Date post: | 18-Nov-2014 |
Category: |
Documents |
Upload: | cassiano-terra-rodrigues |
View: | 105 times |
Download: | 3 times |
CASSIANO TERRA RODRIGUES
A STUDY ON THE CONCEPT OF SCIENCE IN THE PHILOSOPHY OF CHARLES S. PEIRCE
VOLUME II
Programa de Estudos Pós-Graduados em Filosofia
Pontifícia Universidade Católica de São Paulo
São Paulo
2005
SUMMARY
6. The Problem of Induction and Scientific Method204
7. Experience and Expectation299
8. The Genealogy of Sciences 339
8.1 The most natural scheme possible374
9. Mathematics as the most general science398
10. Conclusion: Ulrich’s Dilemma 439
Bibliography481
203
6. THE PROBLEM OF INDUCTION AND THE SCIENTIFIC METHOD
In natural science this rigid method is the Baconian method of induction, a mehod which, if consistently pursued, would have left science where it found it. What
Bacon omitted was the play of free imagination, controlled by the requirements of coherence and logic. The true method of discovery is like the flight of an aeroplane. It
starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute
by rational interpretation.
Alfred North Whitehead, Seção II, Process and Reality.
David Hume, in his Treatise on Human Nature, explicitly
formulated, for the first time, the problem of rational justification of our
inductive inferences. However, he did not use the word “induction”, not
even “inductive reasoning”1. Where the adjective “inductive” would
naturally be used, Hume talks either of arguments or inferences, or yet
reasonings “based on the experience”; or “from causes to effects”; or,
still, “in respect to the question of fact”2. The arguments he discusses
under such denominations, however, are all (with a single possible
exception)3 arguments called inductive. For the Scottish philosopher,
there is no justification for illations because it is impossible to
demonstrate that there is a necessary relation between cause and effect
1 In effect, induction appears only once in the Treatise, in the Appendix, but it seems that there is not the meaning of “argument based on experience”. Cf. HUME (1739-1740), p. 628. 2 Cf. HUME (1739-1740), I: III, section XI; p. 649 seq. (An Abstract of a book lately published entitled A Treatise of Human Nature, etc., wherein the chief argument of that book is farther illustrated and explained); 3 Namely, the class of probable arguments that Hume discuss on section XI of book I, part III, of Treatise, and in the third paragraph of the correspondent section VI of the Enquiry.
204
in things. For the question “how is it possible to know that the sun will
rise tomorrow?” the only answer would be: “by habit”; in other words,
the repetition of the past experience leads to the belief that what
always happened, will always happen: “all our reasonings concerning
causes and effects are derived from nothing but custom”4. In other
words, the experience cannot show that the effect is necessarily
contained in the cause, because our sensations do not give us more
than separate and distinctive perceptions, unrelated one from another:
That our senses offer not their impressions as the images
of something distinct, or independent, and external, is
evident; because they convey to us nothing but a single
perception, and never give us the least intimation of any
thing beyond. A single perception can never produce the
idea of a double existence, but by some inference either
of the reason or imagination. When the mind looks
farther that what immediately appears to it, its
conclusions can never be put to the account of the
senses; and it certainly looks farther, when from a single
perception it infers a double existence, and supposes the
relations of resemblance and causation betwixt them.5
Thus, a supposed relation of necessity between cause and effect is
grounded upon the associations of ideas such as it happened in the
past: nothing can warrant that from the existence of a fact B the
existence of a fact A must necessarily obtain, but for the custom of
thinking or imagining that it is so. Therefore, no inferential conclusion
based on experience is necessary, but all are contingent; it is certain
4 HUME (1739-1740), I: IV, section 1.5 HUME (1739-1740), I: IV, section II.
205
that we cannot state any necessary relation between two distinct facts;
we cannot state, says Hume, the continuous existence of objects,
distinctly and independently of human nature.6
Hume drives our attention to an existent gap between premises
and conclusions in inductive reasoning, showing the problem of the
rational acceptation of hypotheses on inductive bases by putting in
check the procedure of scientific activity; once science is based in
theoretical verifications inductively obtained, there are no steady
grounds for scientific knowledge7. The problem of causality is exemplar
in this respect. Causality, for Hume, “makes me go from something that
was given to me to an idea of something that was never given to me, or
even that is not givable in experience”, in Deleuze’s words8. Or, in
Hume’s own words:
The only connexion or relation of objects, which can lead
us beyond the immediate impressions of our memory and
senses, is that of cause and effect; and that because ‘tis
the only one, on which we can found a just inference
from one object to another.9
We do not draw the idea of the necessity of the causal relation
from some rational knowledge, but from empirical observation. Things
themselves do not furnish us any bases for such knowledge, but only
our experience of them. Thus, one can conclude that Cesar was
murdered in the senate because it is read in history books about the
6 Idem, ibidem.7 TIDMAN; KAHANE (2003), p. 396; COSTA (1993), pp. 33 seq.8 DELEUZE (1974), p. 62.9 HUME (1739-1740), I: III, section VI.
206
murder; one can conclude that the sun will rise tomorrow because one
had always seen the sun rising; in that one feels the hot stone under the
sun, one can infer that the sun is the cause of the heat of the stone.
Hume says:
‘Tis therefore by EXPERIENCE only, that we can infer the
existence of one object from that of another. The nature
of experience is this. We remember to have had frequent
instances of the existence of one species of objects; and
also remember, that the individuals of another species of
objects have always attended them, and have existed in a
regular order of contiguity and succession with regard to
them. Thus we remember to have seen that species of
object we call flame, and to have felt that species of
sensation we call heat. We likewise call to mind their
constant conjunction in all past instances. Without any
farther ceremony, we call the one cause and the other
effect, and infer the existence of the one from that of the
other. In all those instances, from which we learn the
conjunction of particular causes and effects, both the
causes and effects have been perceived by the senses,
and are remembered: But in all cases, wherein we reason
concerning them, there is only one perceived or
remembered, and the other is supplyed in conformity to
our past experience.10
Causality is a relation that allows the surpassing of the given, and
to infer a necessary link that is not in the things themselves, but that is
thought as it were necessary and intrinsic in them. In effect, Hume
postulates the exteriority of relations as to the world: relations of
causality, similarity, contiguity, succession, etc. are creations of human
10 HUME (1739-1740), ), I: III, section VI.
207
imagination to explain the world of particular and contingent
experiences, a world constituted of separated and distinct facts11. Thus,
we infer and believe in relations of causality, similarity, etc. because we
habituate ourselves to certain world experience:
The idea of cause and effect is derived from experience,
which informs us, that such particular objects, in all past
instances, have been constantly conjoined with each
other: And as an object similar to one of these is
supposed to be immediately present in its impression, we
thence presume on the existence of one similar to its
usual attendant. According to this account of thins, which
is, I think, in every point unquestionable, probability is
founded on the presumption of a resemblance betwixt
those objects, of which we have had experience, and
those, of which we have had none [...].12
Therefore, the natural sciences would be based upon a series of
beliefs: because experience has always been of a certain character, one
can trust that experience will always be similar to that, in similar
circumstances. Scientific knowledge is, then, restricted to probability,
because the certainty of knowledge results from the verification of the
repetition of a series of events in experience. And this probability, even
so, can only concern to what was empirically given:
Let men be once fully perswaded of these two principles,
That there is nothing in any object, consider’d in itself,
which can afford us a reason for drawing a conclusion
beyond it; and, That even after the observation of the
frequent or constant conjunction of objects, we have no
11 DELEUZE (1974), pp. 60-63.12 HUME (1739-1740), ), I: III, section VI.
208
reason to draw any inference concerning any object
beyond those of which we have had experience [...].13
The problem of induction, therefore, can be formulated by Hume
in respect to the success of the scientific method in calculating the
probabilities (in determining the approximate similarities among the
objects), based on the reiterated experience of the past:
Thus not only reason fails us in the discovery of the
ultimate connexion of causes and effects, but even after
experience has inform’d us of their constant conjunction,
’tis impossible for us to satisfy ourselves by our reason,
why we shou’d extend that experience beyond those
particular instances, which have fallen under our
observation. We suppose, but are never able to prove,
that there must be a resemblance betwixt those objects,
of which we have had experience, and those which lie
beyond the reach of our discovery.14
Of course, Peirce understands the problem of induction not only
in Humean terms. His comprehension of induction, differently of
Hume’s, was not informed by the idea of simple enumeration, as we will
see. Nevertheless, the philosophical position grounded on the idea of
the exteriority of relations is essentially contrary to the one he has
assumed. Indeed, Peirce understood the problem of induction also in
Humean terms, meaning that it was relatively to the possibility of
amplified knowledge, and by this way the Humean position could be
refuted. Already in 1869 Peirce stated that the problem of knowledge
could be understood on the basis of the question about the possibility of
13 HUME (1739-1740), I: III, section XII. 14 HUME (1739-1740), I: III, section VI.
209
synthesis, explicitly recognizing that his approach comes from Kant’s
philosophy:
According to Kant, the central question of philosophy is
“How are synthetical judgments a priori possible?” But
antecedently to this comes the question how synthetical
judgments in general, and still more generally, how
synthetical reasoning is possible at all [W 2: 267-268,
Grounds of Validity of the Laws of Logic].
To answer this question is, Peirce said, to unlock the door of
philosophy. Early in his writings, he sustained a theory of induction, the
gist of which is the idea of the autocorrecting nature of inductive
reason in the long run. The conceptions of frequency and probability
become gradually more important in his works to ground this idea,
because they show a straight link between the deductive and inductive
inferential processes. These are ideas that, despite the evolution of his
thought, and the improvement of his theories, Peirce has never
abandoned. Accordingly, we will present an interpretation of Peirce’s
theory of induction, starting from his writings in the beginning of his
philosophical career. We will not occupy ourselves with the
development of his ideas in a perspective of historical reconstruction,
but we will show that the strongest theses of his late philosophy largely
occur from the refinement of his early ideas.15
15 ULLIAN (1995), pp. 94-95; RESCHER (1978), p. 17 seq. For a detailed comparison of the Humean and the Peircean theories of induction, as well as for the evolution of the idea of induction in Peirce’s philosophy, cf. BACHA (1999), passim, especially pp. 47 ff., chap. 3: “A evolução histórica do conceito de indução em Peirce”, pp. 114-335.
210
In 1868, Peirce distinguished kinds of valid inferences in
syllogistic terms: apodictic (or deductive) syllogisms, and probable (or
inductive and hypothetical) syllogisms. “An apodictic or deductive
syllogism is one whose validity depends unconditionally upon the
relation of he fact inferred to the facts posited in the premises” [W 2:
215, Some Consequences of Four Incapacities]. That the validity of
deduction does not depend upon the experience of an ulterior
knowledge, but only upon its premises, is a peculiar characteristic of
deduction: either this other knowledge would be in the premises, and
obviously would not be another, or it would be implicit, and the
inference would be incomplete. For this reason, deduction is the only
kind of reasoning that can be called necessary [HL 217]. The truth of
deduction is warranted in a necessary manner in that all the possible
relevant information needed to reach the conclusion is in the premises
[W 2: 175, Questions on Reality, 1868]. Peirce gives two examples of
deductive reasoning:
No series of days of which the first and last are different
days of the week exceeds by one a multiple of seven
days; now the first and last days of any leap-year are
different days of the week, and therefore no leap-year
consists of a number of days one greater than a multiple
of seven.
Among the vowels there are no double letters; but one of
the double letters (w) is compounded of two vowels:
hence, a letter compounded of two vowels is not
necessarily itself a vowel [W 2: 215].
211
It is an important conclusion that in all necessarily valid deductive
reasoning from true premises, it is possible to draw only true
conclusions [id.]. As a matter of fact, this position will always be
maintained by Peirce in his writings; see the following passage, from
1903:
In deduction, or necessary reasoning, we set out from a
hypothetical state of things which we define in certain
abstracted respects. Among the characters to which we
pay no attention in this mode of argument is whether or
not the hypothesis of our premisses conforms more or
less to the state of things in the outward world. […] Our
inference is valid if and only if there really is such a
relation between the state of things supposed in the
premisses and the state of things stated in the conclusion
[HL 225].
The principle stated since 1868 remains the same, which says that
true premises yield true conclusions. Now, the agreement with the
concrete facts, so to say, is another problem, that does not affect the
validity of the deduction. All deduction is reasoning starting from the
general to reach the particular, meaning that it is an inference
according to a general rule of drawing particular propositions from
general propositions. For that reason, the necessity of the reasoning is
in that the truth of conclusions depends on the truth of premises [NEM
3/I: 172, Probability and Induction, 1911]. For the same reason,
deduction can be called analytical inference, because the result
212
attained cannot be discordant from the rule [W 3: 323-326, Deduction,
Induction, and Hypothesis, 1878].
Notwithstanding, Peirce further recognized that deductively
reached conclusions may not be absolutely valid. Deductions are also
forms of probable reasoning, even when the probability of extracting
false conclusions from true premises is minimal; that is, deductions are
inferences that “in the long run of experience the greater part of those
whose premises are true will have true conclusions.”16 [EP 2: 298,
Nomenclature and Divisions of Triadic Relations, as Far as They Are
Determined, 1903]. In this respect, it may be more correct to say that
there are necessary deductions and probable deductions, meaning that
these deductions are of a certain probability [NEM 3/I: 172].
The first important point we want to emphasize is that the logical
validity of reasoning depends essentially on the obeysance of the rule
for passing from conclusions to premises:
The passage from the premise (or set of premises) P to
the conclusion C takes place according to a habit or rule
active within us. […] The habit is logically good provided
it would never (or in the case of a probable inference,
seldom) lead from a true premise to a false conclusion;
otherwise it is logically bad. [W 4: 165, On the Algebra of
Logic, 1880].
In other words, a good habit of reasoning takes into account a
disjunction of the following form: or the premise is false, or the
16 See CROMBIE (1997).
213
conclusion is true. A bad habit of reasoning extracts false conclusions
from true premises [RLT 167].
The second important point to highlight is that, theoretically,
error is impossible in deduction. Nevertheless, two cases of error are
possible: first, since deductions concern mathematical reasonings on
probabilities, the possibility of its application leaves open the possibility
of an error:
Deduction is the only necessary reasoning. It is the
reasoning of mathematics. It starts from a hypothesis,
the truth or falsity of which has nothing to do with the
reasoning; and of course its conclusions are equally ideal.
The ordinary use of the doctrine of chances is necessary
reasoning, although it is reasoning concerning
probabilities.” “Moreover, its application to experience,
or to possible experience, opens the door to probability,
and shuts out absolute necessity and certainty, in toto.
[CP 6.595, A Reply to Necessitarians, 1893].
Second, any mistake can occur in a deduction, and false
conclusions can be obtained starting from true premises, as mentioned
before, resulting from a bad deductive habit or some inattention in
reasoning:
Deduction is really a matter of perception and of
experimentation, just as induction and hypothetic
inference are; only, the perception and experimentation
are concerned with imaginary objects instead of with real
ones. The operations of perception and of
experimentation are subject to error, and therefore it is
only in a Pickwickian sense that mathematical reasoning
can be said to be perfectly certain. It is so only under the
214
condition that no error creeps into it; yet, after all, it is
susceptible of attaining a practical certainty.17 [CP 6.595,
A Reply to Necessitarians, 1893].
Until 1878, the typical logical form of deduction is understood by
Peirce as one of a syllogism, the major term of which must be a
universal categorical proposition, and the minor term of which an
affirmative proposition, seen in the syllogism of the first figure (in
Barbara) that could be written like this:
Rule: All beans in this bag are
white.
All S is P.
Case: These beans are from
this bag.
M is S.
Result: These beans are white. M is P.
To pass to the other kinds of reasonings, it is important to keep
this syllogistic form in mind. We shall return to it later. Now, we pass to
the other kinds of reasonings.
Induction and hypothesis are closely linked with each other by
the difference between logical extension, or breadth, and
comprehension, or depth. In other words, the extension of a term or
proposition is composed of all things or events of which the term is
predicable or that the proposition can represent. The comprehension of
a term or proposition, in turn, relates to the characteristics that can be
predicated to any object, which is in principle unknown [W 2: 79, Upon
Logical Comprehension and Extension, 1867]. In both cases, reasonings
17 Pickwick is an allusion to Charles Dickens’ character, in his novel The Adventures of Mr. Pickwick.
215
depend on an absence of knowledge, related to the question of knowing
if certain objects have or not certain characteristics, what question
places two alternatives:
[...] the absence of knowledge is either whether besides
the objects which, according to the premises, possess
certain characters, any other objects possess them; or,
whether besides the characters which, according to the
premises, belong to certain objects, any other characters
not necessarily involved in these belong to the same
objects. [W 2: 215-216, Some Consequences of Four
Incapacities].
This is not a mere terminological distinction, but a distinction
between two distinct domains of facts, because the assertions are made
either according to the objects themselves, in the case of extension, or
according to the predicates, in the case of comprehension. Related to
extension, we have an induction; related to comprehension, a
hypothesis. Both are distinct cases of synthetic inferences, and
respectively result from the generalization of a particular characteristic
of an object for a whole class, and from the supposition of the existence
of a particular case with certain characteristics. This supposition is
derived from the knowledge of a general rule, in order to explain a fact,
which is strange at first view [W 2: 216-217, Some Consequences of
Four Incapacities].
The difference between breadth and depth can be better
understood if we look at the diagram below [W 1: 459, Lowell Lecture
VII, 1866]:
216
Peirce used the idea of breadth to describe the domain of
nomination, or denotation, or reference, or extension, or the
application of terms to “all the real things of which it is predicable […]”;
and the idea of depth, in turn, is linked to that of meaning, connotation,
definition, intension, sense; in sum, “all the real characters (in
contradistinction to mere names) which can be predicated of it” [W 2:
79, Upon Logical Extension and Comprehension, 1867]. Breadth and
depth, extension and comprehension, denotation and connotation, all
are ideas used in defending the thesis that no term, proposition or
argument is neither absolutely determined, nor absolutely
undetermined. The definitions of extension as denotation, and of
comprehension as connotation, according to Peirce, belong to John
Stuart Mill. Kant, in his turn, had already defined the relation between
extension and comprehension in the following way:
217
What is denotedSphereExtensionBreadth: wider
narrower
What is contained under
What is connotedContentComprehensionDepth: lower
higher
What is contained in
Every concept, as partial concept, is contained in the
representation of things; as ground of cognition, i.e., as
mark, these things are contained under it. In the former
respect every concept has a content, in the other an
extension.18
Extension and comprehension (content), for Kant, are inversely
proportional, that is, “the more a concept contains under itself, namely,
the less it contains in itself, and conversely”19. Thus, “the more the
things that stand under a concept and can be thought through it, the
greater is its extension or sphere”20, and the less it will be as more
things are contained in the concept itself, because it will be possible to
think of a more restrict domain of objects through it.
To say that a term is absolutely undetermined is the same as to
say that it has absolute depth, meaning that it would designate a
characteristic belonged to all things – and this is impossible:
[…] we have propositions whose subjects are entirely
indefinite, as “There is a beautiful ellipse,” where the
subject is merely something actual or potential; but we
have no propositions whose predicate is entirely
indeterminate, for it would be quite senseless to say, “A
has the common characters of all things,” inasmuch as
there are no such common characters [W 2: 50, On a
New List of Categories, 1867].
A completely determined term is also impossible, because it
would mean that such term would be extended to everything, denoting
18 KANT (1799-1800), Ak. 95.19 Idem.20 Id., Ak. 96.
218
everything, indistinctly, what is the same as saying that it would not
denote anything; in other words, to say that a term has an infinite
extension is the same as saying it does not have any extension. This is
impossible, in the first place, because to determine means to relate:
It is incontestable that difference from anything is
determination in respect to being or not being that thing.
A monkey, in differing from a man, is determined
(negatively) in respect to humanity. Difference, then, in
any respect, is determination in that respect [W 2: 150,
Nominalism versus Realism, 1868].
Secondly, an absolutely determined term would be a “logical
atom”, that is, a ”term not capable of logical division”; a logical atom
“must be one of which every predicate may be universally affirmed or
denied” [W 2: 389, Description of a Notation for the Logic of Relatives,
resulting from an Amplification of the Conceptions of Boole’s Calculus
of Logic, 1870]. Now, such term cannot be imagined neither in the
senses, nor in the thought. On one hand, it cannot be imagined in the
senses because our perception does not give us the knowledge of all the
aspects of an object, so that there will always be something else to
determine. For example, the view of an object does not say anything
about its taste; and neither about its color, nor if its surface is rough or
smooth etc.; some further determination is always possible. On the
other hand, because the logical atom is undetermined in the senses, it
is not possible in thought:
219
In thought, an absolutely determinate term cannot be
realized, because, not being given by sense, such a
concept would have to be formed by synthesis, and there
would be no end to the synthesis because there is no
limit to the number of possible predicates. A logical
atom, then, like a point in space, would involve for its
precise determination an endless process [W 2: 390,
Description of a Notation for the Logic of Relatives ...].
Thus, the only way of determining some one thing is to relate it to
another. Terms, arguments, propositions, signs in general are only
determinable in certain ways, and never absolutely: “We can only say,
in a general way, that a term, however determinate, may be made more
determinate still, but not that it can be made absolutely determinate.”
[id.]. For example, “Philip of Macedonia II” can be divided into “Philip
sober” and “Philip drunk”; “Philip of Macedonia II” is interpreted as an
individual term, determined, because it refers to a man in a determined
place in a determined time; but nothing avoids its interpretation as a
general term, in reference to different states of the same Philip in
different moments: a sign is only indivisible, analyzable, complete and
absolutely determinable if the temporal differences are disregarded.21
These remarks open the discussion about the role of
interpretation. The distinction between breadth and depth does not
remain restrict to the differentiations between meaning and reference.
For Peirce, the inverse relation between one and another is not
established in the same way as for Kant. Firstly, we need to remember
21 TIERCELIN (1993b), pp. 278-279.
220
that the distinction between extension and comprehension is extended
also to propositions, and not only to terms or isolated concepts [W 1:
272, Grounds of Induction, 1865]. Secondly, it is possible that two
different terms or propositions have the same extension, but not the
same comprehension, as for example, “Men more than 200 years old”
and “men”22. The whole problem is due to the possibility of increasing
knowledge, that is, to the possibility of knowing more or less. In other
words, the inverse relation between extension and comprehension can
only be defined if it is considered based on the interpretation of
possessed information regarding the objects contained under or in the
concept, that is, regarding everything that is known about the
represented objects: “The sum of synthetical propositions in which the
symbol is subject or predicate, or the information concerning the
symbol” [W 2: 83, Upon Logical Comprehension and Extension].
Now, remember that Kant has differentiated two elementary
kinds of propositions, the analytical and the synthetic ones:
1st Analytical Propositions which are immediately
determinative only of connotation and may be called
connotative
2nd Extensive Propositions which are immediately
determinative only of denotation and may be called
denotative
3rd Synthetic Intensive Propositions which are
immediately determinative both of denotation and
connotation therefore also of information and may be
22 The example is taken from MURPHEY (1993), p. 93.
221
called informative propositions. [W 1: 278, Grounds of
Induction].
The first propositions do not increase knowledge, because the
idea of predicate is already in the idea of the subject. The knowledge
they bring is, then, a mere elucidation, since it occurs from the
decomposition of the concept of the . Now, synthetic judgments amplify
our knowledge, because the idea of the predicate increases the idea of
the subject, adding to it “a predicate which has not been in any wise
thought in it, and which no analysis could possibly extract from it; and
they may therefore be entitled ampliative.” [KrV A 7/B 11]. Extending
the concepts of breadth, depth and information to the propositions,
Peirce, in turn, proposes a division of the propositions into analytical,
intensive synthetical and extensive synthetical:
1st Analytical Propositions which are immediately
determinative only of connotation and may be called
connotative
2nd Extensive Propositions which are immediately
determinative only of denotation and may be called
denotative
3rd Synthetic Intensive Propositions which are
immediately determinative both of denotation and
connotation therefore also of information and may be
called informative propositions [W 1: 278, Grounds of
Induction].
Two ideas are fundamental in order to abandon the Kantian
distinction. First, the key Kantian concept of intensional concepts,
intensionality being understood analytically; that is, the idea of
222
representation based on the essential characteristics of objects. We
shall explain it.
The example of analytical propositions given by Kant is: “To
everything x, to which the concept of body (a + b) belongs, belongs also
extension (b)”23. Analytical propositions have only logic predicates to be
extracted from the concept of the subject; in other words, in an
analytical proposition, the concept of the predicate is extracted from
the concept of the subject because the predicate is understood as a
mark [Merkmal], or constitutive note of the subject. So, analytical are
always logically necessary, and in order to distinguish them from
synthetic propositions it would be enough to apply the principle of non-
contradiction: once the idea of the predicate is deduced from that of the
subject, any contradiction between subject and predicate is impossible
[KrV A 7/B 12]. Analytical propositions, then, only give yield formal
knowledge24.
Synthetic propositions, differently, have determinations, and
because of that, they provide material knowledge. The example is: “To
everything x, to which the concept of body (a + b) belongs, belongs also
attraction (c)”25. In other words, the link between subject (a + b) and
predicate (c) is mediated by the reference to an object that has certain
defined characteristics – a synthetic proposition amplifies our
knowledge about an object x because it give us a determination of the
23 KANT (1799-1800), Ak. 111.24 KANT (1799-1800), Ak. 111.25 Id.
223
object that is not in the concept (a + b), mediately conceiving it by
means of the mark that the mark of the predicate has:
If I say, for instance, “All bodies are extended”, this is an
analytic judgment. For I do not require to go beyond the
concept which I connect with “body” in order to find
extension as bound up with it. To meet with this
predicate, I have merely to analyse the concept, that is,
to become conscious to myself of the manifold which I
always think in that concept. The judgment is therefore
analytic. But when I say, “All bodies are heavy”, the
predicate is something quite different from anything that
I think in the mere concept of body in general; and the
addition of such a predicate therefore yields a synthetic
judgment. [KrV A 7/ B 11]..
Thus, through the marks of the objects, Kant distinguishes
between analytical and synthetical propositions. Human knowledge is
possible because it is possible to represent what is common to many
objects as a “ground for knowledge” [Erkenntnissgrund]. The concept
can be defined, therefore, as repraesentatio per notas communes: a
concept has an extension, that is, it is applicable to many objects,
because it represents them by the characteristic marks they have in
common.26 Thus, the extension of a concept, that is, its reference to the
notas communes of the objects, determines its intension, conferring to
it an analytical unity, making possible to recognize the objects as
pertaining to a certain class. Kant says:
A mark is that in a thing which constitutes a part of the
cognition of it, or – what is the same – a partial
26 KANT (1799-1800), Ak. 58 and Ak. 91.
224
representation, insofar as it is considered as ground of
cognition of the whole representation. All our concepts
are marks, accordingly, and all thought is nothing other
than a representing through marks.27
The process by which the marks are conjointly thought informs
the distinction between the ideas of analytical and synthetical, and
therefore between extension and intension of the concepts. Analytical
notes are partial representations of an “effectively given”
representation, in which the defining notes of the determined objects
can be thought under an a priori concept. Synthetical notes, differently,
are representations only of possible representations, that is, they are
thought a posteriori, after a synthesis of many notes. That is why the
first representations are, for Kant, rational concepts, and the latter are
concepts of experience.28 This first conceptual distinction between sorts
of notes allows for a second distinction between coordinate and
subordinate notes:
Marks are coordinate insofar as each of them is
represented as an immediate mark of the thing and are
subordinate insofar as one mark is represented in the
thing only by means of the other. The combination of
coordinate marks to form the whole of a concept is called
an aggregate, the combination of subordinate concepts a
series.29
27 KANT (1799-1800), Ak. 58.28 KANT (1799-1800), Ak. 59.29 Idem. In effect, Kant distinguishes yet three further sorts of notes, namely: affirmative and negative notes; important and fecund notes, sufficient and necessary notes [Ak 59-60]. We will come later to the distinction between affirmative and negative notes.
225
The total sum of the coordinate notes accomplishes the totality of
the concept, which can only be completed in analytical concepts ,
because the synthetic ones reunite only the immediate notes a
posteriori. This is impossible, then, to determinate the extension of
empirical concepts, once the process of subordination can be infinitely
taken forward in experience. In effect, this is the Kantian explanation
for the principle of nota notae nota rei ipsius, that is, the representation
of a representation is the very thing’s representation. In other words, it
is possible to establish the difference between extension and intension
clearly based on that distinction between notes:
Marks are coordinate insofar as each of them is
represented as an immediate mark of the thing and are
subordinate insofar as one mark is represented in the
thing only by means of the other. The combination of
coordinate marks to form the whole of a concept is called
an aggregate, the combination of subordinate concepts a
series.30
Based on the idea of representing what is common among things,
Kant’s conception of representation distinguishes merely formal
knowledge, in which the analytical unity indicates sufficiently the
totality of notes, from material knowledge, in which there is not such
unity, but only the synthesis, by means of the experience, of notes.
Matter and form can consequently be distinguished unequivocally as
what is a posteriori determinable in general, and therefore, empirically,
and the a priori determination itself, which is analytically definable; at
30 Id., ibid.
226
the same time matter and form are inseparable, in that no
determination can exist without something to be determinate [KrV A
266/ B 322]. The combination of many representations, providing more
determinate representations – nota notae nota rei ipsius – is operated
by the copula that links subject and predicate in the proposition. Kant
can state, then, that to judge is to represent representations; that is, to
unify them in a more general concept, what is the same as to synthesize
representations in a process of increasing generalization: “A judgment
is the representation of the unity of the consciousness of various
representations, or the representation of their relation insofar as they
constitute a concept.”31 In this representation of representations, the
matter is the given knowledge, and the form is the “determination of
the way and the manner [Bestimmung der Art und Weise]” da relação
desses conhecimentos na unidade da consciência.32
Another Kantian idea is the logical distinction between
categorical and synthetic propositions. For Kant, the transformation of
hypothetical judgments into categorical ones is impossible, because
their logical natures are completely distinct. Categorical judgments
have matter and form defined by concepts that directly represent
things: the copula is the form that subordinates the predicate to a
subject in a relation of concordance or conflict between them both: “S
is P” or “S is not P”.33 Categorical judgments, consequently, constitute
31 KANT (1799-1800), Ak. 101.32 Id.33 KANT (1799-1800), Ak. 105.
227
the matter of other judgments, by the reason that they affirm things
directly.
Hypothetical judgments, differently, establish a relation of
consequence between two other judgments:
The matter of hypothetical judgments consists of two
judgments that are connected with one another as
ground [Grund] and consequentia [Folge]. One of these
judgments, which contains the ground, is the antecedent
(antecedens, prius), the other, which is related to it as
consequence, is the consequent (consequens, posterius),
and the representation of this kind of connection of two
judgments to one another for the unity of consciousness
is called the consequentia [Consequenz], which
constitutes the form of hypothetical judgments.34
Thus, the formal relation between subject and predicate
expressed by the copula in a categorical judgment stands for the formal
relation of consequence expressed in a hypothetical judgment between
fundament and consequent. What matters in a categorical judgment is
the veracity of the link between subject and predicate; in a hypothetical
judgment, otherwise, what matters is the form of the link between one
proposition and another, so that the veracity of the link between subject
and predicate in each one of them is independent of the formal
correction of each judgment. The fundamental difference is that in the
categorical judgments “nothing is problematic, rather, everything is
assertoric”; in the hypotheticals, “only the consequentia is assertoric”:
There is an essential difference between the two propositions, All
34 Id.
228
bodies are divisible, and, If all bodies are composite, then they are
divisible. In the former proposition I maintain the thing directly, in the
latter only under a condition expressed problematically.35
Peirce assumes a diametrically opposite position to Kant. Firstly,
he also states that the extension of a term or proposition depends on its
comprehension: “The meaning of a term is called its connotation; its
applicability to things its denotation. Every symbol denotes by
connoting” [W 1: 272]. Only by this statement, one can already see how
the discussion is conducted to another direction. In order to apply a
concept or a proposition to a class of objects, it is needed before to
know what the concept or the proposition mean in a defined state of
information; that is, it is necessary first to know which objects they
comprehend, or in Kantian terms, which objects they contain in
themselves, and only then to predicate them, defining an extension:
For a symbol denotes by virtue of connoting and not vice-
versa, hence the object of connotation determines the
object of denotation and not vice-versa, in the sense in
which the subject of a proposition is the term determined
and the predicate is the determining term. Whence if one
of the terms is an object of connotation and the other an
object of denotation, the latter is the subject and not the
former [W 1: 273, Grounds of Induction].
The essential difference from the Kantian paradigm, we can see
by the following passage:
35 KANT (1799-1800), Ak. 106.
229
Now, so far as the object of a symbol contains the thing,
so far the symbol stands for something and so far it
denotes. So far as its object embodies a form, so far the
symbol has a meaning and so far it connotes. Thus we
see that the denotative object and the connotative object
are in fact identical; and therefore an analytic, an
intensive synthetic, and an extensive proposition may all
represent the same fact and yet the mode in which they
are obtained and the relation of the proposition to that
fact are necessarily very different [W 1: 275, Grounds of
Induction].
Now, the merkmale of the objects do not matter anymore;
differences between propositions will not be based upon the
characteristic marks the objects have in common, but on the way of
referring them. The applicability of a concept to a object or to a class of
objects rests on the group of predicates which are possible to attribute
to the concept. Peirce states:
[…] the Sphere of a term is all the things we know that it
applies to or the disjunctive sum of the subjects to which
it can be predicate in an affirmative subsumptive
proposition. The content of a term is all the attributes it
tells us or the conjunctive sum of the predicates to which
it can be made subject in a universal necessary
proposition. The maxim then which rules explicatory
reasoning is that any part of the content of a term can be
predicated of any part of its sphere [W 1: 462, Lowell
Lecture VII, 1866].
