cassirer and myself. It is this deeper
placement, (and not as reductive physics), which allows an escape from the inconsistent "God's
eye view" implicit in Lakoff's and Edelman's theses, and enables a truly consistent and viable
epistemological relativism.
It is because of Lakoff's Wittgensteinian origins, I think, that he has gone too far, (-and
not far enough). Had he started from Cassirer instead, the case might have been different. I
will return to Lakoff presently to suggest a “cleaner” solution to his problem consistent with his
apparent needs –in the mathematical notion of “ideals”. There is a way to save it, but I think it
is too limited and inconsistent with the dictates of modern biology as espoused, for instance, by
Edelman.
Edelman:
Gerald Edelman has adopted Lakoff’s, (and Putnam’s), logical and epistemological
conclusions as the philosophical underpinning to his own theories of “Neuronal Group
Selection”, (TNGS), and “re-entrant topobiological maps”. He proposed the combined result as
an actual answer to the problem of mind-brain. Though Edelman's is a very plausible theory of
brain development and function, it is limited to dealing with “mind” only reductively -i.e. as
strictly biological and therefore physical process and falls to the same objections that I, (and the
preponderant Naturalist camp as well), have raised. “Mind”, normally taken, is therefore
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superfluous therein! Edelman explicitly denies the “homunculus”, (as do I), but his “Cartesian
theatre” is specifically a physical and spatial one. It is spatially and temporally distributed.
Though he does not explicitly deny the existence of “mind” as ordinarily taken, he tacitly
reinterprets it and reduces it to a description of process. He fits very comfortably, I feel
therefore, within the naturalism, (and “objectivism”), which Dennett, Churchland, et al
espouse.634 I do not question the insightfulness or the importance of Edelman’s work –it is
profoundly important and very solid –but, because of its limitations, (derived from Lakoff), it
falls short of an answer to the problem of consciousness, retains internal inconsistencies, and
does not resolve the mind-body dilemma.
Starting with the nature and limitations of embryology, Edelman makes a case for a very
different concept of “recognition systems”. His exemplar “recognition system” is the immune
system. The immune system, he argues, does not depend on information about the world –i.e.
we do not create new antibodies from informational templates resident in newly arrived
antigens. Rather, science finds that the body randomly generates a huge diversity of antibodies
before the fact and reactively selects from this pre-existing diversity “ex post facto” as he
phrases it. This, the immune system, is a system of process, not of information.
“A recognition system … exists in one physical domain”, (for the immune system it is
within an individual’s body), “ and responds to novelty arising independently in another
domain, (for the immune system it is a foreign molecule among the millions upon millions of
possible chemically different molecules) by a specific binding event and an adaptive cellular
response. It does this without requiring that information about the shape that needs to be
recognized be transferred to the recognizing system at the time when it makes the recognizer
633 i.e. as a legitimate, fundamental "symbolic form" 634 Save on the issue of “information”
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molecules or antibodies. Instead, the recognizing system first generates a diverse population of
antibody molecules and then selects ex post facto those that fit or match. It does this
continually and, for the most part, adaptively.” Edelman, P.78
Cognition, our ultimate “recognition system”, he argues, is a parallel case and must be
reconceived accordingly. Because of the sheer size, and the place and time sensitivity of
embryological neural development, the neural system, (he argues), is progressively “pruned”
ex post facto from random preexisting variety over the stages of its development in like manner
to the immune system.
“given the stochastic (or statistically varying) nature of the developmental driving forces
provided by cellular processes such as cell division, movement, and death, in some
regions of the developing nervous system up to 70 percent of the neurons die before the
structure of that region is completed! In general, therefore, uniquely specified
connections cannot exist.”
“the principles governing these changes are epigenetic –meaning that key events occur
only if certain previous events have taken place. An important consequence is that the
connections among the cells are therefore not precisely prespecified in the genes of the
animal.” Edelman, pps. 23- 25
Of the great diversity of (preexisting) neural connections generated at any stage, particular
connections are reinforced and kept, or pruned and deleted, in tune with place and time
dependent events the scenario of which is too complex “by several orders of magnitude” to be
embodied in the human genome. This pruning is achieved operationally, not informationally.
Embryological development is too complex, too dependent on place and time to be
prespecified. His argument in some ways parallels my own of appendix A wherein I argued
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that there simply hasn’t been enough time in evolutionary history, (nor ever will be), to create
such an information engine.
In his “ex post facto” adaptive “TNGS”, Edelman argues a criterion of competence ,
(as, indeed, did Darwin –and as did I in my first chapter), rather than one of information in the
evolution and development of organisms –and specifically of the human organism.
“The immune selective system has some intriguing properties. First, there is more than
one way to recognize successfully any particular shape. (my emphasis) Second, no two
individuals do it exactly the same way; that is, no two individuals have identical
antibodies. Third, the system has a kind of cellular memory.” Edelman, P.78 (These
comments are directly relevant to my discussion of bounds and limits and the “parallel
postulate” of cognitive science.)
He too disclaims the possibility of a “God’s eye view” by an organism of reality.635 But
competence, as I have argued, does not imply parallelism. It is the question of bounds and
limits that I have argued previously,636 and Edelman falls into the same epistemological trap as
does Lakoff, (and Maturana and Varela as well). Other than this failing, however, I believe his
overall position and arguments are very strong.
On “Presentation”
Edelman challenges ordinary logic and ordinary epistemology, (the classical,
“objectivist”/”naturalist” views), for some of the same reasons that I do. In his TNGS, he has
635 cf: my “Axiom of Externality” and “Axiom of Experience”, (Chapters 3 and 4). 636 Let me repeat a footnote of my Chapter 1: The question, of course, is whether "information" is necessary to
competence. I will argue, (in Chapter 3), that it involves a distinction between "bounds" and "greatest lower bounds" of biologic survival. A given organism, (to include human beings), must reflect a lower bound of competence in the world. But "information" requires that it reflect a greatest lower bound, and this is inconsistent with the fundamental premises of evolution. It is the "parallel postulate" of cognitive science.