Kant’s distinction between matter and form loses its meaning,
once the logical discussion is dislocated from examining the
conformation of matter to form to examining the ways in which it is
230
possible to represent such conformation. This logical operation renews
the Kantian distinction between affirmative and negative notes. By the
affirmative notes, we know what a thing is, by the negative ones we
know what it is not; in other words, negative notes prevent us from
erroneously applying a concept36. If it is the depth of concepts that
define their breadth, so the wider the sphere of concept is, the less
determinate the concept will be. In Kantian terms, therefore, to define
affirmative notes is the same as increasing its sphere, that is, to achieve
a greater degree of generalization. For Peirce, the definition of the
content diminishes extension of the concept, in a process described in
the following manner:
Now this is evidently true. If we take the term man and
increase its comprehension by the addition of black, we
have black man and this has less extension than man. So
if we take black man and add non-black man to its
sphere, we have man again, and so have decreased the
comprehension. So that whenever the extension is
increased the comprehension is diminished and vice
versa. The highest terms are therefore broadest and the
lowest terms the narrowest [W 1: 460, Lowell Lecture
VII].
With the application of the concepts of breadth and extension to
arguments and propositions, the distinction between categorical and
hypothetical judgments loses its meaning:
The forms A -< B, or A implies B, and A ~-< B, or A does
not imply B, embrace both hypothetical and categorical
36 KANT (1799-1800), Ak. 59-60.
231
propositions. Thus, to say that all men are mortal is the
same as to say that if any man possesses any character
whatever then a mortal possesses that character. To say,
‘if A, then B’ is obviously the same as to say that from A,
B follows, logically or extralogically. By thus identifying
the relation expressed by the copula with that of illation,
we identify the proposition with the inference, and the
term with the proposition. This identification, by means
of which all that is found true of term, proposition, or
inference is at once known to be true of all three, is a
most important engine of reasoning, which we have
gained by beginning with a consideration of the genesis
of logic. [*]
[*]In consequence of the identification in question, in S -
< P, I speak of S indifferently as subject, antecedent, or
premiss, and of P as predicate, consequent, or
conclusion.37 [W 4: 170, On the Algebra of Logic, 1880].
A consequence of great importance will be a new conception of
logic. For Kant, logic was “the science of the necessary laws of the
understanding and of reason in general, or what is one and the same, of
the mere form of thought as such”38. Then, logic does not study contents
of knowledge; it is not the study of “real and natural essence of
things”39. As such, logic is an instrument (organon) of knowledge only in
a very straight meaning, being essentially a preparatory technique:
Logic [...], as universal propaedeutic to all use of the
understanding and of reason in general, may not go into
the sciences and anticipate their matter. It is only a
universal art of reason (canonica Epicuri) for making
37 Cf. KANT (1799-1800), Ak. 106, where he states that the ways of linking in the hypothetical judgments are given by the modus ponens and by the modus tollens.38 KANT (1799-1800), Ak. 13.39 KANT (1799-1800), Ak. 61.
232
cognitions in general conform to the form of the
understanding in general, and hence is only to this extent
to be called an organon, which servers of course merely
for passing judgment and for correcting our cognition,
but not for expanding it.40
Already in 1865 Peirce considered the Kantian definition of logic
as the best ever given, till then; although with strong traits of
psychologism, notwithstanding what Kant himself thought, the
definition had already the essence of the one Peirce would adopt [W 1:
306, An Unpsychological View of Logic to which are appended some
applications of the theory to Psychology and other subjects, 1865]. For
the young Peirce of those years, logic should not be understood as a
psychological science; nevertheless, it is not be a science of the laws of
thought either, but a study of symbols – linguistic symbols (words,
propositions, arguments) or not – in general, as symbols can be
expressions of every and any possible thought, and not only as they are
actually thought; logic is universal and does not need to understand
how the mind works in order to understand how symbols represent. So
logic studies the forms of expression of thoughts and their relations to
what they mean, and not thought itself or the constitution of mind,
standing back from any aspect of psychologism: “This manner of stating
the matter frees us at once from all psychological perplexities; and at
the same time we lose nothing, since all we know of thought is but a
40 Id., ibid. Our italics.
233
reflection of what we know of its expression [W 2: 25, On the Natural
Classification of Arguments, 1867].”
If logic is concerned with thoughts, it is only inasmuch as they can
be understood as symbols, that is, in their quality of representations;
then, in Kantian terms, Peirce states in 1865:
In fact, thought may be illogical; it is only correct
thought which is logical. What is this correct thought? It
is thought which represents the intuition. Logic therefore
deals with thought only in so far as the latter is a
representation. And as I said every representation has its
logical relations whether it is actually thought or not. So
that it is more correct to say that logic is the science of
the forms of representation than that it is the science of
the forms of thought [W 1: 322, Logic of the Sciences].
So, logic is restricted to the study of representations inasmuch as
they can be interpreted, that is, insofar as it is possible to understand
them in relation to some object (which can be another representation),
that is, in relation to the information they convey:
The informed breadth and depth suppose a state of
information which lies somewhere between two
imaginary extremes. These are, first, the state in which
no fact would be known, but only the meaning of terms;
and, second, the state in which the information would
amount to an absolute intuition of all there is, so that the
things we should know would be the very substances
themselves, and the qualities we should know would be
the very concrete forms themselves [W 2: 79, Upon
Logical Extension and Comprehension].
234
For Peirce, complete states of essential and substantial
information as extremely imaginary. In truth, it is impossible to know
for sure what is meant, as said before. Nevertheless, there are ways to
define what is meant, though in an uncertain way. To accomplish this
definition it is requisite to abandon the idea of a complete
determination of meaning, an idea which is present, for instance, in the
Kantian presumption that logic deals not with contents. Logic does deal
with contents, informative contents, as it also does deal with the
conditions for the veracity of the information, even though the
possibility of absolute precision or complete demarcation of the domain
of signification is refused. It is illusory to want to begin with precision,
since indetermination is a necessary condition for every interpretation.41
That does not mean it is not possible to have some precision. As a
matter of fact, the new conception of logic as an analysis of expressivity
concerns the very ways of diminishing the indetermination of signs,
through the analysis of the relation between depth and breadth. To
imagine that some degree of indeterminacy is impossible would be
foolishness; the understanding of processes of determination requires
the study of ways to refer to objects. Peirce distinguishes three distinct
ways in which this reference can happen. First, reference to an object
may be direct, so that breadth be defined; second, reference may be
mediated by characters of the objects, so that depth be defined; finally,
reference may be made through a joint determination of connotation 41 We shall see this idea again in the theory of assertion. Cf. TIERCELIN (1993b), p. 279.
235
and denotation, that is, through interpreting the total information or
idea known of the object which is represented [W 2: 83].
We have seen that Kant thought of the relation between extension
and comprehension of a concept as an inverse relation; to Peirce, this
relation depends upon a state of information: if the information about a
term or expression is constant, there is no modification neither of
extension, nor of comprehension; if there can be an increase of
information, either the extension increases and the comprehension
decreases, or vice-versa; and if there is no information, that is, if
nothing is known about the relation of a term or expression with their
representanda, there is neither extension nor comprehension. Then, the
relation between extension and comprehension can be defined by the
formula: Breadth X Depth = Area [id.], which is the same as to say that:
Extension X Comprehension = Information [W 1: 276, Grounds of
Induction]. The reason why is Peirce clearly puts in this way: “The
reason why Extension X Comprehension = Information is that Extension
and Comprehension can only be reckoned by the interpretants, each
interpretant measuring either one or the other.” [W 1: 479, Lowell
Lecture IX, 1866].
Propositions represent facts or objects from a standpoint from
which it will be possible to predicate them with certain attributes. And
the predicate applies to what is represented because it is interpreted as
such in another representation, which is the interpretant. Every
236
representation is a representation of an object from a certain point of
view to an interpretant, which unifies all the information concerning
such object in one conception, interpreting them. The representative
function, therefore, does not depend only upon the material qualities of
the symbol (whether it is spoke or written) or upon its demonstrative
pure application (the definition of its denotation, in an ostensive
gesture, for instance), but chiefly upon the possibility of remittance to
another representation, upon the possibility of its being understood as
such – if a cloud means rain, it is because it is interpreted as a sign of
rain. Even no one in fact interprets it as such, what makes the cloud a
sign of rain, we stress, is the possibility of meaning rain: “And yet if I
take all the things which have certain qualities and physically connect
them with a another series of things, each to each, they become fit to be
signs. If they are not regarded as such they are not actually signs” [EP
1: 40, Some Consequences of Four Incapacities].42
Describing the forms of expressing thoughts and the relations
settled between them and their representanda, Peirce’s logic
simultaneously approaches and distances itself from Kant’s logic, in
some respects which is worth to mention: 1st) logic is universal, but not
because it deals with the rules of the use of the intellect in general, but
because it deals with symbols in general, whatever they may be, in their
capacity of representing their objects in certain ways; 2nd) hence, logic
is not psychological, since it is not interested in the psychological 42 Cf. Hookway (1992), pp. 32-34.
237
apprehension or effective understanding of the symbols, but only to
their capacity of being expressed and interpreted; in other words, logic
deals with the conditions of possibility of meaning, and not with the
actual signification proper of the signs as they are subjectively
understood; 3rd) hence, logic does not study the way in which we
actually think, but which are the formal grounds of our inferences; 4th)
and, consequently, the business of logic is exactly that which was
refused by Kant: the amplification of knowledge. Years later, in 1905,
Peirce Said:
After a series of inquiries, I came to see that Kant ought
not to have confined himself to divisions of propositions,
or ‘judgments’, as the Germans confuse the subject by
calling them, but ought to have taken account of all
elementary and significant differences of form among
signs of all sorts, and that, above all, he ought not to
have left out of account fundamental forms of reasonings.
[EP 2: 424, Pragmatism, 1907].
Deduction, induction, and hypothesis will therefore be objects of
analysis par excellence. Seen from the point of view of the distinctions
between depth, breadth and information conveyed, the three kinds of
reasoning are the subject-matter of exact logic:
Logic (exact): Ger. exakte Logik; Fr. logique exacte; Ital.
logica esatta. The doctrine that the theory of validity and
strength of reasoning ought to be made one of the 'exact
sciences,' that is, that generalizations from ordinary
experience ought, at an early point in its exposition, to be
stated in a form from which by mathematical, or
expository, reasoning, the rest of the theory can be
238
strictly deduced; together with the attempt to carry this
doctrine into practice.43
Inductive reasoning is wider than hypothetical, and the latter are
deeper than the former. Inductive inference is probably true of all
instances of a class of objects, which conclusion results from the
application of the rule to one or more cases known under the terms or
propositions, constituting the universe of known objects. Now,
hypothetical inference is probably true just of one of the instances; we
do not have knowledge of one special instance which is the content of
terms and propositions, it is necessary to figure it out, surmising it,
verifying whether the result fits the rule:
In the former case, the reasoning proceeds as though all
the objects which have certain characters were known,
and this is induction; in the latter case, the inference
proceeds as though all the characters requisite to the
determination of a certain object or class were known,
and this is hypothesis. [W 2: 216].
Let us see Peirce’s examples. Take any piece of writing in English,
called A, of which the number of times that certain letters appear will
be ascertained; insofar we count them, we come to see that some occur
more than others, less and less variably. For example, the number of
times in which the letter “e” occurs makes 11 ¼ percent of the total,
letter “t”, 8 ½ percent of the total, letter “a”, 8 percent, etc. if we find
the same approximate result, say, in more half a dozen other English
43 Entry “Logic (exact)” for the Dictionary of Philosophy and Psychology, edited by James M. Baldwin, 1902. Partially available on-line at: [http://psychclassics.yorku.ca/Baldwin/Dictionary/]. Acessed 13/02/2005.
239
writings, which will be called B, C, D, E, F, G, we will infer that in every
piece of English writing of a certain extension, we will probably find
more or less the same percentage of occurrence to the same letters.
However, if we know of a certain writing H, of which the percentage of
occurrence of the same letters is entirely different, the initial
conclusion loses credibility; if the percentage is the same, the
conclusion gains force. This is one case of induction, in which the
conclusion obtained is valid only if we do not know of any other
different instance from what was analysed [id.].
Consider an analogous instance of a codified writing to decipher.
We find that the code has twenty six characters, one of them occurring
11 ¼ percent of the times in text; another one, which percentage of
occurrence is around 8 ½ percent, and another else, with 8 percent of
occurrences, etc. substituting “e”, “t”, “a”, etc., respectively, for them,
we will see how the code makes sense in English (counting also the
orthographic mistakes). If this piece of codified writing has a
considerable extent, we can say that we have correctly deciphered the
code, with a great probability. Our inference will be valid if we do not
know of any other characteristics peculiar to the code, which are not
peculiar to the English idiom. Otherwise, we will have to take them into
account, to enforce or weaken our hypothesis – and the knowledge of
such other characteristics may, for instance, indicate another way of
deciphering it. [W 2: 217-218, ibid.].
240
Deduction, induction, and hypotheses are then the only three
kinds of valid reasoning, and all thought is of some one of these kinds,
or a combination of them [W 2: 217, Some Consequences of Four
Incapacities, 1868]. This is the basic conclusion Peirce arrives at in
these early writings. The basal difference he in 1868 established
between the three kinds of reasoning is that deduction is a
demonstrative inference that does not increase our knowledge of facts,
for it passes from a general rule, as a premise, to affirm a conclusion
resulting from the analytical unfolding of the relations affirmed in the
premise; induction and hypotheses, differently, are ampliative illations,
different one from another, that increase our knowledge: induction is a
generalization, it proceeds from the verification of a particular
experience to infer a general explanatory rule for such experience;
hypothesis, in its turn, assumes a general rule from the beginning, and
from it seeks to establish relations between particular facts of
experience, otherwise apparently disconnected. Differences are clearer
when we compare them definitions. First, induction:
Induction may be defined as an argument which proceeds
upon the assumption that all the members of a class or
aggregate have all the characters which are common to
all those members of this class concerning which it is
known, whether they have these characters or not; or, in
other words, which assumes that that is true of a whole
collection which is true of a number of instances taken
from it at random. This might be called statistical
241
argument. In the long run, it must generally afford pretty
correct conclusions from true premises. [W 2: 217].
Peirce clears up the definition with the following illustration. If we
have a bag full of beans, white and black, drawing from it a sufficient
number of samples at random, we will be able to approximately
determine the relative number of black and white beans, in a certain
moment, and with a small range for error.
Now, let us remember the syllogistic form of deduction:
Rule: All S is
P.
Case: M is S
Resul
t:
M is
P.
A typical inductive reasoning would have the inverted form of a
deductive syllogism as follows:
Case: These beans are from this bag. M is S
Resul
t:
These beans are White. M is P
Rul
e:
All the beans in this bag are
white.
All S is
P.
An induction can be seen as the deductive inference of the second
premiss, from the conclusion obtained and the particular case affirmed
in the first premises; or, in other words, a probable deduction
consisting in the inference of a general rule from the observation of a
242
result in a certain case [W 3: 328, Deduction, Induction, and
Hypothesis]. Then, deriving the major premiss of a syllogism from its
minor premises, induction is a form of reduction of the multiplicity to
the unity, allowing for an assertion about facts, very likely to be true [W
3: 217]. Induction, amplifying the extension of a certain class of
subjects, amplifies the generality of the conclusion beyond the limits
affirmed in the major premiss of the syllogism, in an operation that
allows to pass from the determination of the existence to the virutality
of the possible, for it reaches a general concept about actual instances;
for such reason we can assure that other similar instances can be
submitted to the same concept44. We will recover this point further on.
Let us see hypothesis:
Hypothesis can be defined as an argument which
proceeds upon the assumption that a character which is
known necessarily to involve a certain number of others,
may be probably predicated of any objects which have all
the characters which this character is known to involve.
[W 2: 217-218].
According to such definition, hypothesis can be defined as the
inference of a minor premiss from two other premises of a syllogism; in
other words, as an inference of a particular instance from a general
rule and the probable result of the application of the rule to the case, in
another kind of the inversion of deduction [W 3: 325-328]. Thus we
44 BACHA (1999), p. 159.
243
have the following formulation of the example of the letters, given
above:
1. Every English writing of some length in which such
and such characters denote e, t, a, and s, has about 11
1/4 per cent of the first sort of marks, 8 1/2 of the
second, 8 of the third, and 7 1/2 of the fourth. This secret
writing is an English writing of some length, in which
such and such characters denote e, t, a, and s,
respectively:
.·. This secret writing has about 11 1/4 per cent of its
characters of the first kind, 8 1/2 of the second, 8 of the
third, and 7 1/2 of the fourth.
2. A passage written with such an alphabet makes sense
when such and such letters are severally substituted for
such and such characters. This secret writing is written
with such an alphabet.
.·. This secret writing makes sense when such and such
substitutions are made. [W 2: 218]
Just as induction, hypothesis also operates a reduction of the
multiplicity to the unity, substituting one affirmation, or a few ones,
which may be linked to other affirmations, for various other
unconnected. Hypothesis can be written as follows:
Rule: All the beans of this bag are white All S is P.
Result: These beans are white. M is P.
Case: These beans are from this bag. M is S.
We then see that through the inversion of the deductive syllogism,
changing the places of subjects and predicates, that is, changing
244
premises, we get different kinds of reasoning. Peirce can conclude then,
in 1883:
Deduction proceeds from Rule and Case to Result; it is
the formula of Volition. Induction proceeds from Case
and Result to Rule; it is the formula of the formation of a
habit or general conception – a process which,
psychologically as well as logically, depends on the
repetition of instances or sensations. Hypothesis
proceeds from Rule and Result to Case; it is the formula
of the acquirement of secondary sensation – a process by
which a confused concatenation of predicates is brought
into order under a synthesizing predicate.45 [W 4: 422, A
Theory of Probable Inference].
We can now proceed to the problem of the validity of induction.
The justification of induction, in Peirce’s early writings, is grounded
upon two basic ideas. The first is that parts make up the whole. To this
idea we will return after examining the second, which is that there is an
independent reality from all subjectivities, a reality possessing some
general features, what ultimately warrants the success of inductions
because it compels opinions to converge in one true final and definite
opinion. If such reality did not exist, no illation would be successful:
Now, since if there is anything real, then [...] it follows
necessarily that a sufficient long succession of inferences
from parts to whole will lead men to a knowledge of it, so
that in that case they cannot be fated on the whole to be
thoroughly unlucky in their inductions. [W 2: 269, id.].
This argument for the validity of induction has a double feature.
First, it puts forward the idea that the inductive method, if sufficiently
45 Cf. BACHA (1999), p. 209.
245
pursued, is successful, to which we will get back further on, for it is a
central idea to validate the thesis of self-correctness of induction.
Second, the argument depends upon the first one, Peirce’s theory of
reality, according to which the real is independent of conceptions,
volitions, or feelings of a certain finite number of people, that it has the
character of remaining the same in the long run, and the character of
being other than the figments of fancy:
And what do we mean by the real? It is a conception
which we must first have had when we discovered that
there was an unreal, an illusion; that is, when we first
corrected ourselves. Now the distinction for which alone
this fact logically called, was between an ens relative to
private inward determinations, to the negations
belonging to idiosyncrasy, and an ens such as would
stand in the long run. [W 2: 239, Some Consequences of
Four Incapacities].
In the 1871 Berkeley review, Peirce contrasts a realist conception
of reality and a nominalist one. Described as the conception that
considers as real something which is outside the mind, constraining our
sensations, and, through them our thoughts, nominalism is refused by
Peirce under the claim that it makes it impossible to recognize any
feature of generality in reality. This nominalist conception of reality,
which is pretty much “familiar, according to him, does not take into
account that universal terms such as man, horse, rose, etc., are real,
that is, that they represent real relations between all individual men,
horses, or roses, independently of how we conceive them; instead,
246
nominalism defends that “these classes are constituted simply by a
likeness in the way in which our minds are affected by individual
objects which have in themselves no resemblance or relationship
whatsoever.” [W 2: 467, Fraser’s The Works of George Berkeley, 1871].
To the nominalist, reality is conceived as the efficient cause of our
sensations, independently of any and every conception about it that
might be [W 2: 469, id.]. in short, the nominalist conception, besides
refusing generality to reality, transforms it into a kind of unknowable
thing-in-itself, the cause of our thoughts, yet even so unattainable:
The nominalist must admit that man is truly applicable to
something; but he believes that there is beneath this a
thing in itself, an incognizable reality.[...] The great
argument for nominalism is that there is no man unless
there is some particular man. [W 2: 240, Some
Consequences of Four Incapacities].
The realist conception, on the contrary, is supported by the idea
that “universals must have a real existence”; an universal is not a mere
flatus vocis, inasmuch as it is not a classificatory mental scheme, as a
nominalist could say. Peirce exhibits the problem of universals in the
following terms:
Are universals real? We have only to stop and consider a
moment what was meant by the word real, when the
whole issue soon becomes apparent. Objects are divided
into figments, dreams, etc., on the one hand, and realities
on the other. The former are those which exist only
inasmuch as you or I or some man imagines them; the
latter are those which have an existence independent of
247
your mind or mine or that of any number of persons. The
real is that which is not whatever we happen to think it,
but is unaffected by what we may think of it. [W 2: 467].
The real must be something independent of a finite number of
people, not relative to subjective determinations. As Peirce says, this
conception of reality involves the conception of a community, with
undefined limits, capable of indefinite increase, that, in its general
conceptions, will represent the real and the unreal, remittently
affirming the former, and the same conditions maintained, denying the
latter in the same way [W 2: 239, Some Consequences of Four
Incapacities].
Remaining through an indefinite time in the run of experience,
reality becomes apprehensible in a certain way – in truth, the real has
the power to constraint our opinions: “Where is the real, the thing
independent of how we think it, to be found? There must be such a
thing, for we find our opinions constrained; there is something,
therefore, which influences our thoughts, and is not created by them.”
[W 2: 468, Fraser’s The Works of George Berkeley].
This character of insistence reality has makes that it is forced
against consciousness to be recognized. Such insistence shows itself
under the guise of regularity: the permanence of the real is the
necessary condition to cognoscibility, and also the warranty of the
objectivity of representations, for it assures that our conceptions about
reality are irreducible to subjective whims.46 This general feature of 46 IBRI (1992), p. 30.
248
permanence makes it impossible not to discover the truth about reality,
in an undetermined future:
[...] human opinion universally tends in the long run to a
definite form, which is the truth. Let any human being
have enough information and exert enough thought upon
any question, and the result will be that he will arrive at
a certain definite conclusion, which is the same that any
other mind will reach under sufficiently favourable
circumstances. […] The individual may not live to reach
the truth; there is a residuum of error in every
individual’s opinions. No matter; it remains that there is
a definite opinion to which the mind of man is, on the
whole and in the long run, tending. [W 2: 468-469, id.].
It is possible to say that the continuous duration of the real in
experience is condition sine qua non for the verifiability of hypotheses –
these latter will only be valid if the can predict how reality will continue
in the future. In other words, in our present conceptions we have to
represent now the future regularity of things; and this regularity is
capable of being represented because the world has a certain spatial-
temporal order which remains independently of our will47. Time in this
way is an essential element to the possibility of conceiving reality; in
order it may be possible to pass from the immediate experience of a
single perception to the recognition of relations and meaningful links
between empirical eventos, time is needed. In the course of time, the
regularity of events will show the errors of the initial surmises, driving
47 IBRI (1994), cap. 1: “Da possibilidade do dever ser: o teorema de Alice”, passim.
249
human opinion universally to the truth that will be expressed in the
final opinion:
This final opinion, then, is independent, not indeed of
thought in general, but of all that is arbitrary and
individual in thought; is quite independent of how you, or
I, or any number of men think. Everything, therefore,
which will be thought to exist in the final opinion is real,
and nothing else. [W 2: 469].
The realist, then, will be led to believe in reality as it is
represented in a true representation, that is, in its general features: the
word “man”, for instance, is true only because it means something real
[W 2: 239]. Differently from what Hume claims, the world Peirce
describes is such wherein relations are real, wherein the continuity of
events allows discovering the way one is linked to another through the
logic of induction.
In fact, inductions and hypothesis can be successful in their
generalizations and predictions because reality remains reacting
against our experience: there is a reality, which permanently reacting
against experience, presents general and continuous characters.
Nevertheless, those are not the only features of reality. In the same
writing from 1869 about the laws of logic, Peirce asks whether it is
possible to ground the validity of induction upon and hypothetical order
of nature. How is it possible to answer to the question that the facts of a
certain species are normally true when other facts, of another species,
are also true? In other words, how is it possible to assert that facts of a
250
determined species have specific relations to facts of another species?
An easy answer would be to assume an order of nature:
The usual reply is that nature is everywhere regular; as
things have been, so they will be; as one part of nature is,
so is every other. But this explanation will not do. Nature
is not regular. No disorder would be less orderly than the
existing arrangement. It is true that the special laws and
regularities are innumerable; but nobody thinks of the
irregularities, which are infinitely more frequent. Every
fact true of any one thing in the universe is related to
every fact true of every other. But the immense majority
of these relations are fortuitous and irregular. A man in
China bought a cow three days and five minutes after a
Greenlander had sneezed. Is that abstract circumstance
connected with any regularity whatever? And are not
such relations infinitely more frequent than those which
are regular? [W 2: 264, Grounds of Validity of the Laws
of Logic].
The regularities of the universe, therefore, happen much less than
the irregularities, what leads to the supposition that not everything in
nature has as determined cause; the idea of an order of nature thus
cannot be presupposed, for experience shows us that there are events
that happen without apparent cause, without a necessary connection
with other events, more often than the ones that happen in determinate
ways48. The knowledge of the existence of some minimal order of nature
would be useful only if we could take it as the major premises of
48 In effect, this idea, constitutive of the metaphysical doctrine of chance (tychism), is presented by IBRI (1992), p. 40 ff., as the first ground of Peirce’s fallibilism, the other foundation being evolutionism. We will not deal with such theme in detail. The reader can find more thorough expositions of the subject, and other connected matters, in HAUSMAN (1993); IBRI (1992), pp. 39 ff.; SANTAELLA (1999); SILVEIRA (1984).
251
deductions, as a basis to explain only how knowledge could be made
more or less certain. However, it is not a matter of certainty, but of
increase of knowledge. Knowledge of an order of nature would not
serve to ground a justification of hypothetical and inductive illations,
that is, it does not explain how it possible to increase knowledge. [W 2:
265, Grounds of Validity of the Laws of Logic]49.
Here we have the other basal idea for the justification of
induction, which is that the parts make up the whole. The gist of the
discussion is in the idea that it is possible to ascertain the proportion of
the relations between known and unknown facts. In short, the only valid
justification for grounding the laws of logic must search for its bases in
a theory of probabilities: “The only attempt of this sort, however, which
deserves to be noticed is that which seeks to determine the probability
of a future event by the theory of probabilities, from the fact that a
certain number of similar events have been observed.” [W 2: 267]. The
success of such attempt in its turn depends upon the definition of
probability as “the ratio of the frequency of occurrence of a specific
event to a general one over it.” [id.]. In other words, it is necessary to
determine how many times it is possible that a certain event happens in
the indeterminate future, when it occurred already a certain number of
times. So, to affirm a general proposition about the future course of
49 Peirce’s argumentation is much more detailed. We show here only a sketch of his conclusions, intending to put the arguments forward. About the question of the certainty of knowledge, see CROMBIE (1997), pp. 460-461. We will get back to the idea of order of nature further on.
252
events is to affirm, from the observations made, the existence of a
certain regularity in nature. The idea is that knowledge is justified
when it is inductively tested; it is not the attempt to prove a natural
regularity previously assumed, but the attempt to discover whether
there is any regularity in facts that may be expressed in general terms,
so that it explains the conduct of facts, the actual and the merely
possible ones [EP 2: 316, , 1904]. This problem involves
several difficulties. Let us see, firstly, which are the terms in which the
issue is presented in 1869.
First, the validity of induction depends upon the fact that in the
long run all the members of a collection to which one wants to prove
that it possesses certain features will be drawn at random, and have the
same chance to be draw in the samples:
Out of a bag of black and white beans I take a few
handfuls, and from this sample I can judge approximately
the proportions of black and white in the whole. This is
identical with induction. Now we know upon what the
validity of this inference depends. It depends upon the
fact that in the long run, any one bean would be taken
out as often as any other. [W 2: 268, Grounds of Validity
of the Laws of Logic].
Thus, the characters of the sample can be taken as an index of the
characters of the whole, because the frequency of occurrence of a given
kind is relative to the whole set. It is mainly important that the
probability of being drawn in the samples be equal to all the beans in
the bag; that is valid to all classes of objects. Following this principle,
253
whatever member of a class could be subject of a premises, and
therefore, predicable of the quality that one wants to discover so much
as the extant. Inductive reasoning, therefore, “is the same as statistical
inference” [W 2: 268].
This is the essence of the idea of the long run: in processes of
long duration, the character of alterity of reality would warrant that the
possibility of determining a certain range of probabilities is effective, a
range wherein it would be possible to estimate in an approximate
degree the truth, that is, the “order of general relations”50 existent
between the events of the world. Thus, through the remittent
continuation of the method, it is possible to reach closer to a true
representation of the mode of happening of facts.
Peirce gradually passes to emphasize the idea of self-correctness
of induction in his writings. By doing so, he abandons the idea that
inductive reasoning is an ampliative kind of reasoning, reserving all
heuristic power to abduction; the business of induction is to test
hypothetical suggestions only, to assure them prognostic reliability. In
1901, for instance, we see the problem displayed in a much more
explicit way:
Induction […] is not justified by any relation between the
facts stated in the premisses and the fact stated in the
conclusion; and it does not infer that the latter fact is
either necessary or objectively probable. But the
justification of its conclusion is that that conclusion is
50 IBRI (1994), p. 105.
254
reached by a method which, steadily persisted in, must
lead to true knowledge in the long run of cases of its
application, whether to the existing world or to any
imaginable world whatsoever. [HP II: 736, On The Logic
of Drawing History from Ancient Documents].
Therefore, differently from the position assumed in his early
writings, induction is no more seen as a kind of inference that brings
true knowledge about the world, but only as a means to ascertain the
validity of hypothesis experimentally, by remittently confronting them
against experience: “Induction is the experimental testing of a theory.”
[HL 218]. Induction so acquires validity inasmuch as it is capable of
self-correcting its own results:
Induction is a kind of reasoning that may lead us into
error; but that it follows a method which, sufficiently
persisted in, will be Inductively Certain (the sort of
certainty we have that a perfect coin, pitched up often
enough, will sometime turn up heads) to diminish the
error below any predesignate degree, is assured by
man's power of perceiving Inductive Certainty. [EP 2:
443, A Neglected Argument for the Reality of God].
In other words, the issue is to determine, even though in a
provisory way, the probability of getting heads or tails in a throw of a
coin. Let us say that it is asserted that a coin, if thrown 10.000 times,
half the throws will be heads, once 50 of the first 100 were heads. Now,
suppose this conclusion is false. According to the theory, it is possible
then to correct this induction merely by observing more and more
throws, basing the conclusion on the relative frequency of heads in the
255
total series of 10.000 throws on the relative frequency in the biggest
available sample in a certain moment. If this experiment is carried on
time enough, in a given moment the correct value will be reached. The
assertion that the process is self corrective is then justified: remittent
applications of the method lead to increasing approximations to truth.
The capacity of self-correctness of the process is due to th
successsive comparisons of the hypotheses with what experience shows
us. If the frequency of occurrence of a property of individuals of the
sample is not proportional to their frequency of occurrence on the
whole set, this difference tends to get clearer in the long run. Thus, by
systematically adjusting the estimations, it is possible to arrive each
time at a more correct measurement.
In truth, it is being asserted that in long run processes the
probability of failure in scientific inquiry can be reduced to very low
levels. It is almost as saying that science is theoretically infallible [CP
7.77-78, c. 1902]51. Let us understand better what means such
infallibility. In the way we have exposed it, everything depends on
determining relations between distinct quantities; nevertheless, one
can never know how much of nature was already discovered, simply
because one does not know how much is yet to be discovered; in a
51 RESCHER (1978), p. 2.
256
word, nature is like a infinite collection [W 2: 265] 52. The concept of
collection helps our understanding of the issue:
By a collection, I mean an individual object whose actual
presence in any part of experience consists in the actual
presence of certain other individual objects called its
members, so that if one of them were absent, the same
collection would not be present; and these members are
such that any part of them might logically be present or
absent irrespective of the presence or absence of any
others; and the truth of any predication concerning a
collection consists in the truth of a corresponding
predication concerning whatever members it may
possess, so that taking any universal proposition
whatever, there is a collection having for its only
members whatever independent objects there may be of
which that proposition makes any given affirmation. [HP
II: 742, On the Logic of Drawing History from Ancient
Documents …].
Thus, to say “Every man is mortal” is to say that there is a
collection of all men that there may be; to say “Every man in Mars is
mortal” is to say that there is in Mars a collection of men that, whatever
they may be, they are mortal. The actual existence of men in Mars
implies only the falsity of the assertion, but it does no change the fact
that the collection continues to be a collection [id.]. A collection,
defined in this way, can be called continuous. In other words, it is an
aggregate of independent objects, but such as cannot be taken as the
52 Following some and opposing others of Georg Cantor’s conceptions, Peirce developed a theory of continuity and “multitudes”, which will not be analyzed here. For a detailed comparison of Cantor’s and Peirce’s conceptions, see PARKER (1998), chap. 4: “Infinity and Continuity”.
257
ultimate constituents, because they are all related in such a way that
there is no possibility of isolating the parts without breaking the
collection, that is, without breaking the continuity. The capacity of
being infinitely divided is a necessary condition to define a true
continuity [NEM 3/II: 748, Mathematical Logic, 1902]. It means that in
between each of its members, there are other members. For instance,
think of the series of natural numbers:
1, 2, 3, 4, 5, 6, 7, ... n.
It is always possible to divide the series between a term a and
another, as follows:
1, 1.1, 1.11, 1.112, 1.1121, ..... 1.n, 2, 2.1, 2.11, 2.112, ....,
2.n etc., 3n etc. ...
Or yet, let us separate the series into two distinct ones, of odd and
even integers:
1, 3, 5, 7, 9, ... n
2, 4, 6, 8, ... n
It is clear that the parts are also infinite, the same as the whole
[EP 1: 317, The Law of Mind, 1892]. Therefore, it is impossible to
ascertain the exact quantity of the members of a continuous collection;
but it is possible to ascertain an approximate value to its multitude: “I
use the term multitude to express that character of any collection which
consists in its being as small as whatever collections it is as small as,
258
and being as great as whatever collections it is as great as.” [HP II:
743, On the Logic of Drawing History from Ancient Documents …].
Even tough it is the first defining character of a true continuity,
infinite divisibility is not a sufficient condition to define it; with this
concept of continuity, irrational numbers cannot be explained, for
instance. As it is known, irrational numbers can be written as decimals,
but not as fractions. In other words, irrational numbers are numbers
that cannot be expressed as the ratio (whence their name) of two
integers. The discovery of irrational numbers is ancient, and it is
related to problems of defining a number for quantities not measurable
by real integers. A rational number is defined as the quotient of h/k,
where h and k are integers, and k ≠ 0. A rational number, therefore, is
such that represents the ratio between two integers. Thus any rational
number can be represented by a point in a straight line. Let it the set of
rational numbers be Q:
However, there are several quantities, as weight, width, time, the
square diagonal, etc. that are not measurable by integers; to express
them we need fractions, which are not quotients of two integers. It is
then possible to indicate points in a line that do not correspond to any
ratio between two integers, that is, not corresponding to any rational
number. Such points are represented by irrational numbers; they are
259
capable to be written as tithes, or they can be graphically represented
in the line as follows:
The most famous irrational number maybe is the square root of 2,
which cannot be written as a fraction, that is, as the quotient of two
integers:
Other irrational numbers are =3,14159...and e = 2, 71828...,
for instance. is an irrational number because there is no exact decimal
value correspondent to it, since it cannot be expressed as the ration of
two integers; nonetheless, it is possible to apply 3, 1415926...
satisfactorily in various instances.53 r decimal exato que lhe
corresponda, embora seja possível aplicar satisfatoriamente em vários
casos.
53 For the account of rational numbers, we follow EVES (2004), pp. 104-107. See still NEM 3/I: On Continuous Series and the Infinitesimals, n.d., wherein Peirce tries to show that the whole series of rational and irrational numbers is not a continuous series. We will not go deep into this debate here.
260
Now, for the definition of continuity as infinite divisibility,
irrational numbers are a problem, for rational infinitude, though it is
numerable, it is not continuous. As I. Ibri says, “the infinite divisibility
does not warrant continuity, due to the non-existence of irrational
numbers associated to the innumerability of the points of the line.”54 For
such reason, Peirce criticizes the way how Kant defined continuity:
Let us now consider what is meant by saying that a line,
for example, is continuous. The multitude of points, or
limiting values of approximations upon it, is of course
innumerable. But that does not make it continuous. Kant
defined its continuity as consisting in this, that between
any two points upon it there are points. This is true, but
manifestly insufficient, since it holds of the series of
rational fractions, the multitude of which is only
dinumerable. Indeed, Kant's definition applies if from
such a series any two, together with all that are
intermediate, be cut away; although in that case a finite
gap is made. I have termed the property of infinite
intermediety, or divisibility, the Kanticity of a series. It is
one of the defining characters of a continuum. [CP 4.121,
The Logic of Quantity].
As a matter of fact, infinite divisibility, for Kant, is defined in
terms of limits: the points in the line and in space, moments of time are
all approximative limits, “places of the limitation of space and time”, so
that continuous greatnesses do not have minimal parts [KrV A 169/ B
211]. Peirce recognized that in a first moment he neglected such
54 IBRI (1992), p. 65. Our translation; see the original: “a infinita divisibilidade não garante a continuidade devido à não-existência dos números irracionais associados à inumerabilidade dos pontos da linha.”
261
character of the Kantian definition; nonetheless, he maintains the
criticisms, renewed:
His true doctrine is not that space is divisible without
end, but that it cannot be so divided as to reach an
ultimate part as clearly stated in the last paragraph of p.
169. […] To the obvious objection that points are
ultimate parts of lines, Kant begins to make the right
answer, that they are not parts but limits. But that he
does not understand this right can be seen by p. 209
where he speaks of a change as passing through all the
instantaneous intermediate states. He thus looks on the
point as existing in the line, while the truth is they do not
exist in the continuous line, and if a point is placed on a
line it constitutes a discontinuity.55 [NEM 3/2: 780, letter
to Paul Carus, 17 August 1899].
Indeed, Kant says:
Esta é, pois, a lei da continuidade de toda a mudança,
cujo princípio é o seguinte: nem o tempo, nem tão-pouco
o fenômeno no tempo, se compõem de partes, que sejam
as menores possíveis; e, no entanto, o estado da coisa, na
sua mudança, transita por todas estas partes como por
outros tantos elementos, para o seu segundo estado. [KrV
A 209/ B 254].
Now, if the points in a line are limits, and not distinct parts, there
cannot be the passage “thorugh all the infinite degrees of the same
reality, whose differences among each other are all smaller than the
difference between 0 and a” [id.]. In a true continuity, infinitude is not
numerable, as the discrete parts of an aggregate would be. Let us take
a closer look up upon the concept of true continuity. Its second
55 Pages referred to by Peirce are from the first edition (A), from 1781, of the Critic of the Pure Reason.
262
character is that its parts share limits.56 This property is called by
Peirce its Aristotelicity: “I made a new definition, according to which
continuity consists in Kanticity and Aristotelicity. The Kanticity is
having a point between any two points. The Aristotelicity is having
every point that is a limit to an infinite series of points that belong to
the system.” [CP 6: 166, 1903]. Indeed, in the Metaphysics, the
Aristotelian definition of the continuous is the following:
[…] two things are called continuous [] when the
limits [] of each, with which they touch and are kept
together, become one and the same, so that plainly the
continuous is found in the things out of which a unity
naturally arises in virtue of their contact.57
The theoretical basis for such definition are to be found in the
Physics, in the books 5 () and 6 (). In book 5, chapter 3 [226b 18-227b
2], and also in the beginning of book 6 [231ª 21-24], Aristotle lays out a
series of definitions: “Things are said to be in contact when their
extremities are together” [226b 23]. Things can also be in succession in
the following way:
A thing is in succession when it is after the beginning in
position or in form or in some other respect in which it is
definitely so regarded, and when further there is nothing
of the same kind as itself between it and that to which it
is in succession, e.g. a line or lines if it is a line, a unit or
units if it is a unit, a house if it is a house (there is
nothing to prevent something of a different kind being
between).58
56 IBRI (1992), p. 66.57 Book 11 (): 12, 1069ª 5-8.58 226b 34-227ª 5; 231ª 23.
263
And things can also be contiguous: “A thing that is in succession
and touches is contiguous.” [227ª 6]. These definitions prepare the way
for the definition of the continuous:
The continuous is a subdivision of the contiguous: things
are called continuous when the touching limits of each
become one and the same and are, as the word implies,
contained in each other: continuity is impossible if these
extremities are two. This definition makes it plain that
continuity belongs to things that naturally in virtue of
their mutual contact form a unity. And in whatever way
that which holds them together is one, so too will the
whole be one, e.g. by a rivet or glue or contact or organic
union. [227a 7-17].
From this, Aristotle argues in book 6 that this definition of
continuous precludes to conceive of it as something composed of
indivisible parts, i.e., as if it was a line consisting in entire points, or of
atoms:
[...] nothing that is continuous can be composed of
indivisibles: e.g. a line cannot be composed of points, the
line being continuous and the point indivisible. For the
extremities of two points can neither be one (since of an
indivisible there can be no extremity as distinct from
some other part) nor together (since that which has no
parts can have no extremity, the extremity and the thing
of which it is the extremity being distinct). [231ª 26-29].
The continuum cannot be composed of indivisible parts each in
touch with the other because that would be a succession of wholes,
each one whole different from the other; they would not therefore be as
the parts of a true continuum, different and spatially separated.
264
Moreover, a true continuum cannot be composed of successive things,
since between successive things there must be something of a different
kind, while between two points there is always a line, between two
moments of time, there is always a time [231b 8-10].
After all these elucidations, Aristotle gives another important
defining character of continuity, to wit, what Peirce calls Kanticity – the
property of being infinitely divisible:
Moreover, it is plain that everything continuous is
divisible into divisibles that are always divisible; for if it
were divisible into indivisibles, we should have an
indivisible in contact with an indivisible, since the
extremities of things that are continuous with one
another are one and are in contact. [231b 15-18].
[And yet:] By continuous I mean that which is divisible
into divisibles that are always divisible [...].59 [232b 23-
25].
We then see that Aristotle already defined both conditions that,
for Peirce, were necessary and, if taken together, sufficient to define a
true continuity. The Stagirite can, after that, say that multitudes, time,
movement are all continuous greatness: they are either composed of
divisible parts, or they are not continuous. However, differently from
what Aristotle seems to mean, it seems that Peirce does not take having
parts with common limits and being infinitely divisible as logically
equivalent definitions of true continuity. In truth, the interesting point
59 Notice that the Greek could be equally rendered “divided into parts ever divided”, perhaps even more literally. See the original: “” And: “”.
265
is that the Peircean definition is parallel to the Aristotelian. In effect,
from what we have seen, the Aristotelian continuum must always be
divisible, so that any parts in which it is divided have the same common
limits. And Peirce’s definition of a true continuity can be expressed in
the following way: true continuity is defined by infinite divisibility,
wherein the parts share common limits.60
We can get a better grasp of the Peircean concept of continuity
going back to the differences between collections. A collection can be
denumeral, for it is impossible to ascertain a precise limit for the
multitude of its parts. In effect, multitude is not the same as numeral
quantity. For instance, a set of three objects and a set of three thousand
objects are both enumerable sets, for it is possible to count the discrete
unities which make up the collection. Any finite collection, for this
reason, is enumerable, for it may have its members discretely
determined. In infinite collections (and, therefore, truly continuous), the
quantity of the members of the collection is not countable, what makes
that they have multitudes, i.e., “That relative character of a collection
which makes it greater than some collections and less than others.” [CP
3.626, Multitude (in Mathematics), 1902]. Multitudes can be defined as
denumeral and abnumeral. The former are enumerable, being the most
basic type of infinite collection, equivalent to the multitude of finite
60 For the account of continuity in Aristotle, we follow Richard T. W. Arthur’s, presented in LEIBNIZ (2001), pp. 347-352. Indeed, this definition of continuum is decisive for the Aristotelian solution for Zeno’s paradoxes. Peirce follows Aristotle in this regard, grounding his own solution also upon the idea of continuity. See, for example, W 2: 207-211, Some Consequences of Four Incapacities; 254-256, Grounds of Validity of the Laws of Logic; NEM 3/I: Achilles and the Tortoise, n.d. See too IBRI (1992), p. 66.
266
integers [HP II: 744, On the Logic of Drawing History from Ancient
Documents...]. Abnumeral multitudes are superior to denumeral ones,
that is, they correspond to multitudes with superior degrees of infinity,
i.e., bigger than the multitude of finite integers: “An abnumeral
multitude is one of a denumeral succession of multitudes greater than
the denumeral multitude; each of these being the multitude of the
different possible collections of members of a collection of the next
lower abnumerable multitude.” [id.].
Such infinite divisibility is the first defining character of a true
continuity. Notice that a collection, to be continuous, cannot be a mere
aggregate of distinct parts. Exactly for the fact that there is a relation
between the parts that defines their inclusion in the collection, the
continuity comes from the fact that it is possible to mark distinctions, it
is possible to determine and divide the continuity without the necessity
of defining the collection itself in function of its parts.61 A true
continuity, therefore, is not what has parts, but what can have parts. In
this way, a true continuum has not the distinction between its individual
parts, for such distinction is merely possible, and not actual. 62 Second,
the infinite divisibility is also applicable to the parts of the whole, as the
61 PARKER (1998), p. 87-88. 62 Cf. PARKER (1998), p. 87-88; IBRI (1992), p. 66. As a curiosity, as to this regard, Peirce’s ideas seem to be parallel to Leibniz’s, who says: “Magnitude is that constitution of a thing by the recognition of which it can be regarded as a whole. It also seems that a whole is not what has parts, just what can have parts.” This leads Leibniz to doubt whether a mere aggregate, namely, something really divided, could be called one, that is, a true whole, and not a composite of parts. See LEIBNIZ (2001), pp. 98-99, or edition of the Deutsche Akademie der Wissenschaften, series VI, v. 3, p. 503: Numeri Infiniti; see too Monadology, § 2. We will not go further into the relation of the concepts of continuity for Peirce and for Leibniz; about this subject-matter the reader may go to LEO (2001), passim.
267
numerical series make clear; in this way, there is never a constituting
part which is ultimate and indivisible – there are no atoms. In other
words, we have once more the two necessary conditions for a true
continuity: infinite divisibility and common limits in between the parts.
For that reason, Peirce can say: “all the parts of a perfect continuum
have the same dimensionality as the whole.” [CP 4.642, Some Amazing
Mazes, 1908]. Or, in other words:
If there is room on a line for any multitude of points,
however great, a genuine continuity implies, then, that
the aggregate of points on a line is ‘too great to form a
collection’: the points lose their identity; or rather, they
never had a numerical identity, for the reason that they
are only possibilities, and therefore are essentially
general. They only become individual when they are
separately marked on the line; and however many be
separately marked, there is room to mark more in any
multitude. [HP II: 745, On the Logic of drawing History
from Ancient Documents …].
The distinction between finite and infinite collections is possible
to be a priori logically determined through the application of what
Peirce calls, following Augustus De Morgan, the “syllogism of
transposed quantity”. The application of such syllogism allows for the
determination the multitude of a denumeral collection. See the
following definition of this syllogism:
Syllogism of transposed quantity: a syllogism in which
the whole quantity of one concluding term, or its
contrary, is applied in a premiss to the other concluding
term, or its contrary, by means of a relation of one-to-N
268
correspondence. As in the following: Some X's are not
Y's, for every X there is a Y which is Z; hence, some Z's
are not X's. [CP 2.579, Syllogism, 1902].
The validity of conclusion depends upon the adjunction of a
further premise, the one that the class of X’s be a finite collection [W 5:
188, On the Algebra of Logic: A Contribution to the Philosophy of
Notation, 1885]. Another one of Peirce’s example is the following:
Every Hottentot kills a Hottentot;
No Hottentot is killed by more than one Hottentot;
Therefore every Hottentot must be killed by a Hottentot.
[CP 5.662, Thelepathy, 1903].
Of course, Peirce remarks, that to reason in such way about an
infinite collection, as the series of integers, for instance, leads to a
nonsense:
Of collections not enumerable it is not generally true that
the part is less than the whole. Every integer has a
square; and thus there are as many squares as there are
integers; although the squares form but a part of all the
integers.
Take this example:
Every woman marries a man,
For every man there is a woman;
.·.Every man is married to a woman.
The necessity of this plainly arises from the fact that
after every woman has got a husband, the collection of
men is exhausted. To say this, is to imply that for every
quantitative relation it would have a maximum, that is, a
last reached, in any order of running it through. [CP
4.104, The Logic of Quantity, 1893].
269
In another very good humoured passage, the same relation is
explained in the following manner:
Balzac, in the introduction of his Physiologie du mariage,
remarks that every young Frenchman boasts of having
seduced some French woman. Now, as a woman can only
be seduced once, and there are no more French women
than Frenchmen, it follows, if these boasts are true, that
no French women escape seduction. If their number be
finite, the reasoning holds. But since the population is
continually increasing, and the seduced are on the
average younger than the seducers, the conclusion need
not be true. [EP 1: 316, The Law of Mind].
What this reasoning proves is that for finite collections, the whole
is bigger than the parts; for infinite collections, nevertheless, the whole
is not bigger than its parts, as we have seen. From this reasoning,
Peirce can derive the definition of a finite class:
Suppose a lot of things, say the A's, is such that whatever
class of ordered pairs λ may signify, the following
conclusion shall hold. Namely, if every A is a λ of an A,
and if no A is λ'd by more than one A, then every A is λ'd
by an A. If that necessarily follows, I term the collection
of A's finite class. [CP 4.187, Multitude and Number,
1897].
With the application of the syllogism of transposed quantity,
enumerable collections are distinguished from denumeral and
abnumeral ones. Now, to distinguish between these latter, it is needed
to apply a special sort of reasoning, the Fermatian inference, or
mathematical induction [EP 1: 317]. It is this special mode of reasoning
that we will examine in what follows.
270
In what regards the theory of induction, it is possible to formulate
two problematical questions63. First, suppose that half of 10.000 throws
of a coin will actually result heads. If the result is heads exactly in the
5.000 throws, then, by deduction, one may unmistakably know that the
relative frequency of heads compared to all the throws of the whole
series of 10.000 throws should be somewhere in between ¼ (if the
extant throws all turn up tails) and ¾ (is the exatnt 5.000 throws turn
up heads). Hence our prediction, that half of the 10.000 throws will
turn up heads, cannot be overcome by more than ± ¼.
In another case, suppose that after 8.000 throws the relative
observed frequency of heads continues to be ½. At this point, it will be
clear that the relative frequency of heads in the whole series of 10.000
throws must be between ⅖ (if the 2.000 remaining throws all turn up
tails) and ⅗ (if the extant 2.000 throws all turn up heads). Hence our
prediction that half of the 10.000 throws will turn up heads cannot be
overcome by more than ± ⅟10. Thus, it is possible to come gradually
closer to the correct value (whatever it may be), since the biggest
possible error in all our predictions is each time less.
The problem is that the estimations come closer a correct value
because each time bigger portions of the series concern past throws,
and are considered as weight of evidence in the estimations referring to
the probability of the results of the future throws, to which less and
less portions of the series would concern. This problem is still more 63 TIDMAN; KAHANE (2003), pp. 397-398.
271
important in respect to infinite series, for the relative frequency of any
given portion of a infinite series is accordable with any relative
frequency of the whole series. For instance, even that the evidence
comes from a million coin throws turned up heads; the limit of a
supposed infinite series still could be equal to zero. How to assure that
induction is capable of self correctness in this case? The problem is that
in some one moment it is possible to say that the conclusions are
getting closer to a correct measure of the relative frequency.
Peirce himself recognized the problem. 64 In 1910, when reviewing
his article The Doctrine of Chances, published in 1878 [W 2: 276-289],
he recognized the lack of sureness and the impossibility to trust his own
early attempts at solving the problem, expressing himself as follows:
But when [in The Doctrine of Chances] I come to define
probability, I repeatedly say that it is the quotient of the
number of occurrences of the event divided by the
number of occurrences of the occasion. Now this is
manifestly wrong, for probability relates to the future;
and how can I say how many times a given die will be
thrown in the future? [CP 2.661].
Now, it is needed to consider the possibility of the occurrence of
events in an infinite series without definite value, that is, with relation
to an unlimited collection. It seems clear the reason for such
formulation: if the collection is finite, because of the insistence of the
method, in a certain moment the samples would begin to repeat. But, in
the case of a set of objects whose limits are unknown, we would never
64 BACHA (1999), pp. 286 seq.
272
know if the samples are being repeated. It is a situation analogous to
the one previously described, as to the order of nature. It is needed,
then, to improve the method. In other words:
For it is plain that, if probability be the ratio of the
occurrences of the specific event to the occurrences of
the generic occasion, it is the ratio that there would be in
the long run, and has nothing to do with any supposed
cessation of the occasions. This long run can be nothing
but an endlessly long run; and even if it be correct to
speak of an infinite “number,” yet / (infinity divided by
infinity) has certainly, in itself, no definite value. [CP
2.661].
To solve this problem two ideas are central: randomness and pre-
designation. It is needed, first, that the samples are fair, that is, that it
is possible the highest degree of randomness in drawing the samples, in
a way that each one of them may happen as many times as any other, as
seen above; and, secondly, one needs to know what one is looking for,
so to be possible to ascertain standards for comparison.
Let us see better these points, taking off from the idea of the long
run. It is from this idea that Peirce defines probability in a non-circular
way. Take the example of a throw of dice, which is essentially the same
of a throw of coins. The probability to obtain any number in a throw is
always 1/6, if the dice are not vitiated. That means that the throws are
independent in between themselves, i.e., to get 5 in a throw is
completely independent of getting 4 or 6 in any other throw. To say that
273
the probability of getting 6 is 1/6 in the long run is the same as to say
that of 10.000 future throws, for instance, 1.600 (16%) will turn up 6. in
other words, the long run means “an endless succession of throws in
the order in which they are thrown.” [NEM 3/I: 173, Probability and
Induction, letter to Kehler from 22 June 1911]. Probability, therefore, is
defined as the ratio of frequency that there is between the occurrence
of known facts and the occurrence of unknown facts:
The probability that if an antecedent condition is
satisfied, a consequent kind of event will take place is the
quotient of the number of occasions, ‘in the long run’, in
which both the antecendent will be satisfied and the
consequent kind of event will take place, divided by the
total number of occasions on which the antecedent
conditions will be satisfied. [NEM 3: 174, Probability and
Induction].
The idea of the long run is essential because it links the ideas of
probability and convergence: the method of induction gives us the
possibility of asserting that, in the long run, the frequency of a certain
kind of event would tend to a definite value, which is not yet known; in
other words, the ratio between the number of times in which this event
could occur and the number of times in which the proper occasion for
this happening arises would indefinitely converge towards a limit. The
idea oc convergence is explained as follows:
The word “converge” is here used in a different sense
from that which is usual in mathematics. The common
definition is that a series of values, x1, x2, x3, etc.,
converges toward a limiting value x, provided, after any
274
discrepancy ε has been named it is possible to find one of
the members of the series xv such that, for every value of
n greater than v, (xn – x) < ε. This ought to be called
definite convergence. No such member, xn can in the
indefinite convergence with which we have to do, be
fixed in advance of the experiment. Nevertheless, there
will be some such value. [HP II: 745, On the Logic of
Drawing History from Ancient Documents…].
Now, it is possible to discover a ratio, that is, an approximate
proportion of occurrence, a statistical probability: “Objective
probability is simply a statistical ratio.” 65 [NEM 4: 59, Carnegie
Application]. It means that our knowledge is reduced to a merely
probable estimation: scientific discoveries are but attempts to diminish
our errors; that is, from an initial sample, to endeavour in defining the
probable characters of the whole universe, correcting the deviations
through successive qualitative inductions.66 In sum, any and every
scientific assertion can be but probable:
To say, for instance, that the demonstration by
Archimedes of the property of the lever would fall to the
ground if men were endowed with free will is
extravagant; yet this is implied by those who make a
proposition incompatible with the freedom of the will the
postulate of all inference. Considering, too, that the
conclusions of science make no pretense to being more
than probable, and considering that a probable inference
can at most only suppose something to be most
frequently, or otherwise approximately, true, but never
65 Cf. PARKER (1998), p. 171.66 In fact, no scientific affirmation can be more than probable. Peirce vehemently rejects any absolute necessity and truth whatever they might be.
275
that anything is precisely true without exception
throughout the universe, we see how far this proposition
in truth is from being so postulated. [EP 1: 299, The
Doctrine of Necessity Examined, 1892].
Scientific knowledge, therefore, is a way of understanding the
distribution of the characters in the sample with relation to the whole
supposed universe. The idea of pre-designation is important in that
scientific knowledge is grounded in the recognition of how the sample
presents certain qualities. Suppose that a ship be loaded with wheat, as
Peirce says [id.]. This load is stirred up so that the grains are all mixed
up. Samples are equally taken out from the fore, amidships, and from
the aft parts, from larboard as well as from starboard, from the top, half
depth and bottom of her hold, and, after analyzing them: “Then we
infer, experientially and provisionally, that the approximately four-fifths
of all the grain in the cargo is of the same quality.” [EP 1: 301, id.]. The
estimated frequency has nothing to do with some wheat that might
have possibly been hidden in the ship and is not drawn in the sample:
By saying that we infer it experientially, I mean that our
conclusion makes no pretension to knowledge of wheat-
in-itself. […] We are dealing only with the matter of
possible experience – experience in the full acceptation
of the term as something not merely affecting the senses
but also as the subject of thought. [...] By saying that we
draw the inference provisionally, I mean that we do not
hold that we have reached any assigned degree of
approximation as yet, but only hold that if our experience
be indefinitely extended, and if every fact of whatever
nature, as fast as it presents itself, be duly applied,
276
according to the inductive method, in correcting the
inferred ratio, then our approximation will become
indefinitely close in the long run; that is to say, close to
the experience to come (not merely close by the
exhaustion of a finite collection) so that if experience in
general is to fluctuate irregularly to and fro, in a manner
to deprive the ratio sought of all definite value, we shall
be able to find out approximately within what limits it
fluctuates, and if, after having one definite value, it
changes and assumes another, we shall be able to find
that out, and in short, whatever may be the variations of
this ratio in experience, experience indefinitely extended
will enable us to detect them, so as to predict rightly, at
last, what its ultimate value may be, if it have any
ultimate value, or what the ultimate law of succession of
values may be, if there be any such ultimate law, or that
it ultimately fluctuates irregularly within certain limits, if
it do so ultimately fluctuate. [ibid.].
We have seen that induction is the kind of inference that allows
for the passage of the particular to the general. In effect, relatively to
this respect, there is the idea of pre-designating the character to be
discovered. Samples are drawn at random, to be examined as to some
specific respect; in the case, of which quality is the wheat. Induction
makes possible to ascertain a general character to the whole cargo
based upon the fact that the samples are of a certain quality. Through
successive sampling a conclusion is reached, that most likely defines
the whole. The procedure can be repeated as many times as wanted.
And in fact, the more it is repeated, the greater assurance the
generalization will attain. Thus, if there is some truth to be discovered,
277
it can be affirmed in terms of the general character, which can be
attributed to a whole class or infinite series, from the verification that a
character of the same species in its members to which we had access;
in other words, induction is a reasoning which allows to recognize what
is true of the whole, in recognizing a general true character of the parts
[NEM 3/ I: 182, letter to Kehler].67
The idea of induction as synedoche is from early on present in
Peirce’s writings. Nevertheless, he came to distinguish three different
kinds of induction, to wit, the crude or rudimentary induction,
qualitative induction, and quantitative induction [CP 7.110-130, Lowell
Lectures – VII, 1903]. Each one of these sorts of induction relates in a
different way the particular to the general, and it is worthwhile to
analyse them more thoroughly. It is with the idea of quantitative
induction that Peirce recovers Fermat’s inference, affirming to be
possible to ascertain in a quantitative way certain distinctive qualities,
so to allow the identification of the events in classes.
The first kind of induction is defined in the following way: “By
‘crude’ induction, I mean that inarticulate, unreflective kind usually but
very inappropriately termed (I suppose in imitation of Francis Bacon)
inductio per simplicem enumerationem [induction by simple
enumeration].” [NEM 3/I: 214, On the Foundation of Ampliative
Reasoning, 1910]. In this kind of rudimentary induction “the collection
to be sampled is an objective series of which some members have been 67 BACHA (1999), pp. 298-299; IBRI (1994), p. 108
278
experienced, while the rest remain to be experienced, and we simply
conclude that future experience will be like the past.” [HP II: 748, On
the Logic of Drawing History from Ancient Documents …].
This is the weakest kind of induction [HP II: 749, id.], for it is
based on the absence of knowledge, i.e.: “Rudimentary induction […]
proceeds from the premiss that the reasoner has no evidence of the
existence of any fact of a given description and concludes that there
never was, is not, and never will be any such thing.” [CP 7.111, id.]. It is
a self-correcting method, since the experimental series is not
interrupted; “and if the series of observations skips a single day, that
day may be the very day of the exceptional fact.” [ibid.]. In other words,
the most that crude induction warrants is that there are not enough
evidence yet to abandon the initial hypothesis. An example given by
Peirce deserves to be quoted:
I find myself introduced to a man without any previous
warning. Now if I knew that he had married his
grandmother and had subsequently buried her alive, I
might decline his acquaintance; but since I have never
heard the slightest suspicion of his doing such a thing,
and I have no time to investigate idle surmises, I
presume he never did anything of the sort. I know a great
many men, however, whose whole stock of reasoning
seems to consist in this argument, which they continue to
use where there is positive evidence and where this
argument consequently loses all force. [CP 7.112, Lowell
Lectures – VII, 1903].
279
Notice this is the kind of induction considered by Hume; in fact,
all the generalizations of common-sense are of this kind: “the Sun
raised every day before today; so, it will raise tomorrow as well”. Also
other examples given by Peirce to illustrate this kind of induction point
to the problem in the terms Hume proposed: the one of the Greek man
that watches the flux and reflux of the tides, and the one to the action of
gravitation measured by the oscillations of the pendulum [HP II: 748-
750]. If the problem of induction is considered only from this point of
view, it certainly would not have any way out of the Humean aporia. In
a word, its weak point is in that if positive contrary evidence to the
initial surmise is discovered it must be abandoned. It seems, then, that
the only possible justification to crude induction is the fact that if such
method is pursued uninterruptedly, making continuous observations
one after the other, its mistakes will be corrected. Yet if one single day
the series of observations be interrupted, the reasoning loses its force;
for instance, the day the Greek did not go to see the tide, it may have
changed as to what he had observed before; once reasoning is based on
the continuation of an uninterrupted series of observations, one
interruption can invalidate the whole reasoning.
For if the tide was going to skip a half-day, he [the
Greek] must discover it, if he continued his observations
long enough. This degree of justification and no more he
would have whether he made a dozen trials, or half-a-
dozen, or three, or two, or one only, or even none at all,
the argument would have precisely the same justification
280
in either case. The method would infallibly correct itself,
provided he continued this series of experiments; but not
if he dropped it and subsequently commenced another
series, as would be the case with quantitative induction.
For this induction not being quantitative, does not
conclude that the probability of the tides rising is 1; but
that it rises every half-day without exception. It has
nothing to do with probabilities or improbabilities; and if
the series of observations skips a single day, that day
may be the very day of the exceptional fact. [HP II: 748].
Now, the only conclusion crude induction reaches is that there is
nothing yet to contradict the hypotheses. As it is not a question of
probabilities, there is no reason why to assume the falsity of the
conclusion; but there is not also a higher reason to assume its truth in
the future. In other words, the probability of the conclusion being true
is 50%. This is a method which, relative to “gratuit hypothesis” it
furnishes some degree of assurance; it is impossible not to use it some
time. Even then, it is the weakest kind of induction. [id.].
Another kind of induction is qualitative induction: “This kind of
reasoning may be described […] by saying that it tests a hypothesis by
sampling the possible predictions that may be based upon it.” In more
detailed terms, the process consists in the following steps:
I seem to recognize a […] genus of inductions where we
draw a sample of an aggregate which can not be
considered as a collection, since it does not consist of
units capable of being either counted or measured,
however roughly; and where probability therefore cannot
enter; but where we can draw the distinction of much
281
and little, so that we can conceive of measurement being
established; and where we may expect that any error into
which the sampling will lead us, though it may not be
corrected by a mere enlargement of the sample, or even
by drawing other similar samples, yet must be brought to
light, and that gradually, by persistence in the same
general method. [HP II: 750-751].
In general lines, then the process above described is equivalent to
the hypothetical-inductive method of verification of theories.
Phenomena are observed, apparently disconnected, that is, apparently
they do not make up the same collection. Two possibilities are then
open to the inquirer: “In the first place, we may look through the known
facts and scrutinize them carefully to see how far they agree with the
hypothesis and how far they call for modifications of it.” [CP 7.114,
Lowell Lectures VII, 1903]. In other words, we seek to understand new
facts creating general conceptions based upon what we already know.
This is the process of abduction, that is, of creation of explanatory
hypothesis for the facts, and it is formally very much like induction, for
it also starts from the particular to reach the general. Nevertheless, to
take one for the other is to commit a fallacy post hoc, ergo propter hoc
(literally: after that, then because of that), i.e., to confound the cause
with what is not the cause (yet: to affirm the consequent). For instance,
to think that a fact A, when temporally previous to B, only for being
previous, is the cause of B. But A can be previous to B without being its
cause, in the same way that B may come after A without being its
282
consequence.68 If this fallacy not committed, the procedure of looking
for the facts we know in the attempt to understand those we do not
know is of a great value to inquiry [ibid.].
The second attempt is not to look at the facts, but to the
hypothesis that we have and to test their capacity to predict what will
happen in the future:
The other line which our studies of the relation of the
hypothesis to experience may pursue, consists in
directing our attention, not primarily to the facts, but
primarily to the hypothesis, and in studying out what
effect that hypothesis, if embraced, must have in
modifying our expectations in regard to future
experience. [CP 7.115, ibid.].
In such way bounded by empirical check, the hypotheses that
better describe the run of experience are continually tested, until the
expectations they created be contradicted by facts. Now, this is the first
step of scientific investigation, for it starts from a surprise in
experience to get to the hypothesis that explains it [CP 2.755, c. 1905].
This reasoning Peirce called retroduction:
The whole series of mental performances between the
notice of the wonderful phenomenon and the acceptance
of the hypothesis, during which the usually docile
68 Aristotle gives the following example for this kind of fallacy: “E.g. the soul and life are not the same; for if coming-to-be is contrary to perishing, then a particular form of perishing will have a particular form of coming-to-be as its contrary: now death is a particular form of perishing and is contrary to life; life, therefore, is a coming-to-be, and to live is to come-to-be. But this is impossible; accordingly, the soul and life are not the same. Now this has not been deduced; for the impossibility results even if one does not say that life is the same as the soul, but merely says that life is contrary to death, which is a form of perishing, and that perishing has coming-to-be as its contrary.” Sophistical Refutations, 167b21-167b36.
283
understanding seems to hold the bit between its teeth
and to have us at its mercy, the search for pertinent
circumstances and the laying hold of them, sometimes
without our cognizance, the scrutiny of them, the dark
laboring, the bursting out of the startling conjecture, the
remarking of its smooth fitting to the anomaly, as it is
turned back and forth like a key in a lock, and the final
estimation of its Plausibility, – I reckon as composing the
First Stage of Inquiry. Its characteristic formula of
reasoning I term Retroduction, i.e. reasoning from
consequent to antecedent. [EP 2: 441, A Neglected
Argument for the Reality of God].