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framed the same problem, and reached largely the same conclusion that I did under the issue of
“presentation”.
“some of the reasons for considering brain science a science of recognition", [under his
special definition of "recognition systems" cited above]. " The first reason is almost too
obvious: brain science and the study of behavior are concerned with the adaptive
matching of animals to their environments. In considering brain science as a science of
recognition I am implying that recognition is not an instructive process. No direct
information transfer occurs, just as none occurs in evolutionary or immune processes.
Instead recognition is selective.”
“a potent additional reason for adopting a selective rather than an instructive viewpoint
has to do with the homunculus. …the little man that one must postulate ‘at the top of the
mind’, acting as an interpreter of signals and symbols in any instructive theory of
mind…. But then another homunculus required in his head and so on, in an infinite
regress… selectional systems, in which matching occurs ex post facto on an already
existing diverse repertoire, need no special creations, no homunculi, and no such
regress.” Edelman pps. 81-82
Presentation, in any sense other than an eliminative one, requires a homunculus, and
this is the problem that Edelman believes he has solved- in essentially the same way that I did.
But, in doing so, he believed he had solved the whole of the mind-body problem.
Re-entrant Maps
To this point, (his theory of “TNGS”), his argument is very plausible and compatible
with my own conclusions. His rationale from that point onward, however, bears examination.
His theory of re-entrant topobiological maps, (reactively linked cortical surfaces), is
quite plausible and highly interesting, but, ultimately, it is tied to a truly topological
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correspondence of those maps with the “real” world, (contrary to his conclusions of the first
part of his thesis). “Maps… correlate happenings at one spatial location in the world without a
higher-order supervisor…”637 These maps themselves do, therefore, embody a “God’s eye
view”, (contrary to the implications of TNGS). I have suggested a different orientation of
Edelman’s schema in the discussion of my Chapter 1, wherein I suggested we step back from
our human (animal) cognitive prejudice and consider the larger “global mapping” also
described by Edelman, (which relates “non-mapped” areas of the brain to the topobiological
maps), as the primary focus of biological process. Under this perspective, the “objects” of our
topobiological maps may be reconceived, not as God’s-eye renditions of ontology, but rather as
organizational foci, (efficacious artifacts), of process.638
Edelman rationalizes his biological solution to the problem of the brain and the mind
upon Lakoff’s, (and Putnam’s), answer. To him that answer is important because it allows a
rationale for the brain which is not based in information as, in fact, he has concluded that it is
637 Edelman, p.87, my emphasis 638 An aside: While I hope it should be clear by now that I have no affinity for traditional idealism, I think it is
worth quoting a short passage from Edelman as it talks about levels of “strangeness” in theories:
“and Berkeley’s monistic idealism –suggesting that inasmuch as all knowledge is gained through the senses, the whole world is a mental matter –falters before the facts of evolution. It would be very strange indeed if we mentally created an environment that then subjected us (mentally) to natural selection.” Edelman, p. 35
Berkeley aside, Edelman seems very put out with the very strangeness of the (recursive, re-entrant?) complication of such an idea. The complication, he implies, boggles the mind! But much of modern science is even more mind-boggling. My thesis proposes an even greater “boggle”, but results in an integration of epistemology and an actual solution to the mind-body problem.
Modern epistemology is radical at both the extremely small and at the extremely large (and fast) scales. It is only as algorithms they are comprehensible. And yet everyone, (read this as “most realists”), seems to accept that at the middle scale epistemology must be simple. Consider instead the truly mind boggling possibility I propose that the middle scale is algorithmic as well! Does this not explain “the prototype” which Rosch demonstrated and which ground Lakoff’s and Edelman’s very logical theses. Prototypes and the logical relations between them would, under this view, represent the “objects” and the “calculus” of algorithmic biology. If this thesis be accepted, then continuity, temporarily removed from epistemology by modern science, is restored across the board. This is a major epistemological and scientific result and worth the price we must pay for it. So was quantum mechanics!
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not, (inconsistently with his theory of re-entrant maps, I maintain). He therefore reaches a
conclusion very similar to my own. But again, like Lakoff’s, his conception is too limited and
incorporates an inherent contradiction. His concept of the world, like Lakoff's is based in a
container schema. We, you and I and Lakoff and Edelman, are organisms too after all. But
then “TNGS” requires that even our brains are not informational!639 It is the generality of
Cassirer’s solution –and of my extension of it –the generality of the Concept and the generality
of the scientific relativism which allows a consistent and meaningful solution640 to the problems
of the brain, mind and epistemology.
The Cartesian Theatre
What Edelman has not solved is the other problem, the problem of the “Cartesian
theatre”641, (i.e. “mind”, ordinarily taken), and this is the most important problem. It is that
which we normally mean when we use the terms “consciousness”, “sentiency”, etc. Its
comprehensive solution is the subject of Chapter 2: the Concept of Implicit Definition and its
integration with biology as the unified rule of ontogenic coupling. Edelman’s solution remains
an essentially naturalist, (objectivist), one itself however and is, I argue moreover,
epistemologically inconsistent. It is compatible with the rest of the eliminativist camp in that
ultimately all his correspondences, (his stated epistemology to the contrary), are from
topobiological maps, themselves topologically corresponding to “the (real) world”! His
“mind” is purely process, spatially and temporally localized –and known! His is “a God’s eye
view”.