The reasoning is called retroduction exactly because the framing
of the hypothesis begins with the observation of a striking fact. Its
logical form is the following:
The surprising fact, C, is observed;
But if A were true, C would be a matter of course.
Hence, there is reason to suspect that A is true. [HL
245].
Every inquiry begins with the observation of something that
appears as striking, something not agreeable to what is expected,
interrupting an habit of expectation. The business of inquiry is to
inquiry into those phenomena, to devise an explanatory hypothesis to
give an account of such “wondering”. Thus, the very first step towards
discovering truth is in the imagination of what this truth could be:
As soon as a man experiences a longing to know the
truth, he begins to imagine what that truth can be. He
very soon finds that [1118] unrestrained imagination is
sure to lead him wrong. Nevertheless, it remains true
that imagination alone, - under proper checks, - can
284
possibly suggest the truth. Hence, the second requisite
for the successful pursuit of science, - coming out after
the desire to learn, - is a scientific and fertile
imagination. […] The scientific man dreams of agencies
by which the phenomena of nature might be brought
about. [HP II: 1117-1118, The Chief Lessons of the
History of Science].
According to this, Peirce states:
Tennyson says:
maybe wildest dreams
are but the needful preludes of truth.
But I would dock the maybe. Wildest dreams are the
necessary “first steps toward scientific investigation”.
[HP I: 157, Early History of Science, 1892].
The imagination of hypotheses is the essential first step of
science, in its search for truth. In fact, the retroductive process of
imagining hypotheses is the only one which is endowed with original
heuristic power:
Abduction is the process of forming an explanatory
hypothesis. It is the only logical operation which
introduces any new idea; for induction does nothing but
determine a value, and deduction merely evolves the
necessary consequences of a pure hypothesis.
Deduction proves that something must be; Induction
shows that something actually is operative; Abduction
merely suggests that something may be. [HL 230].
The modus operandi of scientific method is that from imagined
hypothesis it is retroductively possible to reach certain conclusions
necessarily. Notice that abduction itself does not put any necessity on
285
the hypotheses it suggests, for they can be used only in a deductive
reasoning in the place of the premises. The conclusion necessarily
obtained from this surmise will be inductively tested in experience, in
order to be possible to discard the conclusions which do not describe
facts properly:
Deduction is the only necessary reasoning. It is the
reasoning of mathematics. It starts from a hypothesis,
the truth or falsity of which has nothing to do with the
reasoning; and of course its conclusions are equally ideal.
[…] Induction is the experimental testing of a theory. The
justification of it is that, although the conclusion at any
stage of the investigation may be more or less erroneous,
yet the further application of the same method must
correct the error. The only thing that induction
accomplishes is to determine the value of a quantity. It
sets out with a theory and it measures the degree of
concordance of that theory with fact. It never can
originate any idea whatever. No more can deduction. All
the ideas of science come to it by the way of Abduction.
Abduction consists in studying facts and devising a
theory to explain them. Its only justification is that if we
are ever to understand things at all, it must be in that
way. [HL 217-218].
As the only justification for the validity of abduction is its capacity
to open new boundaries [NEM 3/I: 206, letter to Kehler], it is needed to
test it in experience. Abductions are like Whitehead’s play of free
imagination, which must made acute by the coherence with facts and
logical consistency. The process of imagining hypotheses and their
following test are characteristic of qualitative induction. Qualitative
286
induction thus is the “mix”69 of two processes: the abductive, or
retroductive, the imagining of a hypothesis, and the inductive, the
testing of it. After successive eliminations of explanatory hypothesis
through empirical testing, an explanation will be reached to exhibit the
striking fact as the conclusion of a deductive syllogism. This
explanatory hypothesis finally may be account as plausible [EP 2: 441, A
Neglected Argument for the Reality of God]. In other words: “This kind
of reasoning may be described in slightly different terms by saying that
it tests a hypothesis by sampling the possible predictions that may be
based upon it.” [HP II: 751, On the Logic of Drawing History from
Ancient Documents …]. The development and working out of this
method is tied-linked to the collective practice of science:
One generation collects premises in order that a distant
generation may discover what they mean. When a
problem comes before the scientific world, a hundred
men immediately set all their energies to work upon it.
One contributes this, another that. Another company,
standing upon the shoulders of the first, strike a little
higher, until at last the parapet is attained. Still another
moral factor of the method of science, perhaps even more
vital than the last, is the self-confidence of it. In order to
appreciate this, it is to be remembered that the entire
fabric of science has to be built up out of surmises at
truth. All that experiment can do is to tell us when we
have surmised wrong. The right surmise is left for us to
produce. [CP 7.87, Scientific Method, 1902].
69 RESCHER (1978), p. 3. In fact, Rescher distinguishes abduction from retroduction. In this regard, we follow the account provided by PARKER (1998), p. 175, in its criticism to Rescher.
287
Now we pass to quantitative induction. Take one of its
particularly clear definitions:
This [form of induction] investigates the interrogative
suggestion of retroduction, ‘What is the ‘real probability’
that an individual member of a certain experiential class,
say the S's, will have a certain character, say that of
being P?" This it does by first collecting, on scientific
principles, a "fair sample" of the S's, taking due account,
in doing so, of the intention of using its proportion of
members that possess the predesignate character of
being P. This sample will contain none of those S's on
which the retroduction was founded. The induction then
presumes that the value of the proportion, among the S's
of the sample, of those that are P, probably
approximates, within a certain limit of approximation, to
the value of the real probability in question. I propose to
term such reasoning Quantitative Induction. [CP 2.758, c.
1905].
Quantitative induction seeks to ascertain a quantity, and nothing
more; in other words, it measures the degree of concordance of the
theory with the facts. For such reason, its success is relative to the
amount of extra information not contained in the premises which it is
possible to gather: the probability of its conclusions being true is
proportional to the quantity of positive evidence which is gathered to
prove a theory, “for induction proper consists in judging of the relative
frequency of a character among all the individuals of a class by the
relative frequency of that character among the individuals of a random
sample of that class.” [CP 6.100, Uniformity, 1902]. In this idea the
288
concept of weight of evidence appears, which allows to consider that
the observed frequencies are representative of the actual frequencies.70
Peirce explains quantitative induction in the following manner:
The sample is to be drawn under the guidance of a
precept under which we can enlarge any sample drawn
indefinitely and can also draw an indefinite number of
samples. Now I shall suppose that in some way, no
matter how, we become assured that a relation exists
between four correlates, to wit, the predesignate
character, the precept of sampling, the collection
sampled, and the future course of experience, this
relation being such that, in the long run, the distribution
of the predesignate character in samples drawn under
the precept will be the same as if they had been drawn
strictly at random from an indefinitely large finite
collection composing all our future experience of
members of the same collection. Then, as before, we can
infer inductively the proportional frequency of that
character in future experiences of members of the same
collection; and the induction must approximate
indefinitely, though irregularly, to the true proportion.
[HP II: 746, On the Logic of Drawing History from
Ancient Documents …].
Quantitative induction, to Peirce, is by far the strongest way of
inducing conclusions [NEM 3/I: 183, letter to Kehler]. Firstly, its force
comes from the fact that the procedure could be indefinitely extended,
in a way that a objective probability relative to the occurrence of the
pre-designated character can be defined in fact. Quantitative induction
70 RESCHER (1978), p. 3.
289
serves to measure probabilities in a precise way, and it would lead to a
true answer:
Quantitative induction approximates gradually, though in
an irregular manner to the experiential truth for the long
run. The antecedent probable error of it at any stage is
calculable as well as the probable error of that probable
error. Besides that, the probable error can be calculated
from the results, by a mixture of induction and theory.
Any striking and important discrepancy between the
antecedent and a posteriori probable errors may require
investigation, since it suggests some error in the
theoretical assumptions. But the fact which is here
important is that Quantitative Induction always makes a
gradual approach to the truth, though not a uniform
approach. [CP 2.770, c. 1905].
Quantitative induction, therefore, is a mathematical method used
in determining the proportion of the distribution of the qualities
between the members of a collection. The ascertainment of a statistical
ration has this sole function: to distinguish the proportion of specific
classes of events in relation to the whole of possible events.71 If we think
that induction will be indefinitely carried further on by a limitless
community of inquirers, we have that with time given the method
becomes gradually more reliable. Thus, quantitative induction is a safe
method to prove the validity of hypothesis. Peirce, in a certain moment,
says that for etymological reasons he prefers to call this kind of
71 As a matter of fact, the application of mathematical induction in the operation of distinguishing denumeral from abnumeral collections works as a criterion to distinguish classes of potency 0 א , i.e., capable of being defined by the series of cardinal numbers, from classes fo higher potency. Cf. PARKER (1998), chap. 4 supra cit., passim; CHAUVIRÉ (1984), pp.353-354.
290
reasoning adduction, meaning the process of putting in discussion, the
process of bringing to the center of the discussion the problematic
cases and theories [NEM 3/I: 190, letter to Kehler].72 Remember that
the idea of probable deduction means the deduction of a probability:
through a deductive process, a certain probability is proved certain. In
quantitative induction a similar process happens, with the difference
that the new knowledge suggested is confirmed by abduction, just
because adduction consists in taking the hypothesis further on, putting
it forward, that is, it consists in advancing knowledge, by the
application of the hypothesis to future cases:
The induction adds nothing. At the very most it corrects
the value of a ration or slightly modifies a hypothesis in a
way which had already been contemplated as possible.
Abduction, on the other hand, is merely preparatory. It is
the first step of scientific reasoning, as induction is the
concluding step. [HP II: 752, On the Logic of Drawing
History from Ancient Documents …].73
With this interpretation of the inductive method, Peirce can
present an account of scientific inquiry whose chief merit lies in
explaining how science advances combining moments of interruption
with continuity. Quantitative induction is only one kind of induction,
and induction proper is characteristic of only one stage of inquiry. From
72 Cf. the following: “Yet the bringing forward of instances is just the characteristic of the kind of reasoning or argumentation called ‘induction’. In view of this, I intend to take seriously into consideration, in view of my conception of the essential nature of such reasoning being as different from that of all who preceded me as it is, whether I ought not to have a different word for what I mean and call it adduction.”73 PARKER (1998), pp. 172-173, asserts that induction, differently from deduction, brings new knowledge too. For this quotation, we see it is not exactly like this.
291
this point of view, the experimental test of hypotheses is a way of
monitoring scientific procedure as a whole, so that the self-correctivity
of induction may be stretched out to the whole process. In other words,
scientific method proceeds to use statistical instruments to ascertain a
probabilistic truth, which is the only truth possible of being ascertained.
74
The difference between abduction and induction is crucial. While
the first has as its starting point the facts, and it seeks a theory to
explain them, induction, on the contrary, starts from an explanatory
hypothesis to seek the facts to support it:
Abduction makes its start from the facts, without, at the
outset, having any particular theory in view, though it is
motivated by the feeling that a theory is needed to
explain the surprising facts. Induction makes its start
from a hypothesis which seems to recommend itself,
without at the outset having any particular facts in view,
though it feels the need of facts to support the theory.
Abduction seeks a theory. Induction seeks for facts. [HP
II: 752, On the Logic of Drawing History from Ancient
Documents…].
For this reason, the inductive and the abductive methods differ
one from another being each one the inverse of the other, in an
analogous way as the syllogistic forms of hypothetical and inductive
reasonings were opposed in Peirce’s early writings. Here, specifically,
the logical forms of hypothesis and induction are not opposed, but
inductive reasoning and the very process of imagining hypothesis: “In
74 RESCHER (1978), chap. 1, passim; DELANEY (1995), p. 116.
292
abduction the consideration of the facts suggests the hypothesis. In
induction the study of the hypothesis suggests the experiments which
bring to light the very facts to which the hypothesis had pointed.” [id.].
To Peirce, it is necessary to give up the idea of a completely
certain and absolute knowledge of the world. There is no strictly
infallible knowledge, there is only a very high degree of probability that
certain theories will continue to foresee the course of events. Certainty
is not and cannot be the standard of knowledge. In effect, his account of
the history of scientific thought is centered on the idea of probability,
that is, in the idea that it is possible to ascertain a percentage of truth
for real synthetical general propositions about the future, grounded
upon the presently available evidence [NEM 3/I: 139, Probability]75. The
infallibility of modern science, mentioned in the beginning, is therefore
restricted to a matter of probability – the only certainty we can have is
in short the measure of our own ignorance. However, we should not
because of that begin to believe, as Hume did, in the impossibility of
knowing the truth, even it is a provisional and approximate truth.
From this idea, it is possible to say that no revolution in science
happens simply all of a sudden, as if it was out of the blue. If, as Gaston
Bachelard says, the only way to make science advance is to attack
established science, changing its constitution76, it is impossible that this
attack comes from outside science itself. As a matter of fact, remember
75 Cf. NEM 3/I: 143, The Concept of Probability, Peirce’s account of Phyrro’s philosophy, and the role of Pascal to the history of western thought. 76 BACHELARD (1984), p. 31.
293
what was said before: to refute a mathematician, it is needed to do it
mathematically.
In all sciences revolutions are possible; nevertheless, such
revolutions can only happen if they take as a starting-point the
conceptual marks already existent, as Mario Bunge says77. If we take
the picture of the philosophy of scientific inquiry Peirce offers, we could
even say that there is no possibility of being different, since the
abductive process of creating hypothesis, even though it is not
submitted to strict rules78, is always an attempt to recognize the
surprise and novelty within the boundaries of known conceptual
schemes. Thus, to use another expression of the Argentinean
philosopher, we could say: “There are no revolutionaries without roots,
no revolutions in a conceptual void.”79.
Now, according to the scheme proposed by Peirce, wherein the
procedures of abduction, induction, and deduction are intimately
connected, it is possible to say that the test of theories leads to
revolutions. In this way, at the same time that a Bachelardean rupture
épistémologique implies the abandonment of previous conceptual
marks, it also opens new fields of investigation, even whether it
maintains old conceptual bases. In fact, Peirce’s opinion seems to be
just that when he says: 77 BUNGE (1985), pp. 45 ff. In effect, Bunge’s remarks are very similar in spirit to those of Peirce. What follows is an attempt to think in Peircean terms the ideas presented by the Argentinean philosopher. 78 IBRI (1994), pp. 110 ff.79 BUNGE (1985), p. 47: “No hay revolucionarios sin raíces, ni revoluciones en un vacío conceptual.” Our translation.
294
We cannot ordinarily hope that our hypothesis will pass
through the fire of induction, absolutely unmodified.
Consequently, we ought not to conclude that it is
absolutely correct, but only that it very much resembles
the truth. Insofar as further induction will modify it, as it
must be expected that it will do, if it is not to meet with
downright refutation, it can hardly fail that the
modification should come about gradually. [HP II: 751,
On the Logic of Drawing History from Ancient
Documents …].
Now, instead of supposing facts are incomprehensible, it is
needed to suppose that, notwithstanding they are striking, they
reconcilable with what is known about other facts. In a certain moment,
the quantity of strinking facts – unforeseen facts – will be so much that
it will force a modification of the theory [id.]. Even if enough evidences
are not gotten, so as to demand a modification of the conceptual
scheme, there is no possible return to the same point as before; either
because the striking facts, if they happen again, will then not be as
striking as at first anymore, and they will be in a certain way already
incorporated to the theory, or because they have already led to the
search for another similar facts, to gather enough evidence to abandon
the theory, for instance80. In fact, there are two ways of suggestion
whereby abduction and induction make knowledge advance:
The mode of suggestion by which, in abduction, the facts
suggest the hypothesis is by resemblance, – the
resemblance of the facts to the consequences of the
80 Now, according to BUNGE (1985), p. 48, this is the most important contribution of Thomas Khun. For a comparison between Khun’s and Peirce’s ideas, cf. ROSENTHAL (1994), pp. 13 ff.
295
hypothesis. The mode of suggestion by which in induction
the hypothesis suggests the facts is by contiguity, –
familiar knowledge that the conditions of the hypothesis
can be realized in certain experimental ways. [HP II: 752-
753].
Therefore, to know is also to recognize. In every field of inquiry
and investigation there is the tension between tradition and change,
between invention and recognition. Anyway, the confrontation with
experience is the motive for modifications, whether in the conceptual
re-framing of theories already existent, to accommodate new facts,
whether in the invention of new theories. However, the confrontation
with experience does not say exactly what must be done, not even how
it should be done. This is a decision we ourselves have to take – a
pragmatic decision, which has to be based in the interactive context of
the world surrounding us.81 This idea will be remembered further on, in
the conclusion of this work.
81 ROSENTHAL (1994), p. 14.
296
7. EXPERIENCE AND EXPECTATION
Como poderíamos colocar nossa esperança total no tempo presente, sujeito a todas as instabilidades?
Murilo Mendes, § 527, O Discípulo de Emaús82
A Eternidade está longe(menos longe que o estirão
que existe entre o meu desejoe a palma de minha mão).
Um dia serei feliz?Sim, mas não há de ser já:
a Eternidade está longe,brinca de tempo-será.
Manuel Bandeira, Tempo-Será83
According to Peirce, every thought is a continuous interpretation
of signs, and to interpret is to infer. To infer in turn means to consider a
proposition as true in its statement: “Confining ourselves to science,
inference, in the broadest sense, is coextensive with the deliberate
adoption, in any measure, of an assertion as true.” [HP II: 722, On the
Logic of Drawing History ...]. As we have seen, there are three
fundamental forms of inference: deduction, induction, and abduction
[CP 3.516]. Thought itself s a sign, the whole mind is a sign: “we must
conclude that the mind is a sign developing according to the laws of 82 “How could we put all our hope in present time, subject to all instabilities?” Our translation. 83 “Eternity is far/ (less than the stretch/ that exists between my wish/ and the palm of my hand)/ Will I be happy one day? / yes, but not now it will be: / Eternity is far/ plays of time-will-be.” Our translation.
297
inference.” [W 2: 240, Some Consequences of Four Incapacities]. In this
way, always projected to the future, all thought leads to the formation
of convictions and habits, which are settled in a horizon of experience
and expectation. In effect, we also saw that to each kind of inference
there corresponds a logical modality: the business of deduction is to
establish necessary reasonings, that of induction to establish probable
reasonings, and to abduction the task is to delimitate an expectation:
What, then, is the end of an explanatory hypothesis? Its
end is, through subjection to the test of experiment, to
lead to the avoidance of all surprise and to the
establishment of a habit of positive expectation that shall
not be disappointed. [HL 250].
After the initial definition of the hypothesis, its experimental
verification will say whether the initial expectations were justified. And,
being disappointed, the habit of thinking must be modified, that is, the
initial hypothesis should be abandoned, in favour of another that
renders facts intelligible. This process of modifying hypothesis happens
through establishing new hypothesis, i.e., it always happens as to open
new fields of experience and expectation, making it possible to infer
other abductive reasonings. So, abduction being a process of framing
explanatory hypotheses [HL 230], the link with Peirce’s pragmatism is
evidently essential. Peirce in fact comes to say that all the ideas of
science were originated through abductions, to the point that ““if we
are ever to understand things at all, it must be in that way” [HL 218].
The abductive process of establishing a hypothesis begins with the
298
recognition of a striking fact, to which an intelligible explanation has to
be provided. Not that this fact is an irregular fact; rather, the surprise
is caused by an unpredicted regularity. Indeed, “nobody is surprised
that the trees in a forest do not form a regular pattern, or asks for any
explanation of such a fact. So, irregularity does not prompt us to ask for
an explanation.” [HP II: 724, On the Logic of Drawing History…]. Why
should we expect that irregularity would be surprising to us, when
everywhere in nature we see irregularities? The process of abduction
begins when an unexpected regularity is noticed:
Before dismissing irregularity, I may note, as aiding to
clear the matter up, that a breach of an existing
regularity always stimulates a demand for an
explanation; but where, having expected regularity, we
only find irregularity without any breach of regularity, we
are only induced to revise our reasons for expecting
anything. Irregularity, be it noted, cannot be expected, as
such. For an expectation is, in every case, founded upon
some regularity. For the same reason, merely not finding
regularity where no particular regularity was expected,
occasions no surprise. [HP II: 724-725, On the Logic of
Drawing History…].
Every inquiry and interpretation arises from the observation of a
phenomenon which breaks habits of expectation of the inquirer. This
surprising irruption of a fact in need of explanation marks the first step
in search of a general conception which renders the fact intelligible, so
that it influences the internal logic of the process in delineating an
empiric-expectative horizon:
299
Now what an explanation of a phenomenon does is to
supply a proposition which, if it had been known to be
true before the phenomenon presented itself, would have
rendered that phenomenon predictable, if not with
certainty, at least as something very likely to occur. It
this renders that phenomenon rational, - that is, makes it
a logical consequence, necessary or probable. [HP II:
725].
In short, abduction is a process of adopting a hypothesis which is
suggested by facts. The hypothesis has to say that the facts will very
likely happen in a certain manner, so that it is adopted. Its
characteristic logical form is that of a modus ponens in reverse, so to
say:
The surprising fact, C, is observed;
But if A were true, C would be a matter of course.
Hence, there is reason to suspect that A is true. [HL
245].
The logical form of the modus ponens can be written like this84:
p qp q
Abduction, differently, is a reasoning from the consequent to the
antecedent, a retroduction, therefore; that is, it is the logical conclusion
of the consequence C to the premise still unknown A, which acquires
the status of hypothetical explanation or provisional theory to render C
intelligible. It may be written in the following logical form:
qp p q
84 PARKER (1998), p. 174.
300
Thus, the role of abduction may be said to be to furnish a
”virtual” antecedent premise {CP 2.759, c. 1905]. 905]. Of course, this
idea of inverting logical implication gives abduction a highly
problematic character. The lack of logical sureness for the illation in
synedoque is the highest. However, we have seen that this lack of
sureness can be counterbalanced by the inductive testing of hypothesis,
in a strategy of application of the pragmatic maxim. In effect, the
anticipatory state prepared by abduction perfectly agrees with the
spirit of the pragmatic maxim: “It is a state of mind in which a man
seems to have ground for expecting certain things, and yet has
evidence that those expectations may e falsified.” [HP II: 732, On the
Logic of Drawing History …]. Thus, the development of the rational
purport of a hypothesis, taken as criterion of evidence, holds well
because the maxim works out as a method that relates the probability
and plausibility of the hypothesis with its character of being a possible
description of experience. As a matter of fact, the inductive test of
hypotheses has exactly the function of verifying their effectiveness in
the prediction of future events:
I have already explained to you briefly what these three
modes of inference, Deduction, Induction, and Abduction,
are. I ought to say that when I described induction as the
experimental testing of a hypothesis, I was not thinking
of experimentation in the narrow sense in which it is
confined to cases in which we ourselves deliberately
301
create the peculiar conditions under which we desire to
study a phenomenon. I mean to extend it to every case in
which, having ascertained by deduction that a theory
would lead us to anticipate under certain circumstances
phenomena contrary to what we should expect if the
theory were not true, we examine the cases of that sort
to see how far those predictions are borne out. [HL 249].
The formal inadequateness of abduction is softened through using
the pragmatic maxim as a rule of caution and prudence in the adoption
of hypotheses, in a process Peirce calls the logic of abduction:
If you carefully consider the question of pragmatism you
will see that it is nothing else than the question of the
logic of abduction. That is, pragmatism proposes a
certain maxim which, if sound, must render needless any
further rule as to the admissibility of hypotheses to rank
as hypotheses, that is to say, as explanations of
phenomena held as hopeful suggestions; and,
furthermore, this is all that the maxim of pragmatism
really pretends to do, at least so far as it is confined to
logic, and is not understood as a proposition in
psychology. For the maxim of pragmatism is that a
conception can have no logical effect or import differing
from that of a second conception except so far as, taken
in connection with other conceptions and intentions, it
might conceivably modify our practical conduct
differently from that second conception. [id.].
The maxim is then nothing but a rule to ascertain whether
hypotheses can serve as general descriptions of facts, and, hence, as
guides to fine-tune future conduct. Thus, the meaning of any
hypothesis, term or conception is restricted to the different ways of
302
guiding conduct that the adoption as true of one or another hypothesis
could cause; if there is no difference on the influence over conduct,
then there is no difference at all of meaning between the conceptions.
With this, any possibility of some ultimate and inscrutable residuum of
meaning, echoing resonances of the Kantian thing-in-itself, is excluded
from pragmatism.85
Abduction, from which it is possible to draw necessary
conclusions, effects a double transposition: from an experienced
temporal relation, one at once infers through abduction the analogy
between a logical relation in the inward domain of consciousness and a
causal relation in the domain of outward experience. According to
Apel86, then, abductive inference is then the projection of a logical form
characteristic of the successive temporal elements of its inward
experience over the causally determined outward experience of the
world. Abductive inference therefore has to be always immerse and
unfolding within a broader argumentative connexion. At the same time
it makes the attainment of plausibility for hypotheses possible, the
process also gains heuristic potency, going beyond the limits of factual
experience:
[…] if pragmatism is the doctrine that every conception is
a conception of conceivable practical effects, it makes
conception reach far beyond the practical. It allows any
flight of imagination, provided this imagination ultimately
85 IBRI (2003), p. 12.86 APEL (1995a), pp. 104 f.; APEL (1995b), p.65.
303
alights upon a possible practical effect; and thus many
hypotheses may seem at first glance to be excluded by
the pragmatical maxim that are not really so excluded.
[HL 250].
The link between true theories and conceivable practical bearings
in Peirce’s pragmatism appears as the creation of habits of conduct
capable of orientating future conduct, so that there may be a
convergence between the form of the concept and the course of
possible experience in the future. In truth, the projection of forms over
experience has a twofold sense: on the one hand, it is a way of
ascertaining the verisimilitude of hypotheses with facts; on the other, it
is a way of mediating the construction of ideals of conduct, the latter
being rationally understood.87
The tension preciously mentioned between the life of science,
which asserts nothing as definitely certain, and the commitment of the
scientist with the continuation of inquiry reappears here: it seems that
the scientist does not in fact have practical beliefs, but only theoretical
beliefs. It is decisive because of this to know what are the objectives
when propositions are asserted, for everything resumes in knowing
which are the expectations involved in the assertion of the truth of the
theories. Were we to investigate into the truth of a hypothesis, would
we be disappointed in discovering its falsity? In other words, would we
want to put to test the beliefs we adopted from the suggestion of a
hypothesis? If the supreme aim of scientific inquiry is to reach truth,
87 Idem, p. 10-11; IBRI (2000a).
304
even if a vague and uncertain truth, the answer must be: yes, we would
like to test our beliefs, even because we want to attain a less vague and
more precise truth.
Uma hipótese, stricto senso, não é ainda uma crença.
Paralelamente a essa idéia, crenças, enquanto hábitos de conduta
operativos e eficientes, são naturalmente testadas cotidianamente.
Let us recover the line of the argument up to now. On the one
hand, Peirce holds there is no place for beliefs in science. Here, it
seems there is a problem with the concept of belief. True theories in
science are beliefs of the community of inquiry. However, that does not
mean that they are ultimate, or absolutely certain. There are, therefore,
beliefs in science, though they are not final beliefs. In this sense, we
restate, beliefs are not ultimate or final beliefs. To propose a theory as
valid does not mean to accept its truth as definite: all we can say is that,
up to the moment, no one doubts it as a valid description of facts, but it
may as well be that in the future this theory is replaced for a better one,
and the provisional truths it affirms now may be, either better
formulated and understood, or simply refuted, with the continuation of
inquiry. We have seen that for Peirce beliefs meant dispositions to act
in a certain way in situations of vital crises. On the other hand, it is
necessary to trust in the cognitive capacity of inquiry carried on in the
long run. In the process of inquiring, the scientist must not take up
definite beliefs. Nevertheless, so to engage in the process of inquiring,
305
the scientist needs to believe he or she will be successful. Now, let us
remember what Peirce understands as “belief”:
I use the word belief to express any kind of holding for
true or acceptance of a representation. […] its principal
element is not an affair of consciousness at all; but is a
habit established in the believer’s nature, in consequence
of which he would act, should occasion present itself, in
certain ways. [NEM 4: 39, Carnegie Application].
Thus, belief is a habit of conduct of the individual, which he
deliberately adopts, to act satisfactorily in certain given practical
circumstances. Belief is a habit of conduct of which one is aware, a
habit against which one does not fight, and that can be contracted by
an act of will: contrarywise to other habits, which are acquired only by
the repetition of an action under the circumstance, “belief may be, and
commonly if not invariably, is contracted, by merely imagining the
situation and imagining what would be our experience and what our
conduct in such a situation” [idem]. This simple exercise of fancy would
suffice, according to Peirce, to settle the habit and to determine
conduct in case the actual situation comes to happen. Belief, therefore,
is something inscribed in the soul of a person, whether by the repetition
of certain actions, whether by an exercise of strenght of will.
Differently, a doubt is a problem of consciousness:
It is an uneasy feeling, a special condition of irritation, in
which the idea of two incompatible modes of conduct is
before the doubter’s imagination, and nothing
determines him, indeed he feels himself forbidden, to
306
adopt either and reject the other. [NEM 4: 40, Carnegie
Application].
Doubt, because it is an irritation, forces the search for its
appeasement, that is, it fights against the satisfcation of belief,
compelling to recover it. Therefore, it is not the exact opposite of belief,
but it is a quite different state of mind. Peirce says they are
physiologically different, for they affect different parts of the human
being. Nevertheless, imagination also can suggest a doubt: “The most
important character of doubt is that no sooner does a believer learn
that another man equally well-informed and equally competent doubts
what he has believed, than he begins by doubting it himself.” [NEM 4:
41, idem]. It is not needed actually to find someone in the same
circumstances, to fancy the possibility of someone being in doubt is
enough to cause doubt:
Indeed, it is not necessary that one should actually meet
with a man who doubts; for such is the influence of
imagination in such matters that as soon as a believer
can imagine that a man, equally well-informed and
equally competent with himself, should doubt, doubt
actually begins to set in, in his own state of feeling. [id.,
ibid.].
Thus, the believer may not abandon his or her belief, that is, it
may keep the same habits of conduct, but they inevitably will not be
considered as certain and as indoubitable as before. This is the first
step toward their abandoment, and, according to Peirce, this will
happen with time given, since experience provides evidence for that. To
307
such situation a corolarial is added, which is that if there is no real and
actual doubt as to some belief, the believer cannot see no reason as to
how to doubt it. That does not mean, however, that it is impossible to
question beliefs:
It thus appear that it is one thing to question a
proposition and quite another to doubt it. We can throw
any proposition into the interrogative mood at will; but
we can no more call up doubt than we can call up the
feeling of hunger at will. [ibid.].
Here it is essential to get a clear grasp of the difference between
beliefs and doubts, for upon such difference all the following
argumentation depends. Belief may be acquired by an act of will: the
self-convincement can lead us to consolidate hard to change habits of
conduct. Doubt, on the contrary, is independent of any act of will. That
is why they are regarded even as physiologically different by Peirce.
Doubt needs a concrete occasion to arise in one’s mind: if I do not see
any reason why I should doubt, why should I doubt? The imagination of
another person, equally informed and competent, who doubts the same
things I believe, is not an act of will, but the recognition that doubt is
possible. The important here (to be recovered further on) is that true
beliefs are capable of being doubt in face of contrary evidence. 88 And, in
case the contrary evidence is strong, showing that doubt can exist, an
exercise of self-criticism is unavoidable, in the course of which one may
or may not come to truly doubt one’s beliefs. What matters is that the
88 MISAK (1994b), p. 744.
308
genuine believer, before the mere possibility of doubt, seeks as fast as
possible to get rid out of the doubt. Thus, even before one begins to
doubt, it is possible to question a proposition without in fact doubting it.
In other words, the recognition of the possibility of doubting maybe
does not lead to the abandoment of beliefs, but, it will at least lead to
their relativization: not throwing them away, indeed, but not
considering them as if they corresponded to absolute truths or
fundaments.
Let us get back to the distinction between practical and
theoretical beliefs. In the text Reason’s Rules, above quoted, Peirce
discusses the concept of truth, connecting it in contradistinction
between the two kinds of beliefs. Practical beliefs, according to him,
can be described as “habits of deliberate behaviour”. They are,
therefore, beliefs in the full sense, beliefs that determine the conduct,
according to the definition we just presented. To have a habit of
deliberate behaviour means to act or to have a tendency to act, in
general, in a certain way every time a certain occasion arises. The
example given is the one of the proposition “anthracite is a convinient
fuel”:
Now to say that a man believes anthracite to be a
convenient fuel is to say no more nor less than that if he
needs fuel, and no other seems particularly preferable,
then, if he acts deliberately, bearing in mind his
309
experiences, considering what he is doing, and exercizing
self-control, he will often use anthracite. [CP 5.538,
Reason’s Rules].
The simple example, in fact, is full of details, which are worthy of
detailing. There is a practical situation which, imposing itself, demands
intervention: the man needs fuel. This situation does not need a special
intervention, no special fuel is demanded. The situation is similar,
therefore, to the one of the apple pie: there is a certain general purpose
which needs to be accomplished, and a kind of fuel is enough to solve
the problem; it is, therefore, an undetermined situation. To accomplish
this purpose, Peirce clearly says what it is needed to do. First, to
deliberate about what it is needed to do; this deliberation unmistakenly
makes its way through the calling for past experiences in similar
circumstances, and, next, through the consideration of the situation at
hand, that is, the comparison between what one knows by experience
and what appears as a sudden fact. Thus, the new actual fact is
interpreted accordinf to the general patterns of what was previously
lived, and acquires sense in so far as it can be taken in homology of the
same general nature as what is already known. In the end, it is needed
to control the action to act according to what is known, and not only
now, but also from now on.
By the example, this general determination of a way of acting
happens because the past experience shows that, in circumstances of a
certain sort, certain lines of action are preferable to others. But it may
310
be that past experience never had happened in fact, that is, concretely
happened. According to the definition of belief, such link between the
attention to past memories and the present purpose, together with
selfcontrol, can be made in imagination. The example is clarifying and
explains in detail the process:
But habits are sometimes acquired without any previous
reactions that are externally manifest. A mere
imagination of reacting in a particular way seems to be
capable after numerous repetitions of causing the
imagined kind of reaction really to take place upon
subsequent occurrences of the stimulus. In the formation
of habits of deliberate action, we may imagine the
occurrence of the stimulus, and think out what the
results of different actions will be. One of these will
appear particularly satisfactory; and then an action of the
soul takes place which is well described by saying that
that mode of reaction ‘receives a deliberate stamp of
approval.’ The result will be that when a similar occasion
actually arises for the first time it will be found that the
habit of really reacting in that way is already established.