639 I think that Edelman would comment here, as he did on another occasion, that this conclusion would “boggle
the mind”! Maybe so, but I think we’d better get used to such a state. Modern physics? Edelman’s own conclusions? …
640 by allowing a reorientation of the problem to a consideration of forms rather than of information 641 after Dennett
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Edelman is very derisive of Penrose’s “Emperor’s New Mind”,642 but I think he has
missed a major aspect of it. Penrose, (though he doesn’t say so explicitly), and the “quantum
people” are trying, (Gödel aside), I think, to supply a “non-localization” –i.e. a spatial
universality to the brain’s perceptual and cognitive objects- to make headway on the problem of
knowing. They are trying to conceive an answer to Leibniz’ problem of the “one and the many”
within a physical space. The “chaos theory people” stand in a similar motivation I think, but
attacking the logical problem of the object from a perspective of localized process, conceiving
our objects as “attractors”. But even were such solutions meaningful, (and they are
interesting), they would miss the requirement of a self-standing logical space in depth which
the Concept of Implicit Definition, as combined with the schematic model of biology, supplies
and which furnishes the foundation of “meaning” and “knowing”. Dennett glimpsed such a
possibility643 for a Cartesian theatre based in logic in Shakey the Robot’s program, (as I cited
previously644), but his naturalist/objectivist metaphysical prejudice enervated the concept before
it could bear fruit.
But ordinary logic,645 (Shakey’s program for instance), is inadequate to the problem. It
is essentially dimensional: linear, planar, multi-dimensional, missing the integration in depth –
missing the autonomy and (logical) self-sufficiency which is necessary to knowing and to
meaning. 646 647
642 “Penrose’s account is a bit like that of a schoolboy who, not knowing the formula of sulfuric acid asked for on
an exam, gives instead a beautiful account of his dog Spot.” Edelman, P.217 643 but using an inadequate logic 644 cf the "Dennett Appendix" - "the color phi" 645 “associationist logic” in Dreyfus’ term 646 Wittgenstein’s objection is clearly pertinent here. He raised the question of the necessity for one to have
another rule: i.e. another rule to apply any given rule. C.I.D./biology, however, supplies a consistent rationale. “One” is a rule, “one” doesn’t apply the rule. “One” is the single, “ex post facto” and unified rule of ontogenic coupling!
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That aspect of ordinary mind we call the “Cartesian Theatre” does not work as a linear,
a planar, or even as a multidimensional space648 -even as a logical space. As I argued in
chapter 2, each requires “presentation”, either physical or logical. Nor do such conceptions
supply “knowing”, “meaning” or “motivation”, except as unnatural and gratuitous appendages.
C.I.D. and the schematic model focus logic and cognition in biology. Biology has
innate depth and structure –derived from the single principle of efficacy as coupled with
Darwinian survival –of ontogenic coupling, and these necessarily pass to the logic and the
cognition which are embedded in it! The Concept of Implicit Definition as coupled with the
schematic model649 supplies an integration and a rationale in depth –and an autonomy- implicit
in its biological roots.650 Edelman got very close to this answer, but his efforts were frustrated
by his epistemological beginnings.
Cassirer, (“symbolic forms”), Rosch, (“prototypes” and “basic levels”), and Lakoff,
(ICM’s), demonstrate that dimensional logic is not adequate to the realities of the human mind.
Nor, even putting aside the problem of “information”, (Maturana and Varela, Freeman,
Edelman), can such a logic supply meaning or motivation except in a very unnatural and
perverted sense. It is biology itself which supplies this aspect –in the concept of a schematic
model and an enlarged logic. This is my argument of Chapter 1 as culminated in Chapter 2.
647 and which could provide the enrichment necessary to the possibility of future scientific development moreover.
All the other proposals yet presented are essentially just explanatory –i.e. logically reductive- and hold little promise for further exploitation.
648 cf Wlodek Duch for instance 649 i.e. the “concordance” mentioned in the Introduction 650 It supplies “the rule which we need to apply the rule which we need to apply the rule …”
demanded by Wittgenstein. Ultimately it is a constitutive rule. But one doesn’t “apply" this rule. Rather, “one” is a rule –namely the constitutive rule of ontogenic coupling as the term is used by Maturana and Varela.
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On Epistemology:
But let me be more generous to Lakoff and Edelman. In basing their conceptions on our
ordinary world, or, to call a spade a spade, on our ordinary naïve realistic conception of the
world, (people, baseballs, cars and all the things they do), they are trying to preserve
experience! This they identify with realism. They seek to preserve their logical and biological
conclusions with the objects of that ordinary realism,651 and their relativism is a laudable and
understandable attempt at a reconciliation. I have explained my answer to the same problem in
terms of the multiple possible axiomatic foundations of mathematical systems, but another line
of understanding is possible. Consider the notion of a mathematical “ideal”.
Mathematical Ideals
[Note, December 2009: This subject is better treated and with illustrations in my book
“Exotic Mathematics….” Iglowitz, 2009]
The mathematical definition of an ideal is technical,652 but the example given by
Birkhoff and Mac Clane653, while rather “longish" is more easily understood and is clearly
directly applicable, (by its substance), to the immediate problem.654 It illustrates a very different
651 cf Lakoff’s discussion, (p.262) of the “objects” of our experience –his chair, for instance. “It
is important not to read Putnam out of context here, especially when he talks about objects. An ‘object’ is a single bounded entity…. Putnam, being a realist, does not deny that objects exist. Take, for example, the chair I am sitting on. It exists. If it didn’t, I would have fallen on the floor.” (my emphasis). Compare this reference with my modification of Kant’s position on “objects” which I advocated in the footnote in Chapter 5.
652 “Definition. An ideal C in a ring A is a non-void subset of A with the properties
(i) c1 and c2 in C imply that c1 – c2 is in C;
(ii) c in C and a in A imply that ac and ca are in C”
Birkhoff and Mac Clane, “Modern Algebra”, 1953, pps.372 653 ibid, pps.380… 654 i.e. it deals with well defined "objects"
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and very concrete notion of “relativism”. While encompassing a scope much wider than simple
geometry, that example provides a very clear illustration of the concept:
“The circle C of radius 2 lying in the plane parallel to the (x,y) plane and two units
above it in space is usually described analytically as the set of points (x,y,z) in space
satisfying the simultaneous equations:
(16)
x2 + y2 –4 = 0,
z – 2 = 0.