[CP 5.538].
Even though the assent, or “endorsement”, is not essential, that is
generally linked to practical beliefs. Practical beliefs, thus, involve an
act of assertion, that is, an assumption of responsibility before the
effects that a certain manner of conduct may have. It does not matter
which the conditions are, to act according to a practical belief is to
deliberately act according a previously settled standard, whther by
effectively past experience, whether by means of mental
311
experimentations, to which the same endorsement is given. The chief
notion is the one of the temporal anteriority of that which bases the
decision to act following a certain pattern; to this base Peirce gives the
name of experience: “experience means nothing but just that of a
cognitive nature which the history of our lives has forced upon us.” [CP
5.539]. experience thus in its strong sense is characterized as the
cognitive outcome of living, source of concepts that have the force for
shaping human conduct, both present and future conduct. 89 This
definition of experience is highly important, and to it we shall return
other times from now on.
Theoretical beliefs, in turn, are more complicated. In the
sequence of the argumentation, Peirce comes to admit that theoretical
beliefs are indirectly practical beliefs. However, they are not only this.
Theoretical beliefs have a different status; the determination of a
general way to our actual future general conduct is not questioned, but
how this could happen. In the case of practical beliefs, if I believe the
proposition “Anthracite is a convenient fuel” is true, I will act so that to
use anthracite as a convenient fuel in certain circumstances. In the case
of theoretical beliefs, normative commitment is different: it is possible
that I believe in a proposition without establishing a definte habit of
conduct based in it; at the same time, it is possible to question a
proposition without discarding it for good, that is, without putting it
into doubt in a first moment. 89 Cf. IBRI (1992), p. 5.
312
The first important thing to notice is that the distinction between
two kinds of practical beliefs, “those which are expectations, and those
which are not even that.” [CP 5.539, Reason’s Rules]. This discussion is
strategically important in so far as it involves the concept of experience.
First, we must notice that experience has teh character of fact; linked
to the past, for it is its outcome, experience inevitably imposes itself:
Laconically speaking, experience is esse in praeterito.
[…] Some fact there is. All experience compels your
acknowledgment. What, then, is the fact that is present
to you? Ask yourself: it is past. A fact is a fait accompli;
its esse is in praeterito. The past compels the present, in
some measure, at least. [CP 2.84, Minute Logic, 1902].
Imposed as it is, experience means effort, and brings with itself
the mark of duality between Within and Without: “a sense of effort and
the experience of any sensation are phenomena of the same kind,
equally involving direct experience of the duality of the Without and the
Within.” [CP 5.539]. Though Peirce adimts that every sensation carries
with itself the feeling of this duality, in the sensation of physical effort
this feeling is characteristically present, for there is no effort without
resistance to this effort. The duality then remains clearly and strongly
marked, and it is a clear sign of the reality of the outward world. To
Peirce, to deny this is of a foolishness characteristic of those who
ingenuous ideaists. He gives an ironic illustration to highlight this
point. Suppose an idealist philosopher comes wandering in the streets,
absorbed in musements about the doubtful existence of the external
313
world. Suddenly, a drunk man punches the philosopher in the eye,
taking him out of this speculative world. This “unexpected” is a direct
experience of the duality that makes it impossible to neglected the
reality of the external world. “Experience”, Peirce says, “invariably
teaches by means of surprises.” [EP 2: 194, The Seven Systems of
Metaphysics, 1903]. The chief point is the contrast between an inward
mental state before the experience of this brute fact and the state of
sudden surprise after the same experience. The calm expectation of the
inward state was broken by duality, and the brute unexpected fact
replaced it by a state of surprise.
The difference between practical and theoretical beliefs, with this,
is formulated in the following terms: “In the light of these remarks, we
perceive that there is just this difference between a practical belief and
an expectation so far as it involves no purpose or effort; namely that the
former is expectant of muscular sensation, the latter of sensation not
muscular.” [CP 5.539]. Both are therefore expectations, and all
expectation is an anticipation of experience, to which assent is given or
not. A practical belief, hence, as a determined habit of action, is but the
expectation that the action shall happen in a certain way, if the
occasion arises in a certain way. Thus, in determining a general habit of
conduct, practical beliefs always involve the approvement of what is
expected, for they are entirely based upon what was deliberately
established as a pattern to be followed. It in this exact point that the
314
illustration works: only by means of a surprise a genuine doubt has its
origin [EP 2: 348, Issues of Pragmaticism]. From the moment in which
something surprises me, so to change my inward peace of mind, it is
impossible to return to the same state as before. Even if I wanted to
doubt my positions and theories, before something external comes to
awake my attention, I would not get to doubt, for I would always be
immerse in what I already knew. In this sense, a belief is related to the
truth of its assertions, in a threefold commitment, referring to what can
be expected, to the circumstances under which it is possible to expect
and to the interpretation of the assertion of the belief:
The expectancy consists in the stamp of approval, the act
of recognition as one's own, being placed by a deed of
the soul upon an imaginary anticipation of experience; so
that, if it be fulfilled, though the actual experience will, at
all events, contain enough of the unexpected to be
recognized as external, yet the person who stands in
expectancy will almost claim the event as his due, his
triumphant “I told you so” implying a right to expect as
much from a justly-regulated world. A man who goes
among a barbarous tribe and announces a total eclipse of
the sun next day, will expect, not only “his” eclipse from
Nature, but due credit for it from that People. [CP 5.540].
When future experience happens according to what was
anticipated, our expectations are confirmed, and we feel rewarded by
facts. There is not, then, any surprise, and we feel satisfied. That
happens both in the case of practical beliefs and in the case of
theoretical beliefs. The example of the eclipse shows the point very
315
well. To predict a solar eclipse is to make a scienctific assertion that
also brings expectations.
However, scientific expectations are a little different. It is possible
to question a proposition, as we have seen, but without putting it in
doubt. In other words, it is possible to hold up judgment in relation to
the truth value of certain propositions. This advisable exercise of
methodeutics, as Peirce says, is exactly what determines the specific
difference of theoretical beliefs. With “ca das crenças teóricas. “As to
purely theoretical beliefs not expectacious, if they are to mean
anything, they must be somehow expectative.” [CP 5.541]. At the same
time that to affirm a proposition means, to the scientist, a different
thing than to assert a proposition giving to it full assent, to believe that
things should happen in a certain way is different than believing that
things must happen in a certain way, in which they will happen.
Theoretical beliefs are grounded in past experience, they also can be
determined in fancy and they also have an expectational character, jsut
like practical ones. But, differently from the latter, they do not concern
the past, for they do not deal directly with experience, with the fait
accompli, but with what is expectable from experience in the future;
thus, they cannot concern a well determined manner of conduct, they
have to be connected to the future, that is, to ways of acting that are
not yet fully determined; they report themselves to the future without
316
fixed commitments, therefore. The expectation they create is the one
that future events may come to happen to confirm or refute theories:
The word “expect” is now and then applied by careless
and ignorant speakers, especially the English, to what is
surmised in regard to the past. It is not illogical
language: it is only elliptical. ‘I expect that Adam must
have felt a little sore over the extraction of his rib,’ may
be interpreted as meaning that the expectation is, that so
it will be found when the secrets of all hearts are laid
bare. History would not have the character of a true
science if it were not permissible to hope that further
evidences may be forthcoming in the future by which the
hypotheses of the critics may be tested. A theory which
should be capable of being absolutely demonstrated in its
entirety by future events, would be no scientific theory
but a mere piece of fortune telling. On the other hand, a
theory, which goes beyond what may be verified to any
degree of approximation by future discoveries is, in so
far, metaphysical gabble. [CP 5.541].
As pointed out, to propose a scientific theory does not mean a
commitment with its truth. It means indeed to rely upon the capacity of
the theory to predict the future run of events, but a contingent future,
which may or may not happen as predicted. The scientist expects that,
if he lives time enough, or if inquiry continues indefinitely, his or her
beliefs would be confirmed. In this expectation there is not necessarily
any volition, but only an attitude of awaiting. As we said before, the
scientist waits to know, in an attitude that seeks to prevent every
striking occasion. In truth, the scientist seeks to anticipate surprise,
317
anticipating the novelty. In this awaiting attitude, the scientist has to be
aware, observing in distance every detail.
This observing attitude, of detached awaiting, connected to a
craving to learn, is not easy to adopt. This cold detached attitude, not
mixing emotional involvement and inquiry, is decisive to reach truth.
Because it is an attitude, any one could adopt it; but even for scientists
it is difficult to get to maintain coldness and not being taken by
personal individual passions. This is something Peirce warns:
But veracity apart, do these people suppose that they can
make any pure observation unaffected by fancy passion
or accidental moods or states of the nerves? The most
trained scientific observers cannot do that; and as for
those who are undisciplined and who are unaware of this
weakness of human nature, especially when they are
dealing with a subject as momentous as the other world,
they are incapable of any approximation to it. A physician
won’t prescribe for himself. And if he has too much
interest in the matter to keep his observations cold,
ought not any ordinary person to e regarded as
incompetent to keep cool when an immortal destiny is in
question? [W 2: 345, Whewell].
If experience shows to the scientist enough for doubting the
theories, the scientist must draw assent out of them. If he, on the
contrary, seeks to defend them against all contrary evidences, the
scientific spirit is put aside, and the scientist will be more like the
practical man, who needs certainties to act hic et nunc; or closer to the
318
professor, who needs to know to teach; or even of the religious man,
who is attached to dogmas.
Science, thus, would be the least conservative of human practices,
because it does not admit anything as definitely settled. At the same
time, it is possible to say that it is the most prudent of all practices,
since what the scientist does in the laboratory is only to test
hypotheses, to construct reasonings upon what has already been
proved, to test again, and so forth, avoiding to assert anything as a
categorical definite truth, for experiments may as well result otherwise
than expected. The scientist, because always trying before (and, in our
practical life, the chances to try before are reduced), is always trying to
prove redundancy, and seeking to avoid surprises: “But the influence of
the mind upon observations is not necessarily evil. It may almost be
said that we can only see what we look for.” [idem]. And, as we know,
even that one does not always find what one was looking for, that must
not be a reason for sadness. Someone, another inquirer, another being
or investigative mind will find.
Such parallel between decisions in science and decisions in
practical life brings another problem: to adopt science as a mode of life
is a practical decision of vital importance. Would not it be possible to
ask, then, whether in taking up this decision, one would make it acting
on the ground of full belief, that is, according to what was said,
adopting something which is out of place in science? In other words,
319
the problem presented is that taking up the life of science is a vital
decision – but the life of science does not assume anything as vital! As
we will see further on, Peirce frequently points out that it is reasonable
to act based on what we do not believe, but that we hope to be true.
Remember the pragmatic maxim, in one of its late formulations:
Pragmatism is the principle that every theoretical
judgment expressible in a sentence in the indicative
mood is a confused form of thought whose meaning, if it
has any, lies in its tendency to enforce a corresponding
practical maxim expressible as a conditional sentence
having its apodosis in the imperative mood. [HL 110].
In this context, the meaning of a proposition will be expressed by
another proposition to describe all the phenomenal empirical
occurrences virtually predicted by the first proposition. The meaning of
a proposition is therefore given by a set of hypothetical propositions,
not in the indicative mood, but in the subjunctive mood, which express
a law or willingness to act according to a habit-belief, making up its
ultimate interpretation, yet provisional and incomplete:
I deny that pragmaticism as originally defined by me
made the intellectual purport of symbols to consist in our
conduct. On the contrary, I was most careful to say that it
consists in our concept of what our conduct would be
upon conceivable occasions. [CP 8.208, letter to Signor
Mario Calderoni, c. 1905].
In total agreement with this form of presenting the pragmatic
maxim, there is the idea expressed in 1878, about the difference
between doubt and belief:
320
Belief does not make us act at once, but puts us into such
a condition that we shall behave in a certain way, when
the occasion arises. Doubt has not the least effect of this
sort, but stimulates us to action until it is destroyed. [W
3: 247, The Fixation of Belief, 1877].
Doubt justly prompts to action. People act because they believe in
the efficacy of their actions. Belief, from this standpoint, is seen as a
habit of mind that determines conduct, as a rule of action. This habit is
shaken when an unpredicted striking situation arises, demanding a
change in attitude. The unquiet state caused by doubt demands to be
dismissed, as soon as possible, and it becomes the mobile of action: it is
necessary to inquiry to end doubt. The pragmatic maxim establishes
how doubt would be dismissed if certain conditions were settled:
But [pragmatism asserts], that the total meaning of the
predication of an intellectual concept is contained in an
affirmation that, under all conceivable circumstances of a
given kind (or under this or that more or less indefinite
part of the cases of their fulfillment, should the
predication be modal) the subject of the predication
would behave in a certain general way – that is, it would
be true under given experiential circumstances (or under
a more or less definitely stated proportion of them, taken
as they would occur, that is in the same order of
succession, in experience). [CP 5.467, Pragmatism, c.
1905].
To say “A diamond is hard” (or to say that it has any other
property) is to say that the diamond is subjected to the law, i.e., to a
general mode of determinate conduct, and that, for that reason, it is to
say that in the future it is expectable that the diamond shows certain
321
characters; in other words, if the diamond be scratched one day, it may
not come to be damaged – if it be damaged, that will be a surprise,
which will lead to inquiry into the causes of such unforeseen
occurrence. In other words, the rational purport of a word, expression
or sign lies only in its influence over the conduct of life [EP 2: 332,
What Pragmatism Is]. It is not a mere criterion for verification,
therefore; rather, it is a criterion for ascertaining meaning –
independently of experiential verification, the reality of the hardness of
the diamond is expressed in a proposition which is true, general, and
conditional: “if a substance of a certain kind should be exposed to an
agency of a certain kind, a certain kind of sensible result would ensue,
according to our experiences hitherto.” [EP 2: 357, Issues of
Pragmaticism]. Thus, it is possible to conclude that the meaning of a
habit of action will depend upon the manner how a real objective
possibility can be actualized90, that is, in the way how some one subject
passes from possible immateriality to the concretion of action in
experience, driven according to a general rule to the future, in a
prospective movement which goes from dýnamis to
enérgeia.
In the parallel between science and morality, we can single out
points of contact. Science also concerns individuals. Even though a
moral code concerns the customs of a community, it is to individuals
who follow folkloric rules of conduct that it is directed; the individuals 90 MAGALHÃES (1984), p. 186; IBRI (1992), pp. 99 ff.
322
must behave in a certain way. In the same way, the Peircean definition
of science, with its strongly ethical exigencies, also imposes some lot of
moral commandments over individual scientists. We must notice,
mainly, the weight given to the cooperation among individuals: they
must put aside all personal beliefs, considering them as provisional, for
the sake of the Will to Learn [CP 6.3, The Logic of Events, 1898]; they
must share the results attained in their particular investigations; they
must, above all, remain open to criticisms and to submit their studies to
the criticisms of other inquirers, for the sake of discovering truth, as
well as to be ready to criticize and evaluate other researches when
needed. Science, therefore, naturally comes to be a public activity. It is
not only to address the problem of how individuals behave, but of which
are the ends they choose to themselves, in what regards the conduct of
their lives in an inquiry that seeks to discover something independent of
them. A scientist is someone who does not have personal commitments
to block the discovery of a truth of universal value, that is, “one that
goes toward enlarging the system of what is already known.” [EP 2: 48].
This cooperation among individuals makes science a public activity,
which main feature is to be a living and ever changing process:
But if I am asked to what the wonderful success of
modern science is due, I shall suggest that to gain the
secret of that, it is necessary to consider science as
living, and therefore not as knowledge already acquired
but as the concrete life of the men who are working to
find out the truth. Given a body of men devoting the sum
323
of their energies to refuting their present errors, doing
away with their present ignorance and that not so much
for themselves as for future generations and all other
requisites for the ascertainment of truth are insured by
that one. [CP 7.50, probably c. 1882]
The public agreement and sharing of theories, results,
conclusions, and methods is considered by Peirce as of central
importance to science as he understands it. This agreement is not
limited to human life though. The consensus on scientific truth has to
be really universal:
And the catholic consent which constitutes the truth is by
no means to be limited to men in this earthly life or to the
human race, but extends to the whole communion of
minds to which we belong, including some probably
whose senses are very different from ours, so that in that
consent no predication of a sensible quality can enter,
except as an admission that so certain sorts of senses are
affected. [W 2: 470, Fraser’s Works of George Berkeley,
1871].
Science, in this way, has as its basis for evaluation only and
exclusively a reality that is independent of subjective vicissitudes. It is
fundamental to emphasize the communicative dimension of science: if it
aims at discovering a truth about a reality, which is independent of our
human conceptions, it is a necessary consequence that this true be
valid also to other beings that are not humans. For instance, if it is true
that fire burns, this truth must be verifiable also in such cases, wherein
human sensibility is not at stake: the truth of the proposition must
describe a factual occurrence truly universal, capable of being
324
perceived by all beings – humans, vegetable, aliens, or of whatever
other nature. That is what would allow truth to be communicated
beyond the limits of human consensus.
Let us keep two main ideas, namely, that the scientific inquiry,
such as thought by Peirce, should work on the supposition that its
representations are valid because in first place they describe well the
manner of occurrence of facts, that is, it is a realist conception of
science, wherein reality imposes itself and determines the sign; in
second place, because every scientist must be immersed in a
community of inquiry to the point of being able to work on at and
develop other inquiries different from his or her own, with methods
which are not properly his or hers, but always keeping the same aim of
discovering truth, regardless its further use. In other words, if there is
not the pure wish to learn, there will not be genuine science – and, we
could say that, if there really are scientists devoted to this genuine
search, there is science:
Science consists in the sincere and thorough search for
truth according to the best available methods. Its only
quite indispensable condition is the absolute single-
hearted energy with which it works to ascertain the
truth, regardless of what the character of that truth may
be. It is not science if it is not an intelligently directed
research. But it will come to be so if it is absolutely
sincere and highly energetic. These dispositions will
generate the intelligence required. It is not science, if it
is not a well-informed research. But sincerity and energy
325
will bring about study. It is not science if it does not
invent cunning ways… [NEM 4: xix, s/d].
It can be said that it would be foolishness to exclude from the
scientific community, for instance, those whose aim is to improve
people’s lives. If the true will to learn is present, sooner or later the
study will be genuinely scientific, just as the practical utility of its
discoveries may be, in one way or another, sooner or later, also found.
That does not change the fact, though, that science has as its aim above
all others the discovery of truth, this being its supreme value, in face of
which all the others have to be considered collateral, and because of
which all inquiry is possible to become really scientific. Peirce steadily
affirms:
True science is distinctively the study of useless things.
For the useful things will get studied without the aid of
scientific men. To employ these rare minds on such work
is like running a steam engine by burning diamonds. [CP
1.76, Lessons from the History of Science, 1896].
The point is that the discovery of truth is the only thing of
supreme interest of the genuine scientist. Peirce does not say that the
summum bonum of scientific inquiry has not value – in fact, it is the
most valuable. He says that the inquiry and the Will to Learn must be
taken in genuine science as having a value per se – as ends in
themselves, and not because they make us reach something else, or
because of other things we can make or discover through them. It a
study of the useless that reveals an “interest by disinterest”91, a
91 BOURDIEU (2003), p. 31
326
disinterested interest. Peirce was completely contrary to any kind of
scientific utilitarianism; for him, questions of practical utility should be
“put out of sight” by the scientist [RLT 113]. For instance, take the
particularly interesting following passages:
To demand that man should aim at the stability of British
society, or of society at large, or the perpetuation of the
race, as an ultimate end, is too much. The human species
will be extirpated sometime; and when the time comes
the universe will, no doubt, be well rid of it. […]. I do say,
however, that truth is truth, whether it is opposed to the
interests of society to admit it or not – and that the notion
that we must deny what it is not conducive to the
stability of British society to affirm is the mainspring of
the mendacity and hypocrisy which Englishmen so
commonly regard as virtues. I must confess that I belong
to that class of scalawags who purpose, with God's help,
to look the truth in the face, whether doing so be
conducive to the interests of society or not. Moreover, if I
should ever attack that excessively difficult problem,
“What is for the true interest of society?” I should feel
that I stood in need of a great deal of help from the
science of legitimate inference; and, therefore, to avoid
running round a circle, I will endeavor to base my theory
of legitimate inference upon something less questionable
– as well as more germane to the subject – than the true
interest of society. [EP 2: 60-61, Pearson’s Grammar of
Science].
What to do with the resulting knowledge from scientific inquiry is
an important question, but secondary, given the nature of the scientific
practice. The question about the utility or practical usefulness cannot
327
be taken as the primordial problem according to which we should
concentrate our efforts. That would prevent deviations of purposes, for
instance, as it is seen in the very common conceptual confusions
between science and technology, broadly understood as the application
of the results of the research; but technology cannot be taken as an end
in itself. 92
The political dimension is here, as it is easy to notice, extremely
important. Mainly in Pearson’s book review, Peirce directs hard
criticisms to the way science is made in his days, criticisms that could
very well be kept nowadays:
The worst feature of the present state of things is that
the great majority of the members of many scientific
societies, and a large part of others, are men whose chief
92 According to our knowledge, Peirce rarely uses the word “technology”. However, we believe that the context of the discussions is clear enough to support our account. See, for instance, the context in CP 7.279, undated, wherein he uses “technique” in opposition to creative work; this, however, is not enough to say that technological work is necessarily and exclusively an ideological work directed to make money, for instance. The problem is not of technique in itself, but of the applications made of it, that is, what technique is desired for; for such reason, we prefer to contrast Peirce’s conception of science to the idea of technology. In first place, because technology, differently from mere technique, has heuristic potency, for it involves the formulation of theories, as the name itself points out, linking logic and technique; in second place, because contrarily to science, in the Peircean sense, technology directs its power to the discovery of previously determined ends. Technology, then, can lead to unforeseen discoveries, but its ultimate aim is not the discovery of the new. Furthermore, nowadays, technological ends, if not entirely, in great part are determined by the productive process. Cf. APEL (1995), pp. 192-193; HAACK (1997), pp. 241-261; SANTAELLA (1992), p. 109, makes an interesting remark: “In fact, it would be incurably ingenuous nowadays to ignore the increasing incorporation of the sciences by the hungry jaws of the productive process, a process from which result small differences between the mode of life of a great part of the scientists and the life of CEO’s of big corporations, for instance.” [Seria, de fato, de uma ingenuidade incurável ignorar atualmente a crescente incorporação das ciências às famintas mandíbulas do processo produtivo, de que resultam pequenas diferenças entre o modo de vida de boa parte dos cientistas e a vida de executivos de grandes empresas, por exemplo.].” Our translation.
328
interest in science is as a means of gaining money, and
who have a contempt, or half-contempt, for pure science.
Now, to declare that the sole reason for scientific
research is the good of society is to encourage those
pseudo-scientists to claim, and the general public to
admit that they, who deal with the applications of
knowledge, are the true men of science, and that the
theoreticians are little better than idlers. [EP 2: 60-61,
Pearson’s Grammar of Science].
Science as a market business, technique and science as ideology,
these are dear themes to the 20th century, themes Peirce in the 19th
century was aware of. The business of scientific inquiry, science’s
autonomy in relation to the broader social context, wherein science is
inserted and to which it pertains, hypocrisy found where it is not
expected to be found, against all of this Peirce proposes sincerity,
single-heartiness and obstinacy, as the power of what is genuine and
simple. With vigorous statements he attacks the ideologically forwarded
confusion between science, as inspirited by a pertinacious desire to
learn the truth, whatever it is to be learnt, and the application of the
results of the inquiry, guided by undeclared or suspicious interests. He
also condemns the political-ideological discourse that takes advantage
of this confusion to justify itself to the “general public”, when in fact it
is supported by economic motives. In fact, the relations of force and the
concentration of money and power in scientific production are due to
the fact that the social world of science depends, to its survival as
research in the contemporary world, upon economic decisions that are
329
taken outside its own limits – and such economic decisions give power
and prestige to certain agents inside the scientific community. This is
something Peirce attacks when he speaks about “making science as a
means to make money”: to direct the researches to vindicate the
pretensions of validity of an ephemeral society, or, what is worst, to
make money, this is but another form, maybe one of the worst forms of
utilitarianism, individualism and immediaticism, in vogue since the
beginning to the capitalist industrial society, which transforms science
in a myth, a mere ideology at the service of the justification of a
perverse technocratic system. In short, two aspects of a myth of science
can be refuted on the grounds of Peirce’s position: first, the illuminist
illusion that necessarily unites epistemic progress with social progress;
second, the idea that the means of access to the scientific production
have to be necessarily restricted to channels for distributing
technology. Science as a collective activity is communicative, and the
means of access to it should be overtly public; the production of
technological objects is only one way, among many others, of having
access to scientific production, contrary wise to what may seem, when
inquiry is subordinated to the straight interests of private social groups.
The Peircean conception of science appears as a conceptual
alternative to think the autonomy of the scientific activity in relation to
the external forces and pressures over it, pressures which try to reduce
330
the inquiring activity to a productive activity. In other words, the
internal coherence of the scientific “social group”, according to Peirce,
is given by the fidelity to the phenomena, and not by the fidelity to the
community, whatever it is. This is the only way to make genuine
science, and not science for the advancement of society, mean it
whatever it may mean. The internal coherence thus appears to
scientists as a consequence of the unity of aims, methods and spirit
characteristic of their fidelity to phenomena. This is a problem which is
inherent to scientific production: it is always made by a certain group of
people with a certain interest – yet the result of the researches do not
necessarily have to always be a grotesque and direct answer to the
needs of their authors. Inquiry will always be, because of that unity,
theoretical and empirical; the concepts cannot, for such reason, be
discussed in themselves, but always in regard to what they try to
describe – what interests in this discussion is to put the aims in doubt.
There is this long passage wherein Peirce discusses the relation
between efficient and final causality in science, that is, in what manner
the adoption of diverse means can lead to the same conclusion:
One man may investigate the velocity of light by studying
the transits of Venus and the aberration of the stars;
another by the oppositions of Mars and the eclipses of
Jupiter's satellites; a third by the method of Fizeau; a
fourth by that of Foucault; a fifth by the motions of the
curves of Lissajoux; a sixth, a seventh, an eighth, and a
ninth, may follow the different methods of comparing the
331
measures of statical and dynamical electricity. They may
at first obtain different results, but, as each perfects his
method and his processes, the results are found to move
steadily together toward a destined centre. So with all
scientific research. Different minds may set out with the
most antagonistic views, but the progress of investigation
carries them by a force outside of themselves to one and
the same conclusion. This activity of thought by which we
are carried, not where we wish, but to a foreordained
goal, is like the operation of destiny. No modification of
the point of view taken, no selection of other facts for
study, no natural bent of mind even, can enable a man to
escape the predestinate opinion. This great hope is
embodied in the conception of truth and reality. The
opinion which is fated to be ultimately agreed to by all
who investigate is what we mean by the truth, and the
object represented in this opinion is the real. That is the
way I would explain reality. [W 3: 273, How to Make Our
Ideas Clear, 1878].
Those who engage in scientific inquiry must trust that if the
inquiries are carried on long enough they will reveal a truth to us.
Because the real will always be there, insisting, remaining, and
directing our questions; it is certain that a given time will come when
we will not be able to disagree with it. We trust truth will be reached
one day because all other reasonings from all other investigators
support ours, for they also are directed by the real; we also know that
reasonings are the result of ages of experience, attempts, mistakes and
corrections. Of course, we may be wrong. But, in the scientist the will
to learn lives, the will to discover truth – and even that there are
332
reasons to doubt this will, we should not give up trying, for that would
mean the assumption that there is nothing else to seek, nothing to
search for, that is, it would mean to assume that everything is already
in our hands.
The man of science has received a deep impression of the
majesty of truth, as that to which, sooner or later, every
knee must bow. He has further found that his own mind
is sufficiently akin to that truth, to enable him, on
condition of submissive observation, to interpret it in
some measure. As he gradually becomes better and
better acquainted with the character of cosmical truth,
and learns that human reason is its issue and can be
brought step by step into accord with it, he conceives a
passion for its fuller revelation. He is keenly aware of his
own ignorance, and knows that personally he can make
but small steps in discovery. Yet, small as they are, he
deems them precious; and he hopes that by
conscientiously pursuing the methods of science he may
erect a foundation upon which his successors may climb
higher. This, for him, is what makes life worth living and
what makes the human race worth perpetuation. [EP 2:
58, Pearson’s Grammar of Science].
The passage above indicates that science is prospective, it is yet
an unfinished work: opposed to the recognition of the esse in praeterito,
science views an esse in futuro which is unknown [CP 2.148, Minute
Logic, 1902]. As Apel says, “the world cannot be known or explained
merely by its previously fixed, lawful structure, but must rather
continue to be developed as a historical, social world of institutions and
333
habits for which we must assume responsibility”93. In the passage above
we also see more details to help to understand the scientific attitude:
first, the scientist waits, looking ahead to the possible confirmation of
the theories, hoping his or her inquiry is a small contribution to a
broader inquiry, with a supreme objective: to bring human mind in
agreement with the universal cosmic mind. The scientist’s most sincere
belief is to be able to construct a step above which others may climb, to
reach a higher point, in the future. For that reason, the scientist has an
anticipatory attitude: the truth is thought of as a project yet to be
accomplished. Now, to think truth as a future project still yields room
for manipulations, and the criticisms Peirce directs to pseudo scientists
go straight to this point: we have to assume responsibility on what we
help to create, a responsibility to the future generations, to the
perpetuation of the species. Who produces knowledge? To whom? In
the name of what? With what means – technological, economic? All such
questions deepen the criticisms to the ideological manipulation of
science. To Peirce, the word science “embodies the epitome of the
intellectual development” of human being; the conception of scientific
inquiry concerned primarily and ultimately with a heuristic activity,
teleonomically oriented to a truth we do not know, works in a way to
counterbalance the conception of science as a rational and
systematized knowledge, which is certain and directed to a determined
objective, oriented to the past, therefore. 93 APEL (1995a), p. 193.
334
Peirce’s writings, thus, show to be very important for us. They
remind us that even if we take everything we know as our ground,
absolute certainty in any subject-matter is impossible. Even we find
some definite experience about some subject-matter he says “reasoning
will, from the nature of its rules, be able to draw some inference from
it, whether with great or little confidence.” [W 2: 353, Rules for
Investigation, 1869-1870]. For that reason, we can never have any
pretension to the necessity, universality and absolute certainty of our
propositions. The base of knowledge will always be cultural, historically
built during the centuries – a provisional ground, therefore.
We cannot, therefore, throw this knowledge away and go seeking
for unquestionable grounds, which are certain, indubitable, and
absolute. Inquiry always begins with some kind of disagreement, and it
is exactly to reach agreement that it begins, looking for the reasons of
the disagreement. It does not matter how provisional our knowledge is,
it is all we have, and at the same time it is only what we have. As it is
not absolutely certain, we can only hope to be in the right track, even
though we know our track is not the only track – remember nothing is
vital in science, not even science itself. Therefore, it may take a long
time, but inquiry will be released from the instabilities of the present –
of the immediate practical aims, circumstantial political pressures, and
religious dogmas. Inquiry carried on long enough would reverse any
and every opinion, putting truth always in the future: the opinions of
335
now are always provisional, and we have to put up with it. The long
time inquiry may last is long only for us, human beings, if we consider
the duration of the universe. The time of truth for the inquiry, as in
Bandeira’s poem, never is – will be.
336
8. THE GENEALOGY OF THE SCIENCES
Der Mann war noch nicht auf der Welt, der zu seinen Gläubigen hätte sagen können: Stehlt, mordet, treibt Unzucht – unsere Lehre ist so stark, daß sie aus der
Jauche eurer Sünden schäumend helle Bergwässer macht; aber in der Wissenschaft kommt es alle paar Jahre vor, daß etwas, das bis dahin als Fehler galt, plötzlich alle Anschauungen umkehrt oder daß ein unscheinbarer und verachteter Gedanke zum Herrscher über ein neues Gedankenreich wird, uns solche Vorkommnisse sind dort
nicht bloß Umstürze, sondern führen wie eine Himmelsleiter in die Höhe. Es geht in der Wissenschaft so stark und unbekümmert und herrlich zu wie in einem Märchen.
Robert Musil, Der Mann ohne Eigenschaften.
The aim of every classification of the sciences is to settle an order,
in things and in the thought of things. When one tries to classify
sciences in a certain point of their evolution, this undertaking gives a
faithful yet provisional image of the scientific knowledge of that age.
The classification, by making it possible to be conscious of our
knowledge through such inventory, also works as a spatial-temporal
map of the intercrossing of the cultural ideas of a given period. The
value of a classification of the sciences, however, goes far beyond that
of a mere inventory or “table of contents”, no matter how complete it
may be. The very fact that the classification depends on logical criteria,
which by nature may be objective or subjective, already gives us an
initial idea of the obstacles posed to the classifier, difficulties which are
rarely found in other types of classification, as the preparation of a
catalogue, for instance. Therefore, an effort which is successfully
brought about may serve to lead us to discover the connexions and
analogies between the different fields of knowledge, in a certain time,
within a given social-historic more or less well defined period. The
337
classification of the sciences, therefore, is a picture of a moment of a
civilization. Nevertheless, history and stasis are repealing concepts – all
history is a process in continuous development, an incomplete and very
problematic attempt of reconstructing something which does not exist,
for its very object, when it is past, can only be viewed with the eyes of
the present; and, when one tries to make the history of the present, the
present is no more. We are, hence, obliged to consider the study of
sciences and their classification essentially as a historic process, which
is subject to changes and hence in continuous development.
All such previous considerations, in what regards our present
work, can be summed up in the following way. The question about the
possibility of a classification of the sciences can be understood in a
twofold ways: the first, relative to the normative stress of a general
classification of the sciences, for it is needed to say how sciences should
be organized one in relation to the others; the second, in relation to the
inevitable descriptive task that such a classification has to involve.
Thus, a classification of the sciences is possible only if it concretely
accounts for what each particular science is, and how it is produced.
Peirce could not be satisfied with some abstract definition of science,
for as a scientist himself, he knew that abstract definitions could be
sooner or later overcome, due to new discoveries, fusions of methods
and even to criticisms.
338
To look at what really happens with scientists, when in the
process of investigation, is the key to the classification of the sciences
he offers. Thus, we have to understand what we previously said in the
following way: even though some may conduct scientific inquiries
without the exclusive wish to learn, it would be foolish to put them
aside and say that they do not make part of the scientific community,
because, in fact, that is what happens. He states this because he
considers a mistake of other classifications to try to classify the possible
sciences, and not the present ones; i.e., to attempt at a classification of
which sciences will be in the remote future:
Many of these schemes introduce sciences which nobody
ever heard of; so that they seem to aim at classifying, not
actually existent sciences, but possible sciences. A
somewhat presumptuous undertaking is that of
classifying the science of the remote future.94 [EP 2: 115,
On Science and Natural Classes].
This is a mistake we consider a consequence of what Peirce
himself knew very well to be the case, i.e., that even though there is a
classification to establish limits and demarcations, “boundary lines in
some cases can only be artificial” [EP 2: 125, id.]. In not recognizing
this, the classifications commit the mistake of in general imposing
limiting and abstract definitions with the purpose to fix precise
94 The same idea, slightly modified, appears in the following passage: “But there is one monstrous fault that seems to be common to all published classifications; namely, it is that they attempt, apparently, upon a basis of experience to pronounce upon what sciences are the only ones possible. I shall not venture upon that attempt, but shall confine myself to the sciences that either exist, or whose birth seems to be promised.” [MS 655: 16, Quest of Quest].
339
domains, exactly where it is impossible to draw a clear and precise
demarcation line. The way sciences develop, the mode scientists
effectuate their investigations breaks up classificatory lines, showing
the impossibility of the absolute determination of the limits of human
knowledge – for it is a fact that there is a transmission of knowledge
from generation to generation, resulting in a continuous progress in our
knowledge of the world, what means that at least an increase of
meaning there is in the concepts used. Here we have again the idea
that science is a public communicative activity, wherein it is impossible
to separate the individual work from the collective work of all: “what
we mean by science is the sum of human activity at any epoch in the
path of discovery” [N 1: 156, 1892].
Now, if science is made of collaborations between scientists, if
science means the sum of human activities in the pathway of Discovery,
the classification of the sciences has to take into account the
intercrossing of activities that renders impossible the definite
distinction between one science and another: the work in one science
implies the work in all the others. The development of science happens
by means of collaborations between scientists, through dialogues and
argumentations, acquaintance with what was done before to the
recognition of one’s own work as a part of a bigger work; hence,
boundaries frequently would be very easily blurred, because science
constantly changes: ““Science is not a fixed, unchangeable body of
340
propositions.” [N 2: 213, 1899]. Thus, the historic development of
science is understood by Peirce as a process by means of which each
individual inquirer adds something, the small it may be, to the universal
investigation:
The man of science has received a deep impression of the
majesty of truth, as that to which, sooner or later, every
knee must bow. He has further found that his own mind
is sufficiently akin to that truth, to enable him, on
condition of submissive observation, to interpret it in
some measure. As he gradually becomes better and
better acquainted with the character of cosmical truth,
and learns that human reason is its issue and can be
brought step by step into accord with it, he conceives a
passion for its fuller revelation. He is keenly aware of his
own ignorance, and knows that personally he can make
but small steps in discovery. Yet, small as they are, he
deems them precious; and he hopes that by
conscientiously pursuing the methods of science he may
erect a foundation upon which his successors may climb
higher. This, for him, is what makes life worth living and
what makes the human race worth perpetuation. [EP 2:
58, Pearson’s Grammar of Science, 1901].
The way, then, to avoid an arbitrary schematization would be to
propose a classification based upon what in fact happens in scientific
inquiry; in other words, a natural classification is needed, because it is
related to the way how science is made, that shows the degrees of
interdependence and specificity among sciences.
What is the precise status of such classification? Let us see its
conditiones sine quibus non. At the same time that, to reach a natural
341
classification it is imperative to consider science as it is presently made,
it is also needed to look a little bit ahead, not to lose sight of the
possible development of the sciences: “our classification ought to have
reference to the science of the future, so far as we are now able to
foresee what the future of science is to be” [CP 7.56, Of The
Classification of the Sciences. Second Paper. Of the Practical Sciences,
c. 1902]. This reference to the future, of course, can only be to the close
future – science, as we said above, changes, and this makes it
impossible to foresee its development in a very distant future:
[…] it is plainly important that our notion of science
should be a notion of science as it lives and not a mere
abstract definition. Let us remember that science is a
pursuit of living men, and that its most worked
characteristic is that, when it is genuine, it is in an
incessant state of metabolism and growth. [EP 2: 129, On
Science and Natural Classes].
Therefore, the presumption to try to look very far, to the remote
future, is a vain presumption, when it is the case to understand
scientific knowledge. Thus, the first thing a natural classification of the
sciences is not, it is not a classification of the sciences in the distant
future, simply because these future sciences are yet to be – they do not
exist. To try to classify sciences in this ways would be a methodological
lethal mistake, in so far as science is an activity brought about by living
people, and nothing warrants they remain in creative stasis; on the
342
contrary, they are in constant mutation, for they make part of life in
movement.
There are several statements in Peirce’s writings on the necessity
of a natural classification that would classify the different objects of the
different sciences in the present state of inquiry, as well as the activity
exerted by scientists in their practice; furthermore, it could also give a
brief view of their possible developments in the next future. Such
classification, in this way, accounts for the temporal development of the
sciences, chiefly accounting for how they became what they are, and
what they might likely turn out to be, only in the very close future.
According to Peirce, a natural classification of the sciences necessarily
has to show sciences in their historic development, as if it was “a
classification which displays, in a useful way, the principal general
relations which we have learned from observation concerning the more
important resemblances and differences of the objects classified” [N 3:
170, 1904]. It cannot be a forced classification, that is, a classificatory
model imposed over the facts. The scope of a natural classification is
“to embody the chief facts of relationship between the sciences so far
as they present themselves to scientific and observational study.” [MS
1334: 11/12]. In other words, the classification of the sciences should
be an “usefully expressive diagram of the meaningful inter-relations” of
the sciences [NEM 4: 227].
343
Related to the way how science is produced, the classification
proposed by Peirce will be such a diagram, wherein all the science s
may be simultaneously seen, wherein all scientific activities will be
presented in communication one with another. In his logical notebook,
on 5 September 1906, Peirce wrote on his concept of a diagram. The
purpose of a diagram is:
[...] to represent certain relations in such a form that it
can be transformed into another form representing other
relations involved in those first represented and this
transformed icon can be interpreted in a symbolic
statement. It is necessary that the Diagram should be an
Icon in which the inferred relation should be perceived.
[…] No other kind of sign can make a truth evident. For
the evident is that which is presented in an image,
leaving for the work of the understanding merely the
Interpretation of the Image in a Symbol. [MS 339 D:
544].
Without going further in deep semiotic discussions, for it is not
our aim, we can say that the general idea shown in the passage above is
clear enough. The diagram must be vague enough to allow further
interpretation, that is, it must be vague enough to make us see its scope
in the way it pictures certain logical relations; however, it must have
sufficient precision to present, as a picture, the relations the objects
classified entertain one another. In Santaella’s words, the Peircean
classification of the sciences is like a true “cartography” of the
sciences95. The diagram, therefore, has an abstract generality that
95 SANTAELLA (1992), p. 101.
344
pictures the structural homologies. It is this same abstract generality
that makes it possible to be open to the representation of processes in
development, once the diagram represents relations in a way that can
be transformed; it is a “mobile and dynamic diagram, flexible to the re-
adaptations demanded by the passage of time” 96. In the case of the
classification of the sciences, it means that a natural classification
would have to be sufficiently clear to show the relations of
interdisciplinarity, dependence and evolution among the sciences,
putting to light the historic-temporal dimension of scientific enterprises.
Thus, the diagram of the classification of the sciences would make
the relations of dependence among the sciences evident; such relations
would not be necessarily relations of hierarchy. In presenting the
relations between the various scientific activities in an evident manner,
the diagram of the classification shows how it is possible in the various
ways of approaching the objects to work with the various sciences at
the same time. The diagram, then, makes it possible to pass from the
plan of simultaneity to the plan of sequentiality. By its form of display,
the diagram makes us see the relations, without putting them into a
96 Idem, ibid. Santaella also says, continuing: “The Peircean classification of the sciences, far from working only as a classification in the strict sense, in fact serves as a guide, chart of orientation for those who wish to thread, with some accuracy, the dense forest of the sciences. [A classificação peirciana das ciências longe de funcionar apenas como uma classificação em sentido estrito, serve, na realidade, como guia, carta de orientação para aqueles que desejam percorrer, com alguma acuidade, a espessa floresta das ciências.]” (1992), p. 101.
345
hierarchy, however, leaving thus the interpretations of such relations
undetermined.97
In general lines, the nature of a natural classification of the
sciences is then defined: it has to be a representative diagram of the
inter-relations of the sciences, vague enough to allow further
interpretation and change if needed (therefore, we do not need a
classification of the sciences to tell us what to do with our knowledge,
even because it is already used before classifying the sciences), for it
must show where sciences come from, and whereto they may develop in
the close future; it must be also precise enough so that we do not lose
sight of the relations of dependence and overlapings among the various
scientific domains.
Nevertheless, it is not only this. It also necessary to understand
what is a natural class. According to Peirce, the classification will be
natural only if it is a classification of objects capable of some kind of
description, which is the only possible way to correspond to real
empirical objects. This implies that objects must have some common
character in common capable of description, i.e., this common
character will be like a criterion to put them under a determined class,
and not under another. For Peirce, the only possibly natural
classification would be one that would consider the objects from the
97 For more details on the concept of diagram, see. EP 2: 207, The Three Normative Sciences, 1903; 212, The Nature of Meaning, 1903; 303, New Elements (), c. 1904; LEO (2002), pp. 56 ff.; IBRI (1994), pp. 124 ff.
346
point of view of their aims, what they must be, in a word, from the
standpoint of their final causes:
A class, of course, is the total of whatever objects there
may be in the universe which are of a certain description.
What if we try taking the term "natural," or "real, class"
to mean a class of which all the members owe their
existence as members of the class to a common final
cause? This is somewhat vague; but it is better to allow a
term like this to remain vague, until we see our way to
rational precision. [EP 2: 117, On Science and Natural
Classes].
This is the principle that informs Peirce’s classification of the
sciences. In effect, to him, “Every classification has reference to a
tendency toward an end. If this tendency is the tendency which has
determined the class characters of the objects, it is a natural
classification.” [NEM 4: 65, Carnegie Application]. About aiming at
ends, Peirce declares98:
[…] we must understand by final causation that mode of
bringing facts about according to which a general
description of result is made to come about, quite
irrespective of any compulsion for it to come about in this
or that particular way; although the means may be
adapted to the end. The general result may be brought
about at one time in one way, and at another time in
another way. Final causation does not determine in what
particular way it is to be brought about, but only that the
result shall have a certain general character. [EP 2: 120,
On Science and Natural Classes].
98 From this point on, we follow the account given by HULSWIT (2002), pp. 76 ff.
347
It is important to notice that in the passage above the concept of
final cause is not defined, but only that it is said what is the process of
final causation, i.e., how the process comes about to a final cause.
According to what was said above, it is a process of actualization of a
certain general form to which events must come to agree [N 1: 200,
1893]. We find what Peirce means by final cause in another passage:
“Now, what is a ‘final’ cause? It is merely a tendency to produce some
determinate kind of effect having some relation to the destiny of
things.” [EP 2: 464 n., An Essay toward Improving Our Reasoning in
Security and in Uberty, 1913]. Final causes, then, are not something
actually and concretely existent, but rather a mere possibility that the
facts come to unfold in a certain way with a view to a certain kind of
end:
By a tendency to an end, I mean that a certain result will
be brought about, or approached, and in such a way that
if, within limits, its being brought about by one line of
mechanical causation be prevented, it will be brought
about, or approached, by an independent line of
mechanical causation. […] An end is an intellectual idea
[…]; every intellectual idea governing a phenomenon
produces a tendency toward an end. [NEM 4: 65; 66].99
Now, we have seen that final causes, to Peirce, are general forms
to which events tend in a defined process. They determine the sort of
events that are being caused now by efficient causes. And the process
of actualization of forms acquires sense just by the tendency the facts
99 Cf. SANTAELLA (1999), for a more thorough discussion on the processes of final causation in nature.
348
have to conform to certain ends. This is the meaning in saying that
independent lines of mechanical causation run to the same end: it is
possible to attain the same general aims through several lines of action.
The discussion here is about what is normally called teleological
process, i.e., processes that tend to a final ideal state. The emphasis of
Peirce’s writings is not over the determined manner in which events
happen; we have just seen, it is possible that different lines of action
lead to the same final result. The emphasis is in attaining one final
state, and not another. Once this final state is achieved, it is not
possible to go back, for it is not possible to reverse the lines of
mechanical causation that have acted; in other words, it is not possible
to change the efficient causes because they were actualized already.
This leads us to another character of processes of final causation, such
as Peirce understands them, which is that of being irreversibly oriented
toward a certain direction:
Those non-conservative actions which seem to violate the
law of energy, and which physics explains away as due to
chance-action among trillions of molecules, are one and
all marked by two characters. The first is that they act in
one determinate direction and tend asymptotically
toward bringing about an ultimate state of things. If
teleological is too strong a word to apply to them, we
might invent the word finious, to express their tendency
toward a final state. The other character of non-
conservative actions is that they are irreversible. [RLT
220].
349
As Putnam says, this reveals Peirce’s commitment to an
irreversible conception of time; in other words, we can say that the past
is definitely determined, the future is undefined, and the present is a
state of absolute now [RLT 96]. Finious processes, then, are those
wherein there is a tendency to a general determined end, not being
possible to explain the process by the indication of which forces operate
in it, that is, only by indicating its efficient causes: it is also needed to
indicate how these forces work together in bringing about certain
specific effects and not others, for lines of mechanic causation may
vary, but the result obtained must always be of the same general kind.
The fact that the means to produce these specific effects may be
different is acceptable only if we think of a general regulative idea
directing the whole process, which is what Peirce means with the final
cause of the process..
We can come to a closer understanding of all of this if we look to
some examples given by Peirce. One of them is about gases. One cannot
explain the diffusion of gases, according to Peirce, only with the
concept of force:
Take, for example, the phenomenon of the diffusion of
gases. Force has very little to do with it, the molecules
not being appreciably under the influence of forces. The
result is due to the statistics of the equal masses, the
positions, and the motions of the molecules, and to a
slight degree only upon force, and that only insofar as
there is a force, almost regardless of its character, except
350
that it becomes sensible only at small distances. [NEM 4:
66, Carnegie Application].
Therefore, there are several other factor to influence the
behaviour of gases, and the fact that a gas is composed of “molecules
distributed according to a statistical law” indicates that the
phenomenon of the diffusion of gases is like a irreversersible
phenomenon, with a tendency to occur in one direction and not in
another, i.e., a tendency to achieve a certain end in a certain way
(according to that statistical law); which tendency, “if hindered, within
certain limits, it will, when freed, recommence in such way as it can.”
[id.]. Another example is the one of the falling stone, which in falling
hits a horizontal elastic surface, coming back in the opposite direction,
upwards, until the point wherefrom it started to fall, in the same
velocity of the fall: “Whatever motion conservative forces can effect the
very reverse of that motion they are equally capable of effecting.” [RLT
220]. This does not mean that the process is reversible, but only that
action and reaction are explained according to the same laws,
according to the same general tendencies to occur in a certain
determined way. The movement of the stone, when hindered by an
elastic surface, does not suddenly ends, but, keeping the same general
characters, happens in the reverse order.
The illustration of the lamps is the best to clear up the relation
between final and efficient causes. Lamps are products thought of by
human beings with the main purpose of providing light – which kind of
351
light, directed to what specific place, coloured or not, more or less
shining or more or less dim, flashing or statical, electric or fire-lit – all
such questions are secondary, which the particular circumstances will
help to ascertain. In fact, it is easier to classify objects one already
knows the final causes, that is, objects which finalities are already
known, that is, that to which they were made for. If I want an object to
fulfill a defined function, I know how should act to obtain the desired
result. Human creations, possibly with the exception of artistic
creations, have all a defined role, and their final causes are determined
by their usefulness. The general purpose of a lamp, no one doubts, is to
provide illumination, and that is enough to give us a natural class:
“lamps form a true, real, and natural class, because every lamp has
been made and has come into being as a result of an aim common and
peculiar to all lamps.” [EP 2: 117, On Science and Natural Classes]. In
fact, the example of lamps lets us see how it is with all human product
with a defined function100.
The example of the lamps is clarifying not only because of the
utility of the lamps, but because it contrasts products made by human
beings to fulfill a defined function and things in nature: animals, plants,
stones, mushrooms, viruses; whatever it may be, nothing in nature has
a humanly defined. We, human beings, do not know a priori which the
designs of nature are, and an attempt to classify natural objects
100 One should notice that Peirce is not concerned in this discussion with artistic objects, as we may understand them today, as objects that do not need to have an utilitarian function.
352
according to which purposes they were created is impossible, unless we
know the final causes operating in nature (supposing nature has any
final causes, of course). Peirce says: “In regard to natural objects,
however, it may be said, in general, that we do not know precisely what
their final causes are.” [id.]. in this sense, to speak about purposes of
natural objects is not appropriate, for it may as well be that natural
objects do not have an a priori defined purpose, but that they build
their purposes up unconsciously, in so far as they develop and tend to
actualize a certain end.101
The illustration given, this time, is the one of the animals that
have legs:
The use of legs is clear to us, having them ourselves. But
if we pass the animal kingdom in review, we see that in
the majority of branches there are no such organs of
locomotion; while in the others they are present
throughout some whole classes, are absent throughout
others; and in still others are sometimes present,
sometimes absent. [id.].
The conclusion we can draw is that to have legs is a means of
locomotion that can be connected to the possibility of a form; that “two
animals of the same order could not differ in respect to using
101 We will return to this point ahead. Cf. SANTAELLA (1992), p. 112: “[…] Peirce preferred this term final causation or ideal causation to the term purpose, because the latter could be mistaken by intentionality, which merely is the conscious variation of final causation. Not only causation can be unconscious, one of the cases in which the purpose is unknown, but it may as well be a case of purposes not specifically human, as it is with natural objects. [Peirce preferia esse termo causação final ou causação ideal ao termo propósito, porque este pode ser confundido com intencionalidade que é meramente a variação consciente da causação final. Não apenas a causação pode ser inconsciente, um dos casos em que o propósito é desconhecido, mas pode também não ser uma questão de propósitos especificamente humanos, como é o caso dos objetos naturais.]” Our translation. For more details, see SANTAELLA (1999), p. 501-503.
353
legs.”[ibid.] But we cannot assert that to have legs is in fact linked to
the possibility of a definite form, because we also see that animals with
legs “do not form a natural group; for they are not separated from all
others in any other important particular.” [ibid.] Therefore, regarding
nature, all we can do is to risk, for we do not previously know which its
purposes are, whether exist or not. Our knowledge of nature is based
upon observations we generalize, and everything we do is to construct
hypotheses that can come to be refuted by future experience. The
upshot of this argumentation leads us to conclude we cannot attain
absolute logical exactness: “We thus get a tolerably clear idea of what a
natural class is: it will amply suffice for our present purpose; though we
can hardly hope that it will turn out to be logically accurate.” [ibid.].
The idea of a general class, therefore, is a vague idea. Vagueness,
in this context, is a necessary character of natural classes, if we
remember that differently from all natural things, human objects are
(almost) all made having in sight some sort of actualization. Their
classification a fortiori is not difficult, because it is possible to know a
priori their purposes, meaning, before attempting to classify them, we
already know what the objects to be classified were made for.
This is the exact point concerning the sciences: it is perfectly
possible to obtain a natural classification of the sciences,
notwithstanding the unavoidable vagueness of our natural classes,
because sciences are, more or less in the same way as lamps, human
354
creations; and as such they also serve to human wishes, no matter how
vague such wishes may be: “We also see that, when an object has been
made with a purpose, as is, of course, the case with the sciences, no
classes can be more fundamental nor broader than those which are
defined by the purpose.” [EP 2: 117/118]. Purposes are general and
vague, for they are “operative desires”, according to Peirce. They direct
our efforts towards getting a certain kind of event or thing which is
desired. Thus, that which is desired never is something completely
determined, but something vague and general; even though the fact
that I want is a single and determined fact, that which is the object of
my desire, as Hulswit says, “is of the nature of an idea, or general type”
102 . Peirce gives a delicious example for this claim, one could say. An
apple pie is desired. Not this or that pie, but a certain type of pie, made
of a certain kind of pastry, a certain kind of fruits. The more varied the
degree of generality is, and the more we wish a especial pie made of a
especial type of apple, by an especial particular cook, even then the
object of our wish remains of a general nature. We have an idea of what
kind of pie we want, and the final pie, that pie, made and cooked
according to our idea, ends to satisfy the general specifications of our
will to eat the apple pie. However, if someone eats the pie before, our
desire can be satisfied with another pie; as Peirce says, “Desire is not a
reaction with reference to a particular thing; it is an idea about an idea,
102 HULSWIT (2002), p. 77.
355
namely, the idea of how delightful it would be for me, the cook's
master, to eat an apple pie.” [CP 1.341, c. 1895]103.
Back to the sciences, this vagueness will allow to classify them
without imposing limits and boundaries arbitrarily restrictive between
them, because what this operative desire makes is to create a broad
enough class to include the various kinds of objects that could satisfy 103 The passage is deliciously interesting, and deserves to be transcribed in full: “Let us examine the idea of generality. Every cook has in her recipe-book a collection of rules, which she is accustomed to follow. An apple pie is desired. Now, observe that we seldom, probably never, desire a single individual thing. What we want is something which shall produce a certain pleasure of a certain kind. To speak of a single individual pleasure is to use words without meaning. We may have a single experience of pleasure; but the pleasure itself is a quality. Experiences are single; but qualities, however specialized, cannot be enumerated. There are some two dozen kinds of metals well known to me. I remember to have examined lumps of those qualities. But it is only the limitation of experience which attaches that number; there is simply no end to the metallic qualities I can imagine. I can imagine an infinite variety between tin and lead, or between copper and silver, or between iron and nickel, or between magnesium and aluminum. An apple pie, then, is desired – a good apple pie, made of fresh apples, with a crust moderately light and somewhat short, neither too sweet nor too sour, etc. But it is not any particular apple pie; for it is to be made for the occasion; and the only particularity about it is that it is to be made and eaten today. For that, apples are wanted; and remembering that there is a barrel of apples in the cellar, the cook goes to the cellar and takes the apples that are uppermost and handiest. That is an example of following a general rule. She is directed to take apples. Many times she has seen things which were called apples, and has noticed their common quality. She knows how to find such things now; and as long as they are sound and fine, any apples will do. What she desires is something of a given quality; what she has to take is this or that particular apple. From the nature of things, she cannot take the quality but must take the particular thing. Sensation and volition being affairs of action and reaction relate to particular things. She has seen only particular apples, and can take only particular apples. But desire has nothing to do with particulars; it relates to qualities. Desire is not a reaction with reference to a particular thing; it is an idea about an idea, namely, the idea of how delightful it would be for me, the cook's master, to eat an apple pie. However, what is desired is not a mere unattached quality; what is desired is that the dream of eating an apple pie should be realized in Me; and this Me is an object of experience. So with the cook's desire. She has no particular apple pie she particularly prefers to serve; but she does desire and intend to serve an apple pie to a particular person. When she goes into the cellar for the apples, she takes whatever bowl or basket comes handy, without caring what one, so long as it has a certain size, is clean, and has other qualities, but having once selected it, into that particular bowl she intends to put some apples. She takes any apples that are handy and seem good; but having taken them she means to make a pie of those apples. If she chances to see some others in the kitchen, on her return from the cellar, she will not use them for the pie, unless for some reason she changes her mind. Throughout her whole proceedings she pursues an idea or dream without any particular thisness or thatness – or, as we say, hecceity – to it, but this dream she wishes to realize in connection with an object of experience, which as such, does
356
the desire. The specification of an individual object, in an individual
occasion, happens when there is the intermediary element of will, that
is, our desire becomes clearer and more specific when we begin to
focus our attention upon an object or thing we want above everything
else, and consequently the classes may come to be narrowed. Purposes,
then, are like general desires, they can always be made more and more
specific, insofar as we go pursuing them, trying attain them. The
example of the lamps is once more clarifying. First, one thinks of a lamp
because one wants “economic lighting”. After thinking of some ways to
get economic lighting, it is needed to choose again one further thing in
each thought way – for instance, if we decide by combustion or by
electricity; once it is decided by electricity, if we want burning lamps or
fluorescent lamps, and so forth. Desires, as Peirce says, are in this way
vague, variable and have “longitude”:
[…] while a certain ideal state of things might most
perfectly satisfy a desire, yet a situation somewhat
different from that will be far better than nothing; and in
general, when a state is not too far from the ideal state,
the nearer it approaches that state the better. [EP 2: 118-
119, On Science and Natural Classes].
It is better to have something to satisfy the desire than nothing,
we could say, Besides, one solution can be good from one point of view,
and bad from another: “A brighter lamp than that I use would, perhaps,
possess hecceity; and since she has to act, and action only relates to this and that, she has to be perpetually making random selections, that is, taking whatever comes handiest.”
357
be more agreeable to my eyes; but it would be less so to my pocket, to
my lungs, and to my sense of heat.” [id.]
The conclusion of all these arguments is important. Be the natural
classes as precise as they may be, there will always remain a certain
vaguensess, a certain degree of variability and a certain adjustment of
objects that could be better fit in another classification, which is lacking
at the moment, but it may be found further on. It is impossible then to
draw an exact line of demarcation between natural classes. Even if we
knew the purpose of each object classified, the conclusion would remain
the same, because our desires, as vague and general, are not exactly
correspondent to a specific object, for we do not need this or that object
to satisfy them, but only an object of a certain kind will suffice:
[...] the objects actually will cluster about certain
middling qualities, some being removed this way, some
that way, and [until that] at greater and greater removes
fewer and fewer objects will be so determined. Thus,
clustering distributions will characterize purposive
classes. [EP 2: 119].
When we specify more and more, this does not mean we have
reached the last and ultimate degree of particularization, because more
straight classes would still be possible; that means we can only know
how broad were our previous classes, but not how fine are our actual
ones.
One important conclusion for a classification of the sciences is
that, as we will see in detail, sciences are in constant relation with their
358
areas of acting and they mingle with one another. In this sense, a broad
line of research for one science may as well be a more specific field to
another. A very precise and clear line of separation could not be traced
between them, even if we knew a priori the ends – the final causes – of
their objects, for a further specification could still happen; but, as we do
not know a priori the final causes in every case, we have to deal with
vagueness and some sort of logical inaccuracy [id.].
The most important is yet to be said. In trying to say what a
natural classification of the sciences is to be, Peirce has in view the fact
that, in defining a science as an activity performed by living persons,
united to accomplish a common purpose, he was aware that he could
not force any abstract definition above the sciences, because that would
mean to impose a classificatory model in the same artificial way that
every other attempt he had criticized. It is important to understand
classes, therefore, as ideas corresponding to some existence; in his own
words, it is important to understand classes as ideas of final causation
related to the efficient causation, that is, the idea of a process directed
to an end, allied to a process of actualization of means to reach that
end.
Peirce still gives the following description of the process of
efficient causation:
Efficient causation […]is a compulsion determined by the
particular condition of things, and is a compulsion acting
to make that situation begin to change in a perfectly
359
determinate way; and what the general character of the
result may be in no way concerns the efficient causation.
[EP 2: 120, On Science and Natural Classes].
The difference between final and efficient causation is cleared up:
the latter is a process not directed to a special end, but it is driven by
mere blind compulsion.
The example given is that of a shooter aiming at a bird flying in
the sky. To hit the aim, the shooter does not aim at the bird itself, but a
little ahead, figuring out the velocity, the rout of the bird’s flight, the
time the bullet is to take to hit the moving aim. Thus, the shot has as
finality to hit the bird. However, the moment the bullet leaves the rifle,
the efficient causation commences, that is, the force of the powder
begins to act pushing the bullet in a certain direction. If the bird
changes its route with a loop in the air, the bullet continues in the same
direction as before, without looping to hit the bird. Efficient causation,
therefore, is a mere compulsive power, and has nothing to do with the
result; it only obeys orders blindly [id.].
We said that final causes and purposes are not, according to
Peirce, exactly the same; he himself says it explicitly: “it is a very
common mistake to think that a ‘final cause’ is necessarily a purpose”,
and the reason why one should not think like this is the following:
[…] we must understand by final causation that mode of
bringing facts about according to which a general
description of result is made to come about, quite
irrespective of any compulsion for it to come about in this
360
or that particular way; although the means may be
adapted to the end. The general result may be brought
about at one time in one way, and at another time in
another way. Final causation does not determine in what
particular way it is to be brought about, but only that the
result shall have a certain general character. [ibid.].
Final causation, differently from efficient causation, is relative to
the attainment of an aim: an end or finality. Its result is not specified; as
we said, just a kind of result is indicated, a kind of apple pie, not this or
that special apple pie. Final causation, thus, is of the same form as a
law, that is, it has the power of driving the blind and compulsive
efficient process which produces a particular fact hic et nunc so that
this fact be produced in a certain way, and not in another; it is similar
to a summon, a calling for parts to convene in a convocation; or it is the
aim of the shooter, who directs the shot in a certain sense. As the aim
to be attained is always ideal, the result may vary, depending on the
means used to get it. Now, it is impossible an idea without something to
actualize it, it is impossible to achieve an end without using any means,
it is impossible to think of an aim or purpose to be achieved without a
process to bring it about; that is, “Final causality cannot be imagined
without efficient causality” [EP 2: 121], in Peirce’s words.104
104 HULSWIT (2002), p. 80, says that efficient causation is a dyadic relation, between two individual concrete facts, while final causation is a triadic relation, among the general final cause, the concrete efficient cause and the concrete effect: “The production of the individual effect (B) by the individual efficient cause (A) is determined, or mediated, by the general final cause (C’).” Of course, the result (C) will not be exactly as the ideal result thought of. The same idea is defended by SANTAELLA (1999), pp. 502-503, though in other terms: “Hence, the key to final causality is in the concepts related to Thirdness: continuity, law, mind, law of mind, and habit. However, as Peirce’s categories are omnipresent and interrelated […], considering final causality as Thirdness in isolation from Secondness or efficient causality would be as
361
What that may mean we will be able to see after analyzing both
concepts of causation more in detail:
Efficient causation is that kind of causation whereby the
parts compose the whole; final causation is that kind of
causation whereby the whole calls out its parts. Final
causation without efficient causation is helpless; mere
calling for parts is what a Hotspur, or any man, may do;
but they will not come without efficient causation.
Efficient causation without final causation, however, is
worse than helpless, by far; it is mere chaos; and chaos is
not even so much as chaos, without final causation; it is
blank nothing. [EP 2: 124, On Science and Natural
Classes].
Remember that a natural class is a class of objects grouped
according to a common character they have; for that, they make up a
determined set. To cause a factual process, by the passage above, is to
compose a set of conjoined elements according to a common character.
Efficient causation, thus, is nothing but an aggregation of objects
according to a common character: they can, however, be grouped
otherwise, for the fact they have something in common is not enough to
make a whole out of them, it means only that they may make up a set.
Final causation, in turn, is the calling up of those common characters as
defining characters of the parts of a whole, ordered exactly in function
of this common. A natural class, therefore, would be that through which
we could see how the final causation operates together with efficient
causation – the class exhibits the idea that ordains the set of classified
serious a mistake as it would be to isolate both from Firstness, the category of chance and feeling.”
362
things; that is, the criterion used for classifying must be one such as to
show how the process of coming-to-be of the objects was brought about.
It is only possible to say the reason why things happened as they did
after all the process of efficient causation has passed; only in this way it
is possible to show how things came to inherit the nature they
inherited. A natural classification, then, would have to present the
genealogical structure of what is to be classified – wherefrom it came,
whereto it may develop in the next future, and, most important, in
regard to this development, the reason why it developed in this way,
and not in that way.
This is possible because objects of a class, as Peirce says, derive
their existence from an idea that the class exhibits. This derivation has
a precise meaning: “What I mean by the idea’s conferring existence
upon the individual members of the class is that it confers upon them
the power of working out results in this world, that it confers upon
them, that is to say, organic existence, or, in one word, life.” [EP 2: 124,
On Science and Natural Classes]. When we look at a natural class, in
this sense, we should understand why it is a way to classify those
things, for we would understand, thus, which is the living principle
common to all the individuals of that class. The idea shown in the
natural classification, then, would be an idea of the final cause that
gives coherence to the set, in its turn understood in terms of how its
363
parts became its parts, in a process described as the causal
actualization of this outcome.
Let us recover the reasoning. On the one hand, in the case of non
human productions, we will be able to affirm only the final cause of a
process after we understand its genetic process, for only then we will
have comprehended how things came to be. In the case of human
productions, on the other hand, it is not quite so: we know which is the
final cause, but in the same way there remains to know how it was
attained, that is, we have to explain why we have to do with this final
cause, and not with any other final cause: to know how things happened
and which were the initial reasons of their happening in the way they
did – this knowledge helps us to better understand our own purposes.