These describe the curve C as the intersection of a circular cylinder and a plane. But
C can be described with equal accuracy as the intersection of a sphere with the plane z =
2, by the equivalent simultaneous equations:
(17)
x2 + y2 + z2 – 8 = 0,
z – 2 = 0.
Still another description is possible, by the equations
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(18)
x2 + y2 – 4 = 0,
x2 + y2 – 2z = 0.
These describe C as the intersection of a circular cylinder with the paraboloid of
rotation:
x2 + y2 = 2z.
Therefore the only impartial way to describe C”, (my emphasis), “ is in terms of all
the polynomial equations which its points satisfy. But if f(x,y,z) and g(x,y,z) are any
two polynomials whose values are identically zero on C, then their sum and difference
also vanish identically on C. So, likewise, does any multiple a(x,y,z)f(x,y,z) of f(x,y,z)
by any polynomial a(x,y,z) whatsoever.”, (my emphasis). “This means that the set of all
polynomials whose values are identically zero on C is an ideal. This ideal then, and not
any special pair of its elements, is the ultimate description of C.
In the light of this observation the special pairs of polynomials occurring in
equations (16)-(18) appear simply as generators”, (my emphasis), “ of the ideal of all
polynomials which vanish identically on C. Any polynomial obtained from the
equations of (16) by linear combination with polynomial coefficients, as
The mathematical “ideal” just described opens a door to a better conclusion to Lakoff’s and
Edelman’s arguments, and a simpler understanding of my own. None of these generators stands
prior to any other, nor does it “create” the figure comprehended. Each stands, rather, as an
equipotent and relativistic “logical”, (i.e. explanatory), basis fully exhausting the actuality of the
figure.
But we must consider this example in the larger context of mathematics. Not only can
such descriptions be relativized in relation to a fixed coordinate system, but the very coordinate
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systems themselves stand in like case. Axes need not be orthogonal, nor need they be
rectilinear, (e.g. polar coordinates are possible). Nor need they be fixed. They may be in
translation –e.g. relative motion, (which translates to special relativity), and they need not be
Euclidean, (nor Hyperbolic nor Spherical). Russell, for instance, further argued655 that our
descriptions of phenomena might even be based in projective geometry. But need they be even
spatial? Can we not conceive of such explanations being framed as abstract transformations,
which latter are not defined on spaces, but on abstract sets! Abstract sets, however, fall
naturally within the scope of axiomatics wherein I grounded C.I.D.
Such a relativism of descriptions, combined with a scientific relativism of logic and
epistemology themselves as argued by Cassirer, Lakoff, and myself, (superceding the traditional
“container schema” and broadening the very ideas of “set” and “object” themselves), points to
the further possibility for such an “idealistic”, (in the mathematical sense), foundation of logic
itself. Need mathematics, or logic, be necessarily grounded in objectivist sets, (ultimate
“atomic” –i.e. least objects -and a fixed "Universe" of such objects), or could it not pick itself up
by its own bootstraps, (following the cue of mathematical “ideals”656 and the findings of
Cassirer and Lakoff), and stand without them?657 This is a question –not an easy one to be
sure- for abstract mathematics and the future of logic.
If we think of “experience” in the abstract –i.e. as the “axiom” without interpretation, (i.e.
“impartially” in the sense of “basic realism”), – then I think an “ideal” in this sense is a very
reasonable way of understanding it – beyond any particular “generator”, beyond any particular
655 Russell, “Foundations of Geometry”, 1956 656 though presently itself conceived in set-theoretic terms 657 This would be the truly transcendental logic after which Kant sought.
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interpretation.658 But it is not necessarily a spatial interpretation either. Ideals are broader than
this.
On a narrower focus, the possible generators of an ideal rigorously parallel the
explanatory possibilities which can absolutely preserve the objects of ordinary experience and
naïve realism, (conserving shapes, boundaries, etc.). As such, the ideal they ground is entirely
commensurate with Lakoff’s and Edelman’s conceptions and logically validates their (limited)
relativism.
Within the perspective of that same “basic realism”, the “experience“ we deal with need
not be taken as ultimately informational however,659 but can be taken as specifically
organizational and operative instead660 as I have argued in my Chapter 1 and consistently with
Edelman’s “TNGS”. Though connected with externality, (as representative of successful- .i.e.
adequate process661), it need not be further taken as conveying information about that
externality. It need not be taken as paralleling externality. The latter presumption, I have
argued, goes far beyond the needs and the implications of Darwinian biology.
The deeper issue is that of an adequate definition of “experience” itself. Need we identify it
with the absolute and necessary preservation of ordinary objects? Or, might we not, consistent
with the foundations of their own conceptions and the work of Rosch upon which it is
grounded, consider even our ordinary perceptual objects as “prototypes” of a larger
experience? Prototypes are objects of utility, of efficacy, after all, they are not foundational
658 “context-free” in Van Fraassen’s term 659 This my qualification on Putnam’s 4th requirement of basic realism 660 contrary to Putnam’s 4th requirement 661 “ex post facto”, in Edelman’s words
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objects.662 Could not our ordinary objects be considered, (as I have argued), as prototypes,
(“schematic perceptual objects”), of a biological calculus?
“Experience” in a modern sense must be broadened to include the experience of the
results of scientific experiment, and that experience, at least insofar as modern physics is
concerned, is not commensurate with the preservation of objects, nor is it commensurate with
ordinary spatiality. Without even considering the deeper implications of QM or of Relativity,
one need only consider results of the “twin slit” experiment or the implications of its multiple
execution to see the point. Not even cardinality is preserved!663 Similarly, consider Penrose’s
“most optimistic" view of quantum mechanics, (most optimistic for objectivism/naturalism, that
is):664
"I shall follow the more positive line which attributes objective physical reality to
the quantum description: the quantum state.