A natural classification of the sciences, therefore, should provide
a description of how sciences are created and why they are created in a
certain way, and not in others. The important point would be to give
one interpretation of the process of creation of sciences, the process of
generating guiding scientific principles. This is explained, in a very
characteristic Peircean way, from the the very etymology of the word
“nature”, in a passage which deserves to be transcribed in its full:
Every class has its definition, which is an idea; but it is
not every class where the existence, that is, the
occurrence in the universe of its members is due to the
active causality of the defining idea of the class. That
circumstance makes the epithet natural particularly
appropriate to the class. The word natura evidently must
364
originally have meant birth; although even in the oldest
Latin it very seldom bears that meaning. There is,
however, a certain sub-conscious memory of that
meaning in many phrases; just as with words from
[phýsis], there is the idea of springing forth, or a more
vegetable-like production, without so much reference to
a progenitor. Things, it may be, [phýetai]
spontaneously; but nature is an inheritance. [EP 2: 121,
On Science and Natural Classes].
As he says in the beginning, it is not that each particular
individual should have its existence directly caused by the defining idea
of the class, but that a natural class, if it is to be a genuine natural
class, will express the general idea of the process of becoming of its
members. In the essay where he displays such ideas, Peirce first
explains that processes like those of final and efficient causation
operate in nature conjointly, to contrast them with process we humans
ourselves create. The most important difference between natural
evolution and human production is that a final cause does not
necessarily need to be a purpose, but can be a tendency, as we said
above [EP 2: 122; 464]. Now, it is important to remember also that in
regard to living processes, which can change at any moment, once the
efficient cause is yet operating, it is impossible to state that the
classification is absolutely definite, since the efficient cause, as an
external compulsive factor, can change the original tendency of a
process. A natural class, therefore, must express the idea or ideas,
which are present in the genesis of the objects it classifies conjointly
365
with the idea (or ideas) that influence the process of development of
what is classified. This is exactly the scope of the Peircean classification
of the sciences: to display how sciences are Born one from another, how
it is that they spontaneously spring forth in the investigative practice,
and how they go modifying themselves in their interaction among
themselves and with what they investigate.
Now, how it is in the text, things may be brought about
spontaneously, but they inherit their nature. As with the sciences, the
inherited nature, the characteristic mark of each of them, is an idea,
generated by the distinctive idea of another science: “In considering the
classification of sciences, however, we have no need of penetrating the
mysteries of biological development; for the generation here is of ideas
by ideas.” [EP 2: 122, On Science and Natural Classes]. There is no
other possibility, because in fact “sciences are, in part, produced one
from the others” [EP 2: 126, On Science and Natural Classes]. This is
an extremely important problem:
All natural classification is then essentially, we may
almost say, an attempt to find out the true genesis of the
objects classified. But by genesis must be understood,
not the efficient action which produces the whole by
producing the parts, but the final action which produces
the parts because they are needed to make the whole.
Genesis is production from ideas. [EP 2: 127, On Science
and Natural Classes].
If a science is produced from others, how to distinguish them?
The mixing of one science up with another is no reason to abandon the
366
attempt of a natural classification, because the question on the
precision of boundaries is not at stake. It is possible very successfully to
draw the lines between a class and the other quoting examples:
The descriptive definition of a natural class, according to
what I have been saying, is not the essence of it. It is only
an enumeration of tests by which the class may be
recognized in any one of its members. A description of a
natural class must be founded upon samples of it or
typical examples. [id.].
The emphasis in the generation of an idea by another is more
important for the classification of the sciences in so far as we may want
a natural classification. In describing how one science springs forth
from the ideas of another, we can also see which ideas and principles
inspirit it; in other words, we can see better to which purposes it comes
to answer, why it was produced. The genealogical feature of the
classification, therefore, must be the most important and the only one
upon which we can ground any attempt to establish a natural
classification of anything:
Now genealogical classification, among those objects of
which the genesis is genealogical, is the classification we
can most certainly rely upon as being natural. No harm
will be done if, in those cases, we define the natural
classification as the genealogical classification; or, at
least, that we make the genealogical character one of the
essential characters of a natural classification. It can not
be more; because if we had before us, ranged in
ancestral order, all the intermediate forms through which
the human stock has passed in developing from non-man
367
into man, it is plain that other considerations would be
necessary in determining (if it admitted of determination)
at what point in the series the forms begin to merit the
name of human. [EP 2: 126].
This is how it should be with any intended natural classification:
every natural classification has to be a genealogical classification. The
main task, therefore, of a classification of the sciences, in so far as it is
a natural classification of human products, is in showing how sciences
are brought about – that is, from which ideas they spring forth – and
why they are brought about – that is, to which general desires they give
an answer. In other words, so we do not overlook the motive why we
want the sciences, it is necessary to seek for the origins of sciences.
And, in fact, according to Peirce, science is itself a search for origins:
I remember the days when a pronouncement all the rage
was that no science must borrow the methods of another;
the geologist must not use a microscope, nor the
astronomer a spectroscope. Optics must not meddle with
electricity, nor logic with algebra. But twenty years later,
if you aspired to pass for a commanding intellect, you
would have to pull a long face and declare that “It is not
the business of science to search for origins.” This maxim
was a masterpiece, since no timid soul, in dread of being
thought naive, would dare inquire what “origins” were,
albeit the secret confessor within his breast compelled
the awful self-acknowledgment of his having no idea into
what else than ‘origins’ of phenomena (in some sense of
that indefinite word) man can inquire. [EP 2: 437, A
Neglected Argument for the Reality of God].
368
In peircean terms, a natural classification would describe
processes of efficient causation, displaying the genesis of each science –
that is, describing which final causes operate in sciences. And the
description of the final causes of a science is a means to understand the
problems it tries to solve:
It may be difficult to understand how this is true in the
biological world, though there is proof enough that it is
so. But in regard to science it is a proposition easily
enough intelligible. A science is defined by its problem;
and its problem is clearly formulated on the basis of
abstracter science. This is all I intended to say here
concerning classification, in general. [EP 2: 127].
The genealogy of the sciences, in the end, by showing from which
ideas sciences are generated, would show how they became what they
are in trying to answer specific problems; to solve certain problems is
the end of every science, that is, every science is created to solve
certain problems. Now, in the exercise of an inquiry, there are
problems that arise for which we do not have answers within the
standards wherein we are. Then, it is needed to establish new
parameters and to begin a new inquiry, having as its background the
general ideal of the previous inquiry; the new problem, however, sets
new aims to be attained, and this defines its specificity. The importance
of certain problems defines the specificity of a science, for it indicates
whereto apply, in practice, the precepts it brings with itself. In general
terms, to ascertain the purposes of the sciences is to understand which
369
problems it tries to solve. Once this is understood, we are capable of
understanding the general idea that caused the occasion for the arising
of that precise investigation, seeing, then, where that problem, and,
therefore, where that science came from:
So then, a natural class being a family whose members
are the sole offspring and vehicles of one idea, from
which they derive their peculiar faculty, to classify by
abstract definitions is simply a sure means of avoiding a
natural classification. […]After all, boundary lines in
some cases can only be artificial, although the classes are
natural […]. [EP 2: 125, On Science and Natural Classes].
A last remark before we pass to the other stage. The definition of
a science is possible by means of the definition of its problem. We have
seen that this problem is linked to the general purpose for which a
science is wanted, and such purpose is born from the practice of
another science; we have also seen that purposes are of a general
nature, like general desires, which never completely specify the objects
that may satisfy them, but only the kind of such objects. This
affirmation is a refusal of the idea that sciences are defined by their
objects of study. In truth, it is exactly the opposite: the generality of
purposes of a science allows understanding how a certain object can be
studied by it. The object, so, does not define the investigation, rather it
is the investigation that defines how the objects can be studied, for the
objects may exhibit peculiar characters of more than one class.
Therefore, there is no essence in the objects that determines our way to
370
approach them. If we do not get to interpret an object with certain
means of study and inquiry, this is not a problem of the object, but of
our means, that can be changed. So, the classification of the sciences is
a classification of the ways to interpret objects; this idea is from the
very beginning present in Peirce’s thought. Remember a passage we
have already quoted:
Most of the classifications of the sciences which have
been proposed rest upon a classification of the things
which they treat. This method is objectionable for two
reasons: first that many sciences treat of everything, as
the science of mechanics, that of geometry, that of
chemistry, and so forth; second because the classification
of things needs to rest upon a classification of sciences.
The first great division of things is according to their
functions and hence it is that the homologies or
likenesses which pervade a whole kingdom of nature as
mouths, stomachs, and locomotive apparatus among
animals are functional homologies. Now the function of a
thing in itself considered cannot be determined;
whatever it does or is it is its function to do or be. Hence
any division of the functions of things is only a division of
different sciences which ask different questions about
things, and thus the classification of things rests finally
on the classification of sciences. [W 1: 486-487, Lowell
Lecture IX, 1866].
This is the reason why Peirce states that the objects form groups
according to their classes and purposes: the same objects may be
studied by different sciences, from different perspectives, without this
being an epistemological problem of defining limits between one
371
science and another. There is no need to settle precise limits for each
science, defined regions for acting, for the actual present problems had
their origin in other problems, what makes the will to demarcate
precise boundaries an idealist illusion; as H. Pape says, what counts as
an object pertaining to a class or another never can be decided upon
purely theoretical grounds.105 Thus, for Peirce, the only natural
classification of the sciences, as we said, is the one that takes into
account science as a living thing, in straight connexion with practice:
“What is a science as a natural object? It is the actual living occupation
of an actual group of living men. It is in that sense only that I presume
to attempt any classification of the sciences.” [MS 1334: 13].
8.1. THE MOST NATURAL SCHEME POSSIBLE
We can now see how the general classificatory scheme sketched
by Peirce for the sciences is organized. The scheme was adopted and
adapted from Louis Agassiz, with whom Peirce studied fossils
classification in his youth [EP 2: 118]106. The organization is according
to the generality of the divisions, in the following way:
105 PAPE (1993), p. 584. Cf. PARKER (1998), p. 35: “Classification, then, does not look for essential features of objects (i.e., characteristics that are necessary and sufficient for a thing’s inclusion in a class) because there is no essence that makes a thing what it is. Rather, it is a combination of a general ‘desire’, vague specifications for satisfying it, and various limitations on the resources available to meet those specifications that make a thing what it is.”106 See BRENT (1998), pp. 60 and 364.
372
Branches are characterized by the plan of structure;
Classes, by the manner in which that plan is executed, as
far as ways and means are concerned; […] Orders, by the
degrees of complication of that structure; […] Families,
by their form, as determined by structure; […] Genera, by
the details of the execution in special parts; Species, by
the relations of individuals to one another and to the
world in which they live, as well as by the proportions of
their parts, their ornamentation, etc. [EP 2: 128, On
Science and Natural Classes].
There is still a last division, “variety” of science, “a study to which
men devote their lives, but not, in the present stage of development of
science, so numerously as to justify exclusive societies and journals for
it” [NEM 4: 16, Carnegie Application]. The variety of a science, thus,
concerns more individual researches, the specialization to which each
inquirer dedicates him or herself.
Such organization in levels comes from the more general to the
more particular, aggregating objects “according to the ideas from
which their existence results” [id.]. furthermore, each level of
generality has its specific character. Sciences are divided in:
Branch: the branches divide the sciences according to their
fundamental purpose. In this way, the most general division is between
theoretical science, the purpose of which is only and exclusively in the
knowledge of “God’s truth”, and the practical sciences, oriented “to the
uses of life” [MS 1334: 22].
373
Sub-branch: sub-branches mark a modification in the general
purpose. Thus, the sub-branches of theoretical sciences are the
sciences of research, or heuretic, and the sciences of review, or
retrospective, or synthetical philosophy.
Class: are marked by the peculiarity of their observations, that is,
by the characteristic marks of their kind of research. Thus, for instance,
mathematics is a classe of the sub-branch of heuristic sciences, which
can be divided in three sub-classes, namely, mathematics of logic,
mathematics of discrete series, and mathematics of continua and
pseudocontinua.
Order: sciences divided according to the difference in
conceptions, or according to the intellectual distinct character of each
of them, even though they are within the range of a same general
research, appertain to distinct orders. Thus, for instance, in the
subclass of the normative sciences, esthetics, ethics, and logic are
different orders that study different ways of understanding the duality
existing in our encounter with brute fact.
Family: it is the division under which scientists who deal with the
same subject-matters aggregate, within the same inquiring range, but
with different skills. For instance, in the same order of general physics,
the studies of dynamics and optics constitute different families, because
they are equally pursued by physicists, but physicists with different
skills.
374
Genus: they are the divisions in which it is possible to have
disinformation on the part of the inquirers regarding specific details; as
for instance, in the family of physic-chemistry, the study of particles
(neutrons, protons, and electrons) is related to, but different from the
study of anti-particles (antineutrons, antiprotons, and positrons).
Species: within the same genus of inquiry, a species would be the
division formed by the groups and societies more specific, so that every
student may be able to pass from one species to the other. One
illustration, in the genus of the study of the particles of the matter, the
study of leptons and the study of bosons constitute different species.
Variety: finally, the minutest study, the most specialized division
of science. Maybe we could say that, inside the study of leptons, to keep
the example, we have the varieties that study the electrons, the
neutrinos, the quarks etc., within the species of the study of bosons, the
varieties dedicated to the photons, gravitons, etc. 107.
The classification of the sciences is to be arranged in such a way
that the most abstract and general sciences appear genealogically
before the more specific, ones, since the more general ones provide
principles and the more specific are source of data, examples and
information to the antecedent. This is stated in the following passage:
107 The sources consulted for the presentation of the divisions are: NEM 4: 16-17, 1902; EP 2: 258-262, 1903; and mainly CP 1. 238-272, 1902, wherein the reader will find several examples of Peirce himself. However, he does not come deep to the level of specialization of genus, species and varieties to indicate all the sciences in these levels of specificity.
375
The different sciences help one another, and that in
multiform ways. No rules can be laid down as to where a
science shall seek help; far less as to where it shall not.
Yet in a general way the sciences are related like the
rungs of a ladder. That is to say, some sciences are
broader than others, look over a wider range of facts, but
look less into details. The general rule is that the broader
science furnishes the narrower science with principles by
which to interpret its observations while the narrower
science furnishes the broader science with instances and
suggestions. [NEM 4: 227, Of the Place among the
Sciences of Philosophy and of each Branch of It, c.1904-
1905].
The relation is not revertible, that is, a more abstract science
cannot derive its principles from a less abstract. The organization, then,
must begin from the science that provides more principles, i.e., the
most basic, because from it all the other sciences will draw principles,
to it all the other sciences will run when facing a problem they do not
know how to solve. It is important to stress that a science can only
furnish principles or data to the other; two sciences cannot help one
another mutually in the same way; there may be information exchange,
methodological loans, but two sciences cannot simultaneously provide
principles to one another, for the reason why “no two things can
depend upon each other in the same way.” [MS 693A: 27, Reason’s
Conscience]. In effect, it is the desire to learn that leads the scientist to
become interested in a greater range of objects, so that the movement
always tends to a bigger generalization:
376
Science arises from a genuine and heart-felt, and not
from a fictitious, interest in the objects studied; and
consequently, its birth comes in the study of some single
object. […] So a man, from watching a few stars, will at
length proceed to draw up a catalogue of all the stars he
can see with his naked eye. Next, he procures a
telescope, and he or his successor makes a larger
catalogue, and then some imitator of him with a still
better telescope is able to make a still larger catalogue.
At last, the telescope comes to show so many millions of
stars that from studying individual stars, the astronomers
pass to considering classes of stars, of clusters, and of
nebulae. In this way, every study of individual objects,
which includes to all intents and purposes, a study of all
objects of precisely the same nature, tends to pass into a
study of classes each composed of differing objects.
Meantime, students are becoming interested in parts of
the objects which have similar functions. The
ornithologist becomes interested in wings; and does not
limit this interest to bird’s wings, but extends it to bats’
wings, to the fin’s of flying fish, and to the still more
different wings of insects. Another man will become
interested in the formation of valleys; still another in the
formation of laws. In this way, the study of kinds of
structure, or the comparison anatomy of all sorts of
classes, tends to pass into an interest in the different
ways in which uses are subserved, or kinds of functions
carried on; that is to say, in comparative physiology. [MS
693A: 27-29].
Not every scientist begins to study in this way, in the same way
that not every science arises as Peirce there describes, from the study
of more particular things, to be later on transformed into a study of
377
classes. It is important to notice how he describes the process of
generalization, though, in a way that each science becomes more
general because it tends to embrace more and more objects under its
wings [MS 693A: 32]. These objects are not collected at random, as if
there was no better reason but the scientist’s curiosity; as a matter of
fact, the scientist’s curiosity is guided by the interest in generalizing,
and each object is incorporated as an object of study because it makes
it possible to achieve a higher degree of generalization. In fact, the only
interest a science can have in facts of another science is with a view to
generalization:
When one science furnishes another with a fact, what
causes the latter science to be interested in that fact?
Evidently because it hopes and expects to be able to
utilize that fact as one of the foundation stones of a
generalization. Then the science for which this fact is a
result is plainly a more special kind of science than the
science for which the same fact is a mere datum, or
premises. [MS 693B: 96, Reason’s Conscience].
This idea agrees with what was said before about the creation of
habits of expectation and about the functioning of perception: as no
percept is perceived in isolation, we have the formation of perceptual
judgments viewing generalization, i.e., viewing to say what would be
perceived in analogous circumstances to the ones of the present, so
that it is possible to predict, even though very roughly, the general form
of future experience. In the same way, all knowledge can be understood
378
in the same key, since its proper cognitive value is due to observations
made of present facts with the purpose to anticipate future facts:
Nothing, however, can be called knowledge which might
not be applied to anticipating the characters of future
experiences. Such anticipations must be founded on
general rules, and these can only be the fruit of
generalizations. Consequently, if science is to advance at
all, it must do so by passing from the study of the
characters [to that of] classes of things. [MS 693B: 106-
107].
A good classification, then, would be more than a mere icon of
relations; rather, it would be a diagram through which we could see the
inter-relations of dependence between the sciences, and consequently
which is the most general and which the most concrete, or more
specific in its domain of inquiry. Furthermore, for the fact that the
classification is described as a ladder in which each rung is also a
smaller ladder with its own rungs, each of them also of the same
nature, the possibility of smaller and more specific subdivisions is
extended ad infinitum, in the same way as the ladder leads to the sky,
as in the beautiful metaphor given in Robert Musil’s passage in the
epigraph. As a matter of fact, Peirce says:
A good classification is a diagram usefully expressive of
significant interrelations of the objects classified. The
best classification of sciences is a ladder-like scheme
where each rung itself is a ladder of rungs; so that the
whole is more like a succession of waves each of which
carries other waves, and so on, until we should come to
379
single investigations. [NEM 4: 227/228, Of the Place
Among the Sciences of Philosophy...].
Thus, the organization according to the scheme of logical
dependence has a precise reason why, which is, every knowledge
begins with the knowledge of an undefined class of objects, vaguely
understood, and tends to generalize to a knowledge of a general class;
and from these classes, to the sub-branches, and from the sub-
branches, to the branches of sciences, in a tendency to generalization
each time broader. In this process, every science has the three rungs of
theoretical science, retrospective science and practical science
conjointly [NEM 4: 228]. A possible arrangement of the scheme could
be displayed in the following way108:
A. Branch: Theoretical Science
A.1. Sub-branch: Science of Discovery, heuretic or heurospude.A.1.1. Class: Mathematics
A.1.1.i. Subclass: mathematics of logicA.1.1.ii. Subclass: mathematics of discrete series A.1.1.iii. Subclass: mathematics of continua and
pseudocontinua.A.1.2. Class: Philosophy, or cenoscopy
A.1.2.i. Subclass: Categorics, phenomenology or phaneroscopy
A.1.2.ii. Subclass: Normative sciencesA.1.2.ii.a. Order: AestheticsA.1.2.ii.b. Order: EthicsA.1.2.ii.c. Order: Logic
A.1.2.iii. Subclass: MetaphysicsA.1.2.iii.a. Order: General metaphysics, or
ontologyA.1.2.iii.b. Order: Psychic or religious metaphysicsA.1.2.iii.c. Order: Physical metaphysics
A.1.3. Class: Special science, or idioscopyA.1.3.i. Subclass: Physical sciences
108 Cf. NEM 4: 17, for a different position of practical science. In this regard, we follow here the classification presented in EP 2: 258, 1903; MS 1334: 20 ff., 1905; MS 655: 18, 1910.
380
A.1.3.i.a. Order: NomologicalA.1.3.i.b. Order: ClassificatoryA.1.3.i.c. Order: Descriptive
A.1.3.ii. Subclass: Psychic SciencesA.1.3.ii.a. Order: NomologicalA.1.3.ii.b. Order: Classificatory
A.1.3.ii.c. Order: Descriptive
B. Branch: Science of review, retrospective science or taxospude
C. Branch: Practical science, the arts or prattospude
With this, we can see that Peirce tries a kind of classification
wherein the genealogy of the sciences can be pictured with some
clarity. The sciences of discovery, placed above all the others, furnish
the more general problems, of which all the more specific arise. The
reason why is that they are directed to the discovery of truth only for
truth’s sake, in the name of nothing else. The restrospective sciences
concern in their turn the classification of such knowledge, its
sytematizing, arranged in a digest to make it useful, i.e., to make it the
matter for the practical sciences, to apply it to the uses of life. But, as
Peirce states that every science also contains the three branches, this
actually means that all inquiry joins three distinct ways of making
science in one inquiry, insofar that it is impossible to separate theory
and practice; in other words, it is impossible to separate the intention
to discover from the intention to apply, because the relation between
the sciences is defined by means of the final purpose to which they are
directed – to know for what?
This idea becomes clearer when we look at the specificities of the
different branches of the sciences, to wit, heuretic science, sciences of
381
review, and practical science. Let us see in detail how they are one
from another distinguished.
1. Science, whose main aim is to discover truth for truth’s own
sake, is called “science of Discovery” or, what is the same, “heuretic
science”; this is for Peirce the most primordial signification of science,
because it concerns only and exclusively with the discovery of truth,
and with nothing else [HO II: 825, Reason’s Conscience; EP 2: 372, The
Basis of Pragmaticism in the Normative Sciences]. Such conception
belongs to the first and more general branch of the classification and
will be remembered further on.
2. The second branch is that of the sciences of review, or
retrospective sciences, which seek to form a systematized digest of the
whole or of part of human knowledge, using whatever science of
discovery has brought to light and filling up its gaps according to their
own purposes, by means of proper investigations. This is science is
Coleridge’s sense, and embraces all the way from Comte’s Cours de la
Philosophie Positive, Spencer’s Synthetic Philosophy, passing by von
Humboldt’s Kosmos, and all the dictionaries and digests, up to scholarly
books and popular presentations, according to Peirce [EP 2: 372; MS
655: 19]. We see here that Peirce does not exclude from the
classification the Aristotelian-romantic conception we saw in the
beginning. The systematization of knowledge is necessary, and has its
well defined place in the domain of scientific inquiry.
382
3. The third branch of the classification is the branch of practical
sciences, concerned mainly with the circumstantiated utility of the truth
sought, and not with its “august nature” [EP 2: 372]. In Peirce’s words,
practical science is “the theory of the arts, [it] is that science which is
selected, arranged, and further investigated in details as a guide to the
practice of an art.” [NEM 4: 191]. Here, it is interesting to make a little
exercise of etymology. In this particular context, Peirce uses the word
“art” differently from its use nowadays, approaching the early
etymological sense of it. The word comes from the Latin ars, used to
translate the Greek “” [techné], from which come the words (and
some of the sense too) “technique” and “technology”, for instance. The
meaning of the term is better understood if we get back to Aristotle:
All art [] is concerned with coming into being, i.e.
with contriving and considering how something may
come into being which is capable of either being or not
being, and whose origin is in the maker and not in the
thing made; for art is concerned neither with things that
are, or come into being, by necessity, nor with things that
do so in accordance with nature (since these have their
origin in themselves). Making and acting being different,
art must be a matter of making, not of acting.109.
Such conception of téchné, as it is clear, concerns the production
of some object whose existence is contingent. It is not necessary that
this object exists, and the choice between it existing or not is due to
whom is going to make it. Techné, therefore, has to do with the
109 Nichomachean Ethics, VI, 1149a 4.
383
capacity to create an artificial object, as the shoe-maker makes a shoe
that does not need to be necessarily of that very form. As H. Murachco
says:
is, before everything, practical possession of the
necessary processes to execute this or that deed; it is the
practical ability, handicraft or potential ability that is
named talent. From this meaning others derive, by
metaphor or methonymy: knowledge of the means,
articulation of such means, expedient, ability, cunning,
tricks, and even office and business. But it is not wit; it is
an aprenticeship […]110.
The objects made through some art are, hence, the outcome of a
determinate ability of some artisan, who deliberately endeavours to
accomplish a specific type of production. Thus, we see that, for such
reason, it is an activity with an interest in a particular end, which is the
production of a specific object, and a fortiori contingent objects,
through a just the same specific practice.
Cicero, for example, still reports such use of the word, joining
besides the idea of creation, in his De Natura Deorum: “Zeno thinks
proper to each art to create and to bring about” 111. And it is in this
110 MURACHCO (1998), p. 13. Our translation; see the original: “é, antes de tudo, a posse prática de processos necessários para executar este ou aquele ato; é a habilidade prática, manual ou a habilidade potencial que chamam de talento. Deste significado derivam outros por metáfora ou metonímia: conhecimento dos meios, articulação desses meios, expedientes, habilidade, artifícios, artimanhas e até ofício e atividade. Mas não é o engenho; é um aprendizado [...].”111 “Zeno [...] censet enim artis maxume proprium esse creare et gignere”, De Natura Deorum, book 2, section 22, paragraph 57. Available on line at URL: [http://www.thelatinlibrary.com/cicero/nd2.shtml#57]. Acessed on 10 April 2005; see too Academica priora 2, 7, 22; De Officiis 2, 3, 12 seq. Cf. still Charlton T. Lewis and Charles Short, A Latin Dictionary: “ars, artis, f. [v. arma] , skill in joining something, combining, working it, etc., with the advancement of Roman culture, carried entirely beyond the sphere of the common pursuits of life, into that of artistic and scientific action, just as, on the other hand, in mental cultivation, skill is applied to morals, designating character, manner of thinking, so far as it is made known by external
384
sense that Peirce also uses the word “art”, specifying, however, that an
art produces things with a view to a practical necessity. A sign of this is
that, for instance, in distinguishing the three kinds of scientific inquiry
listed above, the notion of art is straightly connected to the idea of
utility, while the notion of heuretic science, in its turn, as the name
itself says, is related to the idea of discovery, and not to the one of
production, without immediate relation to what is to be done with what
is discovered. This relation to a determined end to be produced is
clearly expressed by Peirce in the following passage:
When a general purpose is quite fixed and settled, as, for
example, that dwellings must be made warm in winter, a
skill is gradually developed in accomplishing that
purpose. If the operations required to accomplish the
purpose are complex, and if the purpose itself is
complicated with secondary considerations that vary
considerably on different occasions, it becomes desirable
that the skill in accomplishing it, which already involves
a good deal of special information, and as such is called
an art, should be guided by a general theory of the
relation of means to the purpose in question. This theory
of an art is a practical science. [HP II: 831, Reason’s
Conscience].
An art is an ability to effectuate something, accompanied by the
special information needed to such effectuation, i.e., by the technical
knowledge needed to the accomplishment of the task. The bridge
actions (syn.: doctrina, sollertia, calliditas, prudentia, virtus, industria, ratio, via, dolus). I. Skill in producing any material form, handicraft, trade, occupation, employment ()”. Acessed on 05 May 2004, at URL: [http://www.perseus.tufts.edu/]. In fact, such notion of or ars still echoes in our idea of artisanship.
385
between practical sciences and the ancient conception of techné or ars,
therefore, is just the idea of how to perform the application of such
special knowledge to attain a pre-designed end. Practical sciences
determine the directioning of a specific activity, in a practical defined
context, toward the accomplishment of a specific aim. By itself a
technique is unable to perform the connection between means and
ends. As Ibri says, “the technique that provides the success of a
practice has not in itself, so to say, heuristic power to new pathways”112.
This heuristic power, in the peircean classificatory scheme, as we have
seen, is majorly confined to the domain of the sciences of discovery,
what would distance him from the use reported by Cicero. 113
Nevertheless, within the range of arts as techniques, it is more
important to know which are the more adequate ways to attain an aim
previously ascertained, and this is settled by practical sciences.
It may seem so that practical sciences do not concern discoveries
at all, contrary to what we said before. It is not so. Remember that, as a
matter of fact, the supreme aim of any and every science is to inquiry
and investigate to discover. The difference is in the modality of such
discoveries; it is in the end ascertained to the inquiry:
It is true that all scientific men are engaged upon nothing
else than the endeavor to discover. This is true of the
taxospudists and the prattospudists as much as of the
heurospudists. But the difference is that the
112 IBRI (1998), p. 154113 Notice Peirce does not use “technology” in this context.
386
prattospudists endeavor to discover for the ultimate
purpose of doing, and the taxopudists endeavor to
discover for the purpose of applying knowledge in any
way, be it in action or more especially in cognition. [MS
1334: 21-22].
Hence it is also an aim of practical sciences to investigate truth,
with a view to accomplish something by means of applying the
knowledge in specific circumstances. That is why practical sciences are
considered as the theory of an art, for they try to discover the best
procedure to actualize a specific purpose, bridging between means and
ends, what the art-techniques cannot do by themselves. And, as it also
seems clear to us, it is one of the aims of theoretical sciences to
discover with a view to what is to be done with knowledge, even though
not for any immediate practical applicability. One of the aims, not the
highest, nor the greatest, nor the ultimate; in fact, theoretical sciences
envisage knowledge as an end in itself, and not as a means to other
accomplishments.114
In general lines, these are the differences between each specific
kind of science. There is to notice once more that they are not dry
114 If we believe in what Nietzsche says, this is a historic novelty of great importance. In The Gay Science, book III, § 123, he states: “‘Die Wissenschaft ist Etwas von zweitem Range, nichts Letztes, Unbedingtes, kein Gegenstand der Passion’, – dieß Urtheil blieb in der Seele Leo's zurück: das eigentlich christliche Urtheil über die Wissenschaft! Im Alterthum war ihre Würde und Anerkennung dadurch verringert, dass selbst unter ihren eifrigsten Jüngern das Streben nach der Tugend voranstand, und dass man der Erkenntniss schon ihr höchstes Lob gegeben zu haben glaubte, wenn man sie als das beste Mittel der Tugend feierte. Es ist etwas Neues in der Geschichte, dass die Erkenntniss mehr sein will, als ein Mittel.” If Nietzsche evaluates such novelty positively or negatively, this is a theme we will not develop here. However, we can briefly mention that, in dealing with what is called will to truth, the German philosopher asks exactly for the assumptions and aims of scientific knowledge, in an analogous reflection to Peirce’s: truth for what? To whom?
387
separations. Each type of investigation and inquiry has its determined
objectives, but that does not mean that the range of heuretic sciences is
completely separate from the range of the sciences of review, or from
the practical sciences. Thus, not forgetting the inter-relations, we have
the differences in purposes clear between sciences concerned with
discovering truth, sciences concerned with the organization and
systems of knowledge, and sciences concerned with practical
application of what we know, even though all inquiry often combines
the three purposes when carried on.
Through Peirce’s scheme, we see that the sciences would
gradually tend more and more to a higher degree of generalization and
abstraction, for if the more general and abstract sciences are on the
top, in the condition of sources of principles, once the more specified
problems of the more concrete sciences are resolved, there would
remain the more general ones to busy us. The general orientation of
scientific inquiry, then, converges toward a supreme aim, which Peirce
describes as the discovery of the truth of God: “I recognize two
branches of science: Theoretical, whose purpose is simply and solely
knowledge of God's truth; and Practical, for the uses of life.” [CP 1.239,
1902]. As a matter of fact, even when inquiry is of the highest branch,
some practical accomplishment is always envisaged:
The widest division among the sciences is into the work
of Discovery, the work of Systematizing knowledge, and
the work of planning how to apply knowledge to the
388
attainment of a special purpose, - or the science of
discovery, the science of review, and practical science.
Almost every discoverer has made some pretty extensive
studies of the science of review, though it is a common
vanity to pretend to be a stranger to it; and the majority
of scientific men do some work in the way of practical
science. [MS 693B: 80].
Practical sciences are linked precisely to the investigation into the
best way to use the already discovered and systematized knowledge to
solve specific problems. And the sciences of review also envisage to
discover ways of applying knowledge. Thus, theoretical sciences
envisage discovery, pure and simply discovery; the sciences of review
would be those that would investigate the conditions of possibility of
actualization of theory in practice, for they are busied with what is to be
done with our knowledge; they thus bridge between the discovery of
something new and its actual utility. As Peirce himself says, little can be
done with knowledge not yet systematized and organized, in this way
indicating the practical need of organizing our theoretical discoveries.
And practical sciences, in their turn, discover the diverse possible uses
of the obtained knowledge, in straight link with heuristic practice.
There is not, therefore, a hierarchy between the several kinds of
science, once new discoveries can arise from practical applications, and
vice-versa. There is, indeed, a differentiation as to the ultimate aims of
inquiry: to investigate to discover, or to investigate to apply the
knowledge. The application of knowledge must result as a natural
389
outcome of the genuine interest in learning, and not as an a priori
requisite of inquiry.
Finally, some last remarks on the applicability of knowledge. It
would be ingenuity to say that scientists investigate without any
interest in the applicability of their discoveries. In fact, knowledge is
valid only if it can be adapted, in some sense, to the accomplishment of
human interests: “Knowledge is a plastic, applicable stuff – a putty
whose solid part, the barytes or the lead, is the percepts, of which more
and more is worked up in the oil of reflection.” [MS 693B: 113]. Science
is understood as a form of human activity capable of transforming the
environment which we live in according to our interests. Now, it is an
essential constitutive part of such pragmatist conception of science that
there is harmony between the aims of this inquiring activity and the
means available to us to actualize them, to make them concrete. In this
way, the questioning of the objectives with which this activity is
pursued appears under the form of the reflective questioning of the
responsibilities taken up in the inquiry, since all knowledge is an
attempt to anticipate unrealized possibilities:
Indeed, the idea of knowledge is very imperfectly
realized as long as it is confined to existent individuals. A
lifeless mummy is a knowledge that cannot be applied, -
and [it is a] metaphysical mummy at that, a mummy of
straw. But how can there be any practical application to
the past [?] The future is the practical part of life.