"I have been taking the view that the 'objectively real' state of an individual particle
is indeed described by its wavefunction psi. It seems that many people find this a
difficult position to adhere to in a serious way. One reason for this appears to be that it
involves our regarding individual particles being spread out spatially, rather than always
being concentrated at single points. For a momentum state, this spread is at its most
extreme, since psi is distributed equally all over the whole of space, (my emphasis),...It
662 see Lakoff for a discussion of Rosch, prototypes, and the logical significance of the latter. It
is a very illuminating discussion. 663 In answer to a question I asked on this point, a physicist correspondent of mine replied that “Yes, you can have
many slits one after another, (it is better with Mach-Zehnder interferometers than slits, with the same result that one doesn’t know if the photon went through or was reflected by a mirror…. We can say that one photon may be in an arbitrary number of places at once.” (Wlodek Duch, private correspondence) My point was that even the cardinality of this basic object, (the photon), was purely arbitrary –it could be 1 or 2 or 3 or 1,000,001 or …, depending on the branching structure of successive slits and the design of the experiment. But innate cardinality is perhaps the most basic “property” we ascribe to ordinary objects, so I think the conclusion is significant.
664 Repeating a section of a prior appendix
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would seem that we must indeed come to terms with this picture of a particle which can
be spread out over large regions of space, and which is likely to remain spread out until
the next position measurement is carried out...."
The particle -this smallest part of our "object"- is not included, (spatially, reductively,
nested), within the spatiality of the atom or within the molecule -or even within the human scale
object of which it is the theoretical (and supposed material) foundation. Naturalism/objectivism
can no longer support, therefore, even a consistent hierarchy of spatial scale!665 At the human
level, of course, it is a very useful tool, and that is just what I propose it is -constructed by
evolution! Science and logic suggest other, non-scaled and non-hierarchical organizations -i.e.
they support any other efficacious organization. It is a simple matter of utility.
Conclusion
To conclude this appendix, let me repeat that I truly admire Lakoff’s and Edelman’s
work. It is both profound and crucial to the resolution of the ultimate problem. But then I
really like the work of all the authors I have cited –even those most contrary to my own
conclusions. (I would not cite or spend much time on anything of lesser quality –the problem is
too huge and too difficult to be distracted.) Dennett’s work, for example, is very beautiful to
me in his honorable and perceptive pursuit of the hard implications of naturalism. P.S.
Churchland, as another example, has a “clean” mind and frames the problem wonderfully from
the perspectives of biology and philosophy. None of them has resolved the fundamental
problem, however, though all have come very close in different aspects of it. This is a hard
665 Compare Lakoff, p.195: “In the case of biological categories, science is not on its [objectivist philosophy’s]
side. Classical categories and natural kinds are remnants of pre-Darwinian philosophy. They fit the biology of the ancient Greeks very well….but they do not accord with phenomena that are central to evolution. … Objectivist semantics and cognition and, to a large extent, even objectivist metaphysics are in conflict with post-Darwinian biology. I’d put my money on biology.”
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problem, the hardest one, I maintain, that the human mind has ever dealt with. To solve it
requires an intellectual ruthlessness, and specifically, a ruthless realism!
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Appendix I: a few Illustrations
I. EDELMAN'S COGNITIVE ONTOLOGY: TOPOBIOLOGICAL MAPS AND A GOD'S
EYE PARALLELISM
II. A METACELLULAR PERSPECTIVE: COGNITIVE OBJECTS AS ORGANIZERS OF
PRIMITIVE PROCESS THROUGH A BLIND INTERFACE
III. UPPER AND LOWER BOUNDS OF A BIOLOGICAL ORGANISM'S PERFORMANCE
/ RESPONSE
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GOD'S EYE REALITY I.E. ONTOLOGY
EDELMAN'S EPISTEMOLOGICAL ERROR: TOPOBIOLOGICAL MAPS AND A GOD'S EYE VIEW
GLOBAL MAPPING
NON-MAPPED PROCESS IN THE BRAIN
COGNITIVE INTERFACE: A TOPOLOGICAL PARALLELISM / ISOMORPHISM
COGNITIVE INTERFACE: A TOPOLOGICAL PARALLELISM (REPRESENTATION)
THE BRAIN AS A CORRESPONDENCE MACHINE
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GOD'S EYE REALITY?
(I.E . ONTOLOGY)
A METACELLULAR PERSPECTIVE: COGNITIVE OBJECTS AS VIRTUAL ORGANIZERS OF PRIMITIVE PROCESS THROUGH A BLIND INTERFACE
GLOBAL MAPPING
NON-MAPPED PROCESS IN THE BRAIN
TOPOBIOLOGICAL MAPS: SPECIFICALLY AS COORDINATORS OF PRIMITIVE PROCESS
THE BRAIN AS A VIRTUAL 3-D GRAPHIC USER INTERFACE / CONTROLLER
A BLIND INTERFACE :
BASED IN APPROPRIATENESS RATHER THAN INFORMATION
HOW COULD A BIO/MECHANICAL ORGANISM KNOW REALITY?
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Upper and Lower Bounds of a Biological Organism's
1
2
3
BOUNDS OF SURVIVAL
(1) and (3) represent the best and the least possible performance for an organism over the domain of its behavior in absolute (ontic) reality. Less than (3) results in lessened survivability or death; greater than (1) is impossible as it is perfect performance with perfect knowledge in actual reality. Between the two bounds, adequate performance, ( (2), (2'), (2''),…), need not match, nor even parallel these outer bounds. (Note: 2' and 2'' parallel 1, but 2 does not!) Any curve within them is consistent with evolution. Edelman, for instance, talks about the multiple, non-commensurate antibody responses to a given antigen. The same must surely apply to cognition, another "recognition system". Cognition and response must be adequate, but it isn't obvious that there is only one way -a mirroring way. Nor is it inherent that all ways be commensurate!
An organism's performance in its environment is measured, fundamentally, not in perfection or in rationality, but in simple adequacy. It is very easy to envision multiple, noncommensurate blind-though- adequate responses to a given situation. It is not easy to envision rational responses informed by information.
2'
2''
AADEQUACY
RANGE OF NECESSARY RESPONSES
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Appendix J: (An elaboration of the possibilities of the discussion)
(Hyperlinked to Chapter 1)
The acceptance of even the possibility of such a free formation of an interface, (calculus
plus objects), and the further possibility of a fluid correlation, (i.e. one not constrained a priori –
denotationally- by classical logical categories), from a substrate to that interface is difficult,
admittedly. There are two primary difficulties.
The first sticking point is that an interface must correlate to "experience", (to have any
value), and experience already has objects, it seems. "Experience" can be taken in a wider,
more scientific sense666, however, to include the experience of the results of scientific
experiment. Most generally, it can be taken as that which must be dealt with, (incorporated), in
any comprehensive theory of reality.667 (Remember the Marxist's problem with the royalist's
"God" in section A.1) I argue, (in Chapter 4), that it is the invariants, ("that which must be dealt
with", taken in the most general sense- to include experience of the results of empirical
science), that define “experience” in its widest sense and it need not, (as in fact science does
not), necessarily conserve the objects of our normal naive realism as objects.
The second difficulty has to do with logic itself. Within the classical, Aristotelian
conception of categories and logic, (which still underlies the whole of modern logic), all logical
operations ultimately come down essentially to the intersection, union and complementarity of
sets, (of properties for instance). Even "relation" is defined as a set of n-tuples. How then can a
cognitive object viable668 in the world, (even a conceptual object), be conceived except as a
666 cf Chapter 4 667 See Chapter 3 for a definition of “experience”, and Chapter 4, (the “King of Petrolia”), for an elaboration. 668 correlating to and existing in it in some manner
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collection of properties collected into like sets –preserving hierarchy669, spatiality and
ultimately the real contiguity of properties in ontological objects, (their extension), in the world
therefore?670 How can it relate to other objects except in terms of a commonality or disjunction
of those primitive properties? It is a question of logical possibility. I will deal briefly with this
question here and expound it more fully as the subjects of Chapter 2 and Chapter 4.671
Modern cognitive theorists, (Lakoff for example), arguing from extensive and generally
confirmed empirical data on how human beings, cultures and languages actually do categorize,
(as opposed to a priori, philosophical and logical conclusions as to how they must categorize!),
and the biologist Edelman suggest a very different constitution of our categories and concepts -
and, in consequence, a very different constitution of the logic built upon them.672
Based in Rosch’s empirical researches demonstrating “prototype effects” and extensive
other linguistic and anthropological findings, Lakoff argues673 for the existence of
"metonymic", “metaphorical”, and “radial” categories which are not commensurable with
classical set-theoretic categories, (though the latter are maintained as a special case –the
“container schema”). These new categories are established by “association”, “similarity” and
“motivation” rather than on the set theoretic intersection of properties. In the case of “radial”
categories, they may be built by historical accident!
669 See "Afterward: Lakoff & Edelman for a detailed discussion of "hierarchy" 670 cf Lakoff, 1987, pps. 157-184. Lakoff has outlined this overall problem and the foundations
of what he calls “objectivism” with great precision and lucidity. In spirit I think he is correct though I do not agree with the whole of his answer. See Afterward: Lakoff and Edelman
671 also see Afterward: Lakoff / Edelman 672 As Lakoff noted, “most of the subject matter of classical logic is categorization”. Lakoff,
1987, p. 353, (my emphasis) 673 with lucid concrete examples and case studies
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Lakoff’s “category” illustrates a conceptual “free formation” of a sort, (these criteria
encompass any rule674), but I question aspects of it because it appears to be an anthropological
blank check, losing credibility as the ground for an extension of scientific logic thereby. 675
Lakoff makes a good case, but it is too strong! Association, similarity and motivation –and the
logic Lakoff grounds in them establish categories and a consequent logic with no bounds. They
encompass whatever we can imagine!
In chapter 2 I will argue a similar but more constrained case from the more classical
and formal logical position proposed by Ernst Cassirer676 over three quarters of a century ago
and, sadly, largely overlooked. Cassirer's reformulation of the formal logical concept,
(category), was based firmly in the actual history of modern mathematics and physical science
themselves. Mathematics and physical science have already expanded, (tacitly, he argued), the
classical, Aristotelian Concept. Cassirer’s "Functional Concept of Mathematics", (which is a
broadening of the general logical “concept” based in mathematical considerations and not a
specifically mathematical entity), is broad enough to encompass the essence of Lakoff’s
“category”, (concept) -and that of classical logic as a completely plausible and natural limit case
as well. It does so in a more comprehensive and cogent manner I feel however, one from which
a new working logical “calculus” could more plausibly be expected.677 Cassirer's category is
674 Lakoff argues against rule basing in general. But what are “association” or “motivation” … themselves? It is
the classical, (set based rule), that he questions, I think. Cassirer, (see Chapter 2), would call it the rule of identity.
675 It is a triviality that if logic can prove anything, then it can prove nothing! Lakoff’s case is considerably better than this I admit, (ultimately it is logically grounded in ICM’s -idealized cognitive models), but still involves a fundamental epistemological contradiction as I will discuss in the preface to Chapter 2 and in the Afterward: Lakoff/Edelman.
676 Lakoff bases his logical stance in the ideas of Wittgenstein and Putnam who also question the classical concept. 677 The reasonable prospect of such a calculus is, of course, crucial. It is the existence of powerful, simple and
highly pragmatic algorithms based in classical logic, (formal logic, mathematical set theory, and the digital computer for instance), -and the lack of the prospect of any viable alternative –that severely challenges the credibility of any counterproposal for fundamental logic.
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“freely formed” as well, based on any (consistent) rule, any rule of series. It is "a new 'object' ...
whose total content is expressed in the relations established between the individual elements by
the act of unification... [But it is] a peculiar form of consciousness”, (and therein supplies a
unique clue to the nature of consciousness incidentally!), “such as cannot be reduced to" [i.e. set
theoretically abstracted from] "the consciousness of sensation or perception", (i.e. sensory
objects).678 But please note that it is specifically an act, i.e. an independent (internal)
construction, and by implication I will argue eventually, a biological act, (an act of the
organism)- rather than a passive, (i.e. informational), derivation or abstraction from perception.
Cassirer's case is made solely for intellectual concepts, (conceptual categories), however.
Lakoff and Edelman make an explicit distinction between perceptual categories and
conceptual categories, (as does Cassirer between percepts and concepts). From an operational
standpoint, (from the standpoint of biology for instance),679 this is clearly an artificial
distinction however. These are simply the parts of operative categorization by a biological
organism –i.e. non-verbal vs. verbal motor function.680 They are just the aspects of biological
categorical function vis a vis environment. The extension of the formal logical "Concept"
which I will eventually argue681 encompasses them both: both ordinary concepts, (conceptual
categories), and, in Kant's usage, "constitutive" concepts, (perceptual categories), as well.
There is a last issue involved in "free formation". Under the classical perspective, under
the set-theoretic operations of intersection, union, complement,… of properties, what I will call
678 my emphasis. He argues that the rule of a series, -with which he equates the actual scientific “concept” -cannot
be derived from any finite exhibition of its instances. It is, therefore, an independent act –a free creation- of the mind, and, by extension, of the brain.
679 Or from the critical perspective of Kant, for instance 680 This clearly ties in with Lakoff/Edelman's "embodied" concepts. 681 In Chapter 2
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"hierarchy"682 must be maintained at some level. It describes the requirement for the
preservation of contiguous logical properties, (in a logical category), into contiguous physical,
(really metaphysical), properties in ultimate reality: i.e. properties of logical683 objects,
(categories), must correlate hierarchically to properties of objects in the world. Logical objects
must be constituted as topology-preserving collections, (vis a vis properties), of their
“objects”.684
Even Gerald Edelman, (though acknowledging Lakoff), preserves this kind of hierarchy
in his thesis of the connectivity between the brain's myriad "topobiological maps"685. Given
Cassirer’s extension of the category however –or even Lakoff’s, (which Edelman incorporates
into his own thesis), hierarchy is not an a priori requirement of categories or of function,
however. Indeed, Edelman himself speaks of the existence, (besides the massive, topology-
preserving connectivity between his multiple “topobiological maps” in the brain), of the
existence of another kind of connectivity in the brain -of the connectivity of a "global mapping
... containing multiple reentrant local maps ... that are able to interact with non-mapped , (i.e.
non-topological), parts of the brain..".686
Though framed in a different context and for a different purpose, (and getting ahead of
myself a bit), I think this non-topological connectivity from Edelman’s topobiological maps,
682 Lakoff would call it a preservation of the properties of the “container” ICM. See the Afterward: Lakoff and
Edelman for a fuller discussion of “hierarchy”. 683 or operational 684 cf Afterward: Lakoff-Edelman 685 -which themselves are supposed to preserve the property-topology, (i.e. the contiguity of the properties in real
discrete objects), of reality as sensory maps. This is an epistemological error, supplying the very "God's eye view" against which he argues so strongly. To move beyond it requires a fundamental reevaluation of epistemology itself. That is the subject of my Chapters 3 and 4. Lakoff's and Edelman's, (and Putnam’s upon which they are based), Maturana’s -and indeed any thesis denying a "God's eye view" -requires some version of or alternative to the scientific relativistic epistemology I will propose, (in Chapter 4), in order to maintain internal consistency.
686 Edelman, 1992, P.89, his emphasis
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and specifically the connectivity from the "objects" of those maps to the non-mapped areas of
the brain, (the "global mapping"), -the general case687 -supplies a fortuitous illustration the kind
of potential I wish to urge for a GUI, and ultimately688 for the brain itself. It allows
"...selectional events”, [and, I suggest, their “objects” as well], “occurring in its local maps ... to
be connected to the animal's motor behavior, to new sensory samplings of the world, and to
further successive reentry events."689 Edelman, however, correlates the topobiological maps,
(as sensory maps), directly with "the world" -inconsistently supplying thereby the very "God's
eye view" whose possibility he emphatically denies.
But what if we take the converse perspective?690 What if we take Edelman’s stated
epistemology seriously and blink our "God's eye"?691
Instead of adopting the perspective, (Edelman’s), wherein we look from the objects of
the topobiological maps back towards the distributed process of the brain, let us step back from
687 retaining hierarchical mapping as a special case 688 epistemologically reentrantly 689 ibid 690 I will supply my answer to this epistemological problem in Chapter 4. 691 An aside: Edelman seems very put out with the very idea of “mentally creat[ing] an
environment that then subjected us (mentally) to natural selection”. (Edelman 1992, p. 35 ). The complication, he implies, boggles the mind! But much of modern science does likewise. I wish to suggest an even greater complication- we might as well face it right now.
I wish to suggest a conception wherein the visual cortices, (for example), do not receive a (metaphysically) topological correlate of their surroundings. I wish to look at a case wherein the cortex we view and the world which maps upon it are both aspects of (the same) internal process and not “God-given”!
Modern epistemology is radical at both the extremely small and at the extremely large (and fast) scales. It is only as algorithms that they are comprehensible. And yet almost everyone, (read this as “most realists”), seems to deny even the possibility that at the middle scale epistemology can be other than simple. Consider instead the possibility that the middle scale is algorithmic as well! Does this not fit better with the “prototypes” which Rosch displayed and which ground Lakoff’s and Edelman’s logical theses. Prototypes and the logical relations between them would, under this view, represent the “objects” and the “calculus” of practical algorithmic biology and epistemology would therein regain continuity across the board!
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the prejudice of our human (animal) cognition and consider the converse perspective: beginning
instead with the non-mapped areas of the brain, (distributed process), and proceeding to the
"objects" of the topobiological maps themselves. Consider the converse perspective wherein
"the objects" and the topobiological maps they operate in are taken as functions of, (organizing
nexuses of), distributed process, and not the standard perspective wherein the distributed
process is presupposed to serve the objects692. What if the maps and their objects both were
taken, instead, as existing to serve primitive process? This is the case I wish to suggest as an
illustration of the most abstract sense of the GUI, (and which I will argue shortly).693
We have here a concrete model, (in Edelman's "global mapping"), which illustrates the
more abstract possibility of a connection of "objects"694, (in a GUI), to non-topological process,
fundamental rationale is "Neural Darwinism", the ex post facto adaptation of process, not
“information”, and that rationale is consistent with such an interpretation. It does not require
“information”. It does not require “representation”. Mathematics illustrates the general case in
abstract transformations -whose ultimate biological application would be competence -i.e.
survival, not information.695 What we are dealing with here, ultimately, are transformations,
and transformations are defined on abstract sets, not on spaces!
692 which would mirror the objects of ultimate reality. For Edelman this is an epistemological error. 693 This reorientation of perspective suggests an interesting possibility. It suggests that
evolution’s “good trick”, (after P.S. Churchland’s usage), was not representation, but rather the organization of primitive process in a topological context. It suggests that the “good trick” was in the evolutionary creation of the cortex itself!
694 in the brain's spatial maps 695 The question, of course, is whether "information" is necessary to competence. I will argue, (in Chapter 3), that
it involves a distinction between "bounds" and "greatest lower bounds" of biologic survival. A given organism, (to include human beings), must reflect a lower bound of competence in the world. But "information" requires that it reflect a greatest lower bound, and this is inconsistent with the fundamental premises of evolution. It is the "parallel postulate" of cognitive science.
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For the GUI I urge, similarly and in the general case, that the "front end" of a GUI, (an
interface), may be freely constructed, (ad hoc), based on pragmatic considerations which boil
down, ultimately, to operational efficacy. It can be formulated, for all intents and purposes, in
any consistent way we desire. The real trick, then, (because of the requisite simplicity of rules),
is in the conception, (correlation), of the "objects" of the interface themselves so as to
accomplish what is intended. But the example above suggests that the definition,
(correspondence/linkage), of "an object" itself can, in a real sense, be freely formed as well. It
may be linked to whatever "things" or processes -or parts of things or processes- we choose.
We, (or evolution), can, therefore, freely construct a "GUI", a calculus-plus-objects to
efficiently organize, (control), profoundly complex process. It is made good in the correlations,
(connectivity), of the "objects" themselves –in the “global mapping”. ( Click here for a few
drawings illustrating the concept: GRAPHICS). [RETURN TO CHAPTER 1]
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Dedication:696
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1 This dedication will be different from what you are used to. If you choose to skip it therefore, that is your
decision. What I choose to put into it, however, is mine. I have lived long as a relative hermit and as a fanatic to the cause of these ideas. Many people dear to me have been forced to pay the price. I dedicate this book to all these compassionate and forgiving souls who have had the tolerance to put up with, and some even to love me:
To my (few) intellectual friends: to Ruelle Denney, whose kindly, (and genuinely aristocratic), response to my youthful naivete and arrogance I will forever remember, to Tom Owens who, in the kindness of his heart was the first willing to risk apoplexy from my initial two and three-page quotations and quivers of "!"'s, to Dr. Arnold Leiman who was the first comprehending being to tell me I was not a raving megalomaniac, to Dr. Hubert Dreyfus who caused me to read Maturana and Varela, to Dr. David Elliott who, over the last year and a half, through his generosity of spirit and kindness has helped me to endure the unendurable. And lastly, mostly, to my dear friend, David Casacuberta who, though he remains an unrecalcitrant Naturalist, (:-) ), in his largeness of spirit and innate decency, has helped me to perfect what is, from his point of view, an enemy's plan of battle. I can never thank him enough.
To my family: I could never give back what you gave to me. I lacked the normal background of human interaction, (because of the circumstances of my childhood), to communicate to you the real love I have always felt for you. And beyond that, my fanaticism and almost total distraction towards the resolution of the problem set for me have robbed you of precious time and attention. But my purpose, beyond the duties of my own spiritual obligation, was to do you honor! I hope that happens. But, if my answer is right, it is important for you as well as for me -I hope it will make life better for you, and, if not for you, then for your grandchildren and theirs.
To "Pops", to "Momma Jung", to Doug, to Rich, to "Bee", (Burbank Jr.), and to Matt, who unselfishly gave me the real family I never had, I am truly and forever grateful.
To my mother and father -I wish I could have made your lives better, and to my brother Ron -I wish we could have been closer. It was probably my fault.
To my wonderful daughters, Chenin-blanc Yic-mun-fuung Iglowitz and Mook-lan Sauvignon Iglowitz. In you, God has truly blessed me, and I know it every day. I love you guys.
And finally and especially, to my wife of 24 years, Christina Teresa Sun-Jung Iglowitz, I could never have done it without you. This is the holy crusade we talked about on our first date high in the Berkeley hills, (Chinese girls don't kiss?!) I guess it's how I "conned" you into marrying that strange creature. Well, here it is. I have learned, (so far as I am capable of learning it), decency and compassion from you who, I still think, embodies these traits more fully than any other human being I have ever met, and I will be forever in awe of you. I love you now, and, whatever happens, will love you till the day I die.