Applicable knowledge, the only knowledge deserving the
390
name, is the anticipation of future percepts. Now that
which is in the future only is not among the things that
now exist. Hence in order to realize the idea of
knowledge the man of science must broaden the scope of
his study by adding to the cash collection of existing
things to which he has heretofore limited it, the
corresponding classes of things that are to be. [MS 693B:
115-116].
Our imperfect knowledge of the possibilities of the future is the
only way we have to leave the immediate and limited range of our
concepts and thoughts. This is so because our knowledge depends,
above everything, on the interpretations it receives. Remembering the
distinction between depth and breadth, we can say that to Peirce the
meaning of a concept is related to the way in that the concept is
interpreted: a sign means its object because, within a certain
informative context, it is interpreted as a representation of the object.
In other words, a sign acquires meaning because it informs something
about its object, thus creating with such operation a rule for
interpretation, according to which it can be understood – in one word, it
creates a habit of possible conduct to say how the sign will be able to
be interpreted [MS 693B: 100].
Of course, science in this way understood cannot give answers to
the instabilities of the present. However, the scientific activity carried
on in the long run can lead to the determination of habits of expectation
391
that function as hypothetical imperatives of prudence, to prevent us
from surprises:
Our first imperfect knowledge of what is to come to pass
is virtually based upon a state of execution which, if it
were formulated would appear as an assumption that
nothing very surprising is going to occur. I say it is
virtually based on this state of expectation; for no
conclusion is actually based upon an assumption not
deliberately adopted. Now the state of expectation is not
a proposition at all; far less has it been deliberately
embraced. Uncontrolled, uncriticized, and merely
subconscious actions of the mind form no part of
reasoning and are not subject to logic. It is simply a fact
that so we think, and that a state of mind brings about a
belief which is related to a possible formulation of that
state of mind as a conclusion to the premises. [MS 693B:
116-117].
Science, consequently, we repeat, is based on a whole “cultural”
background we do not put into doubt. The creation of meanings and
habits of expectation seems to be, for Peirce, the only way to leave the
unavoidable domain of common-sense beliefs, and to fly higher flights,
to dream wilder dreams, in his own words. The assertion of the
propositions in the scientific community thus allows for their
interpretation from an external point of view, external to their own
rationale, since the whole group of background assumptions is not
exactly the same for all inquirers, even though there is a common
experience being constructed and shared. However, because of the own
nature of the logic of abduction, allowing for the specification of what
392
the practical results of a given hypothesis may be if it is taken as true, it
is exactly the biggest problem to know how the construction of such
facticity is brought about in the practice of inquiry, and how is it
possible to favour one interpretation instead of another; and even to
decide which theories count as valid interpretations and which do not
count. One of the conclusions to be drawn from Peirce’s theory of
assertion is that every speech act threefold, i.e., someone utters an
assertion and simultaneously makes reference to what is talked about,
for another. Discourse, whatever it is, is therefore at once referential,
intentional, and self-reflective, and the identification of a new meaning
can itself only be constructed collectively, by at least two: a speaker
and a hearer (who can be the same person). Language, therefore, is
understood by Peirce for the first time as communication, that is, as
interaction. The possibility of interpretation is not anymore given by the
capacity of the other to understand the references mentioned by the
speaker, but by the capacity to share the same experience (and, hence,
because of this, to be able to understand references), that is, by the
capacity to interact within certain worldly context.
In fact, the link between pragmatism and ethics is not fortuitous.
The pragmatic maxim is not only a logical maxim to clarify concepts,
but also a moral maxim. This seems clear when Peirce states the
following: “Pragmatic anthropology, according to Kant, is practical
393
ethics. Pragmatic horizon is the adaptation of our general knowledge to
influencing our morals.” [CP 5.1, Pragmatic and Pragmatism, 1902].
The reference to Kant is unequivocal in indicating the ethical
purport of pragmatism, and agrees with the idea presented before, that
the essential nature of knowledge is its capacity to mould to the ends to
which we want it. As a matter of fact, in refusing William James’
interpretation of the pragmatic maxim, Peirce says:
In 1896 William James published his Will to Believe, and
later his Philosophical Conceptions and Practical Results,
which pushed this method to such extremes as must tend
to give us pause. The doctrine appears to assume that the
end of man is action – a stoical axiom which, to the
present writer at the age of sixty, does not recommend
itself so forcibly as it did at thirty. If it be admitted, on
the contrary, that action wants an end, and that that end
must be something of a general description, then the
spirit of the maxim itself, which is that we must look to
the upshot of our concepts in order rightly to apprehend
them, would direct us towards something different from
practical facts, namely, to general ideas, as the true
interpreters of our thought. [CP 5.3, Pragmatic and
Pragmatism].
Now, this is exactly the key idea of the classification of the
sciences: to direct knowledge to the accomplishment of ends, which are
of the nature of general ideas. And the description of the process of
how ideas can influence conduct and even to produce facts is not only
the other side of the question, for future conduct is guided by ideas
themselves. The construction of ideals of conduct, therefore, appears to
394
be the ultimate aim of human actions. All knowledge, in short, is based
in an interest, even if this interest is interested in itself. Science, in
Peirce’s thought, appears as a prospective activity, directed towards
the discovery of the self-development of [phýsis], i.e., to the most
supreme possible aim, for it is entirely directed to the domain of what is
merely possible. Thus, science is also an activity of confrontation, for it
is not content with the existent, and seeks the reality of what is not yet.
This reality, however, only reveals itself in so far as science is
produced. Consequently, action appears as an actualized mode of a kind
of general conduct, that is, as a constant adaptation of human beings to
a reality in continuous evolution, by means of the application of
knowledge to the accomplishment of the general ends that are being
built. New fields of experience go arising, new interactions happen,
new revolutions are prepared, always related to other interests: it is
necessary to begin the inquiry with all the concepts and prejudices we
have. This process of constructing ourselves can only be hinted at here.
We hope that in the conclusion of this work these remarks get clearer.
395
9. MATHEMATICS AS THE MOST GENERAL SCIENCE: FORM OF EXPERIENCE AND CATEGORIES
Se Deus fosse à escola aprenderia somente matemática.Murilo Mendes, Conversa Portátil115
Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
Alfred North Whitehead, Science and the Modern World
Mathematics is, in a certain sense, the mother of all sciences. It is
the first of the heuretic sciences, the one immediately preceding
philosophy, and for such reason we will examine it here. Placed on the
top of the classification of the sciences, it makes up the first class of the
sciences of discovery, the most abstract and general heuretic science,
the one that makes the supremest discoveries. Because it is the most
abstract of the sciences, we can say it is the most basic one, that from
which all the sciences borrow principles, taking its own principles from
no other; it is a self-founding science. Because it is the most general
science, its discoveries concern the discoveries of all other sciences, at
the same time in that they do not concern any special state of things. In
other words, mathematics does not concern the nature of reality.
Hence, it “never can be positive science, that is, science of the real.”
[MS 283: 155], though it is a heuretic science. That does not mean
mathematics cannot be an experimental science, for it is possible to
make experiments by merely observing a geometrical figure.
Mathematics is not concerned with the truth of fact because its
115 “If God went to school He would learn only mathematics.” Our translation.
396
conclusions are purely hypothetical, depending only and exclusively on
the diagrams and formal constructions used in proofs and calculi: “it is
the only one of the sciences which does not concern itself to inquire
what the actual facts are, but studies hypotheses exclusively” [RLT
114], Mathematical truths, therefore, must have a different
epistemological status than the truths discovered by positive sciences.
Notwithstanding, to rescue philosophy from the lawless rovers of the
sea of literature, giving it the sureness of reasoning it has lost, it is
necessary to mirror it in mathematical thought:
Philosophy requires exact thought, and all exact thought
is mathematical thought. [NEM 4: x, Detached Ideas on
Vitally Important Topics, 1898]
[And:] My special business is to bring mathematical
exactitude, - I mean modern mathematical exactitude
into philosophy, - and to apply the ideas of mathematics
in philosophy.
I don’t mean to shackle anybody with any condition other
than that they should work at the rendering of philosophy
mathematically exact and scientifically founded on
positive experience of some kind. [NEM 4: x-xi, letter to
F. Russell, 23 September 1894].
To understand what it means for Peirce to bring mathematical
precision and accuracy of reasoning to philosophy, furnishing this latter
with scientific exactness and groundings, it is necessary to understand
the definition of philosophy and the place it occupies in the
classification of the sciences. It is not a case of quantifying or
mathematizing philosophy, but only to explicit how formal homologies
397
are established between the two sciences. Peirce says philosophy
should be based on some positive experience. The precise meaning of
this is in the requirement that philosophy should be knowledge of real
things, in opposition to the mathematical knowledge, which should be
merely hypothetical. Thus, two senses can be attributed to the word
“philosophy”:
Two meanings of the term ‘philosophy’ call for our
particular notice. The two meanings agree in making
philosophical knowledge positive, that is, in making it a
knowledge of things real, in opposition to mathematical
knowledge, which is a knowledge of the consequences of
arbitrary hypotheses; and they further agree in making
philosophical truth extremely general. [EP 2: 372, The
Basis of Pragmaticism on the Normative Sciences].
The meanings of philosophy are:
a) Philosophy understood as cenoscopy, that is, as a positive
science, for it rests upon the most general familiar
experience, “and does not search out occult or rare
phenomena”; this meaning, according to Peirce, is more
proper to philosophia prima than what is usually called
ontology;
b) Philosophy understood as sythetical philosophy, or
philosophia ultima, that is, a science that seeks to provide
the results obtained by the different special sciences with
a general sense, which results from the organized
398
reunion of such results that no one of the special sciences
can alone provide. [EP 2: 372-373]. 116
To Peirce, these two meanings are neither opposed, nor
complementary; they are just different. In the classification of the
sciences, cenoscopy would come before idioscopy, that is, the special
sciences. The terms “cenoscopy” and “idioscopy”, Peirce says he took
them from Jeremy Bentham [HL 151; EP 2: 373]. The words are, in fact,
adaptations of Greek words, [koinoscopia] and
[idioscopia], respectively. means exactly “look up upon
the common”; , “look up upon the particular”.117 Special sciences
are special just because of this: they offer a fragmented view of reality,
i.e., they concentrate upon phenomena taken individually, or upon
specific groups of phenomena, and do not venture upon remarking
about the nature of the totality of being. This is the very task of
cenoscopy: “The business of cenoscopy is to construct, as best as one
may, a true comprehension of the omne, - and if possible, of the totum, -
of being and of non-being, and of the principal divisions of this omne.”
[EP 2: 374, The Basis of Pragmaticism on the Normative Sciences]. In
other words, the main business of cenoscopy, though not the only one,
is to provide us with an universal conception of the world: “Its principal
116 “For one of them [the meanings of the term philosophy], which is better entitled (except by usage) to being distinguished as philosophia prima than is ontology, embraces all that positive science which rests upon familiar experience and does not search out occult or rare phenomena, while the other, which has been called philosophia ultima, embraces all that truth which is derivable by collating the results of the different special sciences, but which is too broad to be perfectly established by any one of them.”117 Cf. CP 1.241-242, editor’s notes 1 and 2.
399
utility, although by no means its only utility, is to furnish a
Weltanschauung, or conception of the universe, as a basis for the
special sciences.” [HL 151]. To attain this total view of the universe,
cenoscopy should rest upon the total experience of the world, rather
than in some special experience:
Cenoscopy is not to resort to special experience, or only
upon the most exceptional occasions, in order not to
break the discussion of one question. There is no
veritable exception. To say that cenoscopy is not to resort
to special experience is to say it is to be science in the
seminal condition. [EP 2: 374].
Thus, cenoscopy should begin its inquiries scrutinising everything
experience shows us that is universal and pervasive, general and
evident. The method of cenoscopic inquiry, as the very name says, rests
upon the careful observation of all manifestations of usual experience:
“Philosophy is positive science, in the sense of discovering what really
is true; but it limits itself to so much of truth as can be inferred from
common experience.” [EP 2: 259, An Outline Classification of the
Sciences]. In effect, the philosophical inquiry, to Peirce, has a positum
– our common-sense experiences:
Class II [of heuretic sciences] is philosophy, which deals
with positive truth, indeed, yet contents itself with
observations such as come within the range of every
man's normal experience, and for the most part in every
waking hour of his life. Hence Bentham calls this class,
coenoscopic. These observations escape the untrained
eye precisely because they permeate our whole lives, just
400
as a man who never takes off his blue spectacles soon
ceases to see the blue tinge. Evidently, therefore, no
microscope or sensitive film would be of the least use in
this class. The observation is observation in a peculiar,
yet perfectly legitimate, sense. If philosophy glances now
and then at the results of special sciences, it is only as a
sort of condiment to excite its own proper observation.
[CP 1.241]
In the beginning, the biggest difficulty in philosophical inquiry is,
indeed, to cope with the certainties of common-sense, which are
extremely vague and general, such certainties as expressed in
propositions such as “fire burns”118. Such experiences inform our world
view, before any scientific world view. For such reason, it is very
difficult to observe critically common-sense beliefs, for we consider
them natural, when in fact they are beliefs, as falsifiable as any other;
thereby the necessity to have high attention and critique in cenoscopy:
The method of cenoscopic research presents a certain
difficulty. In commencing it we are confronted with the
fact that we already believe a great many things. These
beliefs, or at least the more general of them, ought to be
reconsidered with deliberation. This implies that it
should be conducted according to a deliberate plan
adopted only after the severest criticism. Each criticism
should wait to be planned, and each plan should wait for
criticism. Clearly, if we are to get on all, we must put up
with imperfect procedure. [EP 2: 373].
This description of philosophy as the second theoretical science of
discovery, in order of generality, answers a series of questions as to the
118 TIERCELIN (1993b), pp. 11-15.
401
nature of philosophical activity. A clear feature of Peirce’s definition of
philosophy is that any person can have access to philosophical inquiry.
Differently from special sciences, as physics or biology, for instance,
whose procedures several times require the use of budgets if special
observations, the observations of philosophy consider as data the most
usual and common experiences of everyday life:
I have already explained that by Philosophy I mean that
department of Positive Science, or Science of Fact, which does
not busy itself with gathering facts, but merely with learning
what can be learned from that experience which presses in
upon every one of us daily and hourly. It does not gather new
facts, because it does not need them, and also because new
general facts cannot be firmly established without the
assumption of a metaphysical doctrine; and this, in turn,
requires the cooperation of every department of philosophy; so
that such new facts, however striking they may be, afford
weaker support to philosophy by far than that common
experience which nobody doubts or can doubt, and which
nobody ever even pretended to doubt except as a consequence
of belief in that experience so entire and perfect that it failed
to be conscious of itself; just as an American who has never
been abroad fails to perceive the characteristics of Americans;
just as a writer is unaware of the peculiarities of his own style;
just as none of us can see himself as others see him. [HL 207-
208].
The starting point for philosophy is the here-and-now of every
human being, the world of common-sense of which there are no reasons
to doubt, because one does not perceive it can be doubted, being
immerse in it as we are. Thus, any person also could put to test the
conclusions of a philosophical inquiry, to confirm or to refute its
402
veracity.119 Therefore, the only reliable method for the confirmation of
the conclusions of cenoscopy is the inductive method, because it is the
method that raises the possibility of generalization to the infinite [EP 2:
373]. If the conclusions of philosophy consider from the start and
concern the most usual and general experience, their force is to be in
the possibility of being plainly universal, with the minimal probability of
exceptions. Thus, philosophical inquiry turns ab ovo to life, and not to
books: “Certainly, in philosophy what a man does not think out for
himself he never understands at all. Nothing can be learned out of
books or lectures. They have to be treated not as oracles but simply as
facts to be studied like any other facts.” [HL 139].
Then, in sum, philosophy can be understood as the science of the
clash with experience, the science that seeks to render experience
intelligible in its most disturbing and resistant features, as well as in its
most universal and quotidian features. Each of its subclasses is defined
by the characteristic manner of understanding the world of experience.
In first place, there comes phenomenology:
This must be a science that does not draw any distinction
of good and bad in any sense whatever, but just
contemplates phenomena as they are, simply opens its
eyes and describes what it sees […]. This is the science
which Hegel made his starting-point, under the name of
the Phänomenologie des Geistes – although he
considered it in a fatally narrow spirit, since he restricted
himself to what actually forces itself on the mind and so
119 HANTZIS (1987), p. 292; TIERCELIN (1993b), p. 9.
403
colored his whole philosophy with the ignoration of the
distinction of essence and existence and so gave it the
nominalistic and I might say in a certain sense the
pragmatoidal character in which the worst of the
Hegelian errors have their origin. I will so far follow
Hegel as to call this science Phenomenology although I
will not restrict it to the observation and analysis of
experience but extend it to describing all the features
that are common to whatever is experienced or might
conceivably be experienced or become an object of study
in any way direct or indirect. [HL 120].
Therefore, phenomenology is not the science only of what
appears, but of what seems to be in a certain way. It is not a matter of
interpreting experience to understand what is it that it says about the
reality of the outward world, but to inspect experience itself, resting
upon the observation and the description of its most essential
elements.120
The normative sciences make up the second subclass of
cenoscopy; they can be briefly defined by means of “the analysis of the
conditions of attainment of something of which purpose is an essential
ingredient.” [CP 1.575, Minute Logic]. Because they are inquiries into
the ways for attaining certain ends, these sciences are called
normative, because they settled the conditions for controlled action,
that is, according to a norm, to the fulfillment of such ends. That is why
they distinguish between what ought to be and what ought not to be
[EP 2: 259, An Outline Classification of the Sciences].
120 IBRI (1992), p. 13; HANTZIS (1987), p. 294.
404
Finally, metaphysics is the third subclass of philosophy, being the
science that seeks to give an interpretation of the universe of mind and
matter [id.], that is, it is the science that seeks to say what is reality in
its most general features and characteristics [EP 2: 375]. For Peirce,
the situation of metaphysics in his time was lacking rigour and scientific
parameters: “But in its present condition it is, even more than the other
branches of cenoscopy, a puny, rickety, and scrofulous science.” [id.].121
The only science philosophy borrows principles from is
mathematics. Therefore, philosophy must analise the data of common
experience according to mathematical criteria. How is it possible? The
answer to this question lies in the answer of another: what is the form
of experience? Remember what was already said on the nature of
experience: it is defined by Peirce as the cognitive final outcome of
living:
Experience may be defined as the sum of ideas which
have been irresistibly borne in upon us, overwhelming all
free-play of thought, by the tenor of our lives. The
authority of experience consists in the fact that its power
cannot be resisted; it is a flood against which nothing can
stand. [CP 7.437, Grand Logic, c. 1893].
According to such definition, mental hallucinations, ilusions,
imaginations of everyt sort and kind also make up experience, which is
121 We will leave the divisions of philosophy for now. For a more detailed account, the reader can look up, for instance, about phenomenology, the works mentioned in note 8 below. On the normative sciences: MCCARTHY (1980); PARKER (2003); PARRET (1994); POTTER (1967); SANTAELLA (2000); SHERIFF (1994), cap. 5: “Esthetics, Ethics, and Logic”; SILVEIRA (2003). On metaphysics: HAUSMAN (1993), passim; HOOKWAY (1998); IBRI (1992), passim; IBRI (2003).
405
not reduced, then, only to the notion of “sensible perception” [CP 6.492,
c. 1896]. But there is another characteristic, namely, compulsiveness,
which was already mentioned. See the following passgem where once
more the link between the idea of experience and expectation is
clarified:
We live in two worlds, a world of fact and a world of
fancy. Each of us is accustomed to think that he is the
creator of his world of fancy; that he has but to
pronounce his fiat, and the thing exists, with no
resistance and no effort; and although this is so far from
the truth that I doubt that much the greater part of the
reader’s labor is expended on the world of fancy, yet it is
near enough the truth for a first approximation. For this
reason we call the world of fancy the internal world, the
world of fact the external world. In this latter, we are
masters, each of us, of his own voluntary muscles, and of
nothing more. But man is sly, and contrives to make this
little more than he needs. Beyond that, he defends
himself from the angles of hard fact by clothing himself
with a garment of contentment and of habituation. Were
it not for this garment, he would every now and then find
his internal world rudely disturbed and his fiats set at
naught by brutal inroads of ideas from without. I call
such forcible modification of our ways of thinking, the
influence of the world of fact, experience. But he patches
up his garment by guessing that those inroads are likely
to be and carefully excluding from his internal world
every idea which is likely to be so disturbed. Instead of
waiting for experience to come at untoward times, he
provokes it when it can do no harm and changes the
government of this internal world accordingly. [EP 2:
406
369-370, The Basis of Pragmaticism in Phaneroscopy,
1906].
Experience has a clear power to shape conduct, as well as to
modify it. It is by means of clashing with the outward world of fact that
we get to create habits of expectations, so that we are not anymore
surprised by the “brutal inroads” from the ideas of outside. Thus, linked
to the idea of “outward clash” [W 5: 225, An American Plato],
experience is the coup that fecunds consciousness and begins
knowledge [EP 2: 374]. In other words, experience has an unavoidable
feature of constraint:
[…] the concept of experience is broader than that of
perception, and includes much that is not, strictly
speaking, an object of perception. It is the compulsion,
the absolute constraint upon us to think otherwise than
we have been thinking that constitutes experience. Now
constraint and compulsion cannot exist without
resistance, and resistance is effort opposing change.
Therefore there must be an element of effort in
experience; and it is this which gives it its peculiar
character. [CP 1.336, Phaneroscopy or the Natural
History of Concepts, c. 1905]
For such reason, experience is characteristically a factor of
modification of consciousness. Now, in truth, as Peirce himself asserts,
experience teaches us to foresee the general future mode of conduct of
events, and not only by means of external sensible perception. Not
restricted to the actual object of perception, experience also has the
feature of possibility; so, it is not reduced to merely actual and physical
407
compulsions. Contents of thoughts can also exert compulsion and
change the course of thinking:
Experience is double, as much as reality is. That is, there
is an outward and an inward experience. Under the latter
head ought particularly to be reckoned a mathematical
experience, not usually so called, which has compelled
the development of pure thought to take a determinate
course. [CP 7.440, Grand Logic].
Now, if philosophy is the attempt to conceive a Weltanschauung
grounded on the observation of experience, to ask for the form of
experience is to ask for the way how knowledge begins. In other words,
it is necessary to explain how mental content in general can be
organized and structured. Philosophy, then, is defined as a search for
the primordial constitutive elements universally present in every
experience. To Peirce, such elements are its universal categories of
firstness, secondness, and thirdness.122 The passage above suggests that
the determination of such universal features of experience can be made
mathematically, in a way that it becomes possible to project abstract
forms over reality. Thus, mathematics can be conceived by Peirce as an
activity of construction of general structures or models that can be
combined with any sort of experience.123 It would so be possible to
isolate a basic framework, relatively simple, universally applicable to
122 Cf. TIERCELIN (1993b), p. 15 and especially chap. 1: “Pour une analyse logique des produits de la pensée”; HOUSER (1990), p. 4. We will not see here in detail each of Peirce’s categories. The literature about the subject is extense. We briefly indicate: APEL (1995a), pp. 109-110; DE TIENNE (1996), passim; IBRI (1992), cap. 1: “A Fenomenologia: as categorias da experiência”; ROSENTHAL (1994), chap. 4: “Pragmatic experimentalism and the derivation of the categories”.123 HOUSER (1990), pp. 3-4; APEL (1995a), p. 119-120.
408
experience, that would reveal its ubiquitous form. In effect, the
examination of omnipresent experience presupposes mathematics:
This science of Phenomenology is in my view the most
primal of all the positive sciences. That is, it is not based,
as to its principles, upon any other positive science.
Phenomenology […] if it is to be properly grounded, be
made to depend upon the Conditional or Hypothetical
Science of Pure Mathematics, whose only aim is to
discover not how things actually are, but how they might
be supposed to be, if not in our universe, then in some
other. [HL 120-121].
Then, there is put the problem of the mathematical and the
phenomenological forms of the categories: does experience has a
mathematical or a phenomenological form? If the principles of
phenomenology are in pure mathematics, then phenomenology must be
able to give an account of every and any kind of experience, or better,
form of experience, including one that is not familiar to us in this world,
but indeed of all possible experience in any possible world. We can
fancy two possibilities, to wit: if, on the one hand, the categories of
experience are conceived as kinds of relations, experience will
essentially possess a mathematical form; if, on the other hand,
categories are kinds of consciousness, experience essentially is
phenomenological. As a matter of fact, Peirce adopted both accounts,
saying it is possible a mathematical as well as a phenomenological
extraction of the categories. The problem of the form of experience,
seen as a problem of the relationship between mathematics and
409
phenomenology can thus be understood as the problem of the
conditions of possibility for projecting mathematical forms over
experience 124. This problems goes back to the remote begnnings of
history of science and philosophy, at least to Pythagoras, and we can
suspect Peirce had it in mind when he wrote the following:
Pythagoras may be said to have originated the whole
science of physics by observing a connection between the
intervals of the tones of strings and the weights which
stretched them. This probably belonged to the secret
doctrine; for as it has come down to us, it is so totally
wrong that the least experiment would show it. Yet
without experiment the idea could not have arisen.
Namely the statement made is that the ratios of weights
12 : 6, 12 : 8, 12 : 9 are respectively an octave, a fifth,
and a fourth. Now the true ratios are precisely the
square roots of these. Evidently, Pythagoras must have
known the truth. It is a historical fact then that he was
the father of physics. No small glory that.
[…]
Pythagoras thought that numbers were the substance of
things. What he meant, I do not believe he knew or
thought he knew. It was his highest aperçu. He felt he
could not quite grasp it. [HP I: 176-177, Early History of
Science].
Peirce sought to unite all these elements in a realist conception of
mathematics as heuretic science. What he himself thought of
Pythagoras’ thought maybe is the following:
124 APEL (1995a), p. 120 ff.; HOUSER (1990), p. 2; PARKER (1998), pp. 103 ff.
410
A state of things is an abstract constituent part of reality,
of such a nature that a proposition is needed to represent
it. […]
A mathematical form of a state of things is such a
representation of that state of things, without definitely
qualifying the subjects of the samenesses and diversities.
It represents not necessarily all of these; but if it does
represent all, it is the complete mathematical form. Every
mathematical form of a state of things is the complete
mathematical form of some state of things. [EP 2: 378,
The Basis of Pragmaticism in the Normative Sciences].
From the quotation above we can grasp the aim of mathematical
inquiry: to represent in a general and abstract manner all possible
forms of states of things, no matter whether existent or not. According
to such idea, we can quote the following Peircean definition of
mathematics:
The first is mathematics, which does not undertake to
ascertain any matter of fact whatever, but merely posits
hypotheses, and traces out their consequences. It is
observational, in so far as it makes constructions in the
imagination according to abstract precepts, and then
observes these imaginary objects, finding in them
relations of parts not specified in the precept of
construction. [CP 1.240, A Detailed Classification of the
Sciences]. 125
125 See LUCAS (2003), p. 143. For the interpretation of Peirce’s philosophy of mathematics, we basically follow HOOKWAY (1992), pp. 192 ff. and MURPHEY (1993), chap. 12: “Pure Mathematics”. For a detailed discussion of Peirce’s philosophy of mathematics as well as his mathematics, the reader can consult RLT 1-54, the introduction written by Ketner and Putnam; besides, see MURPHEY (1993), pp. 183-288, and PARKER (1998), chapters 3: “The Mathematics of Logic: formal aspects of the categories” and 4: “Infinity and Continuity”; cf. also HOUSER (1990); JOSWICK (1988); TIERCELIN (1993a); KERR-LAWSON (1997).
411
In other words, the mathematician is not concerned with the
positive truth of what in fact is, but only with his or her hypothetical
truth, that is, with what could or could not be necessarily concluded
from the imaginary hypotheses constructed. Mathematics, therefore, is
the science that seeks to define pure possibilities. The mathematician
first frames hypotheses, and next observes what necessarily it is
possible to conclude as consequence from such constructions. After
that, it is possible to generalize the conclusions obtained to every
occasion possible of being described in the terms of the imagined
hypotheses. Mathematical knowledge, thus, is purely hypothetical:
Modern science, even from the first, took away from
demonstratively certain knowledge much of its luster;
and mathematicians who alone produce such knowledge,
now see clearly that such knowledge can only be
knowledge of hypothetical states of things, or say of the
implications of arbitrary hypotheses; and never can be
positive science, that is, science of the real. [MS 283:
155, 1906].
Therefore, the imaginary constructions of mathematics can be
applied to any situation of fact, any actual occasion, because they can
be applied to some situation of fact.
Already in 1885, in On the Algebra of Logic: A Contribution to the
Philosophy of Notation, Peirce recognized a difficulty in defining the
scientific status of mathematics:
It has long been a puzzle how it could be that, on the one
hand, mathematics is purely deductive in its nature, and
412
draws its conclusions apodictically, while on the other
hand, it presents as rich and apparently unending a
series of surprising discoveries as any observational
science. Various have been the attempts to solve the
paradox by breaking down one or other of these
assertions, but without success. [W 5: 164].
Shortly after, Peirce tells the key to solve this dilemma, to wit, a
correct understanding of the nature of deduction. We have seen that
deduction is the only form of necessary reasoning. In mathematics,
there are two kinds of deduction, theorematical and corollarial
deduction:
My first real discovery about mathematical procedure
was that there are two kinds of necessary reasoning,
which I call the Corollarial and the Theorematic, because
the corollaries affixed to the propositions of Euclid are
usually arguments of one kind, while the more important
theorems are usually of the other. The peculiarity of
theorematic reasoning is that it considers something not
implied at all in the conceptions so far gained, which
neither the definition of the object of research nor
anything yet known about could of themselves suggest,
although they give room for it. Euclid, for example, will
add lines to his diagram which are not at all required or
suggested by any previous proposition, and which the
conclusion that he reaches by this means says nothing
about. I show that no considerable advance can be made
in thought of any kind without theorematic reasoning.
When we come to consider the heuretic part of
mathematical procedure, the question how such
suggestions are obtained will be the central point of the
discussion. [NEM 4: 49, Carnegie Application].
413
Now, “reasoning essentially consists in the observation that
where certain relations subsist certain others are found” [W 5: 164].
What the distinciton between the two forms of deductive reasoning
shows is that mathematical reasoning is not only the observation of
what is evident in a formal representation of a state of things, but it is
also a constructive activity of such representations, by means of
observing and modifying other representations. This is the heuristic
part of mathematics, the one that makes us see something not implied
in the premisses, clearly involving an abductive reasoning.126 We can
take yet another passage, wherein the difference between the two kinds
of deduction is expressed in other terms:
A Corollarial Deduction is one which represents the
conditions of the conclusion in a diagram and finds from
the observation of this diagram, as it is, the truth of the
conclusion. A Theorematic Deduction is one which,
having represented the conditions of the conclusion in a
diagram, performs an ingenious experiment upon the
diagram, and by the observation of the diagram, so
modified, ascertains the truth of the conclusion. [EP 2:
208, Nomenclature and Divisions of Triadic Relations].
Mental experiments, according to the quotation above, are the
same as observations of the diagram. In corollarial deduction, the
procedure starts from the observation of a diagram such as it is,
without any modification, to affirm the conclusion. The conclusion,
therefore, is necessarily obtained only from what is expressed in the
126 CROMBIE (1997), p. 465 ff.
414
diagram, without any further adjunction to the conclusion.
Theorematical deduction, in turn, modifies the diagram to discover new
relations not evident in its initial form of presentation. Thus, it is the
process whereby the truth of mathematical conclusions is ascertained
“by performing a variety of experiments in our imagination.” [NEM 4:
xiv, s/d].
Such definitions of mathematics in Peirce’s works abound. One of
them says the following:
The first [science of discovery] is mathematics, which
does not undertake to ascertain any matter of fact
whatever, but merely posits hypotheses, and traces out
their consequences. It is observational, in so far as it
makes constructions in the imagination according to
abstract precepts, and then observes these imaginary
objects, finding in them relations of parts not specified in
the precept of construction. This is truly observation, yet
certainly in a very peculiar sense; and no other kind of
observation would at all answer the purpose of
mathematics. [CP 1.240, A Detailed Classification of the
Sciences, 1902].
The quotation above shows very well the link between the
theorematical and the corollarial processes in mathematical reasoning.
Once more there appears the idea that the mathematician is not
concerned with the positive truth of what actually is, but only with what
could or could not be necessarily concluded, from the imaginary
hypotheses framed. By showing the intertwinement of the moments of
creation of formal models and of deduction of the conclusions
415
necessarily implied in such models in the mathematical procedure,
Peirce relates two distinct ways of defining mathematics:
relaciona duas maneiras de definir a matemática:
[...] it is an error to make mathematics consist exclusively
in the tracing out of necessary consequences. For the
framing of the hypothesis of the two-way spread of
imaginary quantity, and the hypothesis of Riemann
surfaces were certainly mathematical achievements.
Mathematics is, therefore, the study of the substance of
hypotheses, or mental creations, with a view to the
drawing of necessary conclusions. [NEM 4: 268, On
Quantity].
In this way, Peirce follows the definition of mathematics given by
his father Benjamin Peirce, according to which mathematics is the
science that draws necessary conclusions, in contradistinction to logic,
which is the science of drawing necessary conclusions:
The philosophical mathematician, Dr. Richard Dedekind,
holds mathematics to be a branch of logic. This would not
result from my father's definition, which runs, not that
mathematics is the science of drawing necessary
conclusions – which would be deductive logic – but that it
is the science which draws necessary conclusions. [CP
4.239, Minute Logic].
Notwithstanding, if we focus on the definition of mathematics, we
will be able to conclude that, in a certain sense, mathematics is logic, or
at least, that logic is a constitutive part of the mathematical procedure.
In fact, the most important difference between logic and mathematics is
in the interest of each science. Take for instance the following passage:
416
For my part, I consider that the business of drawing
demonstrative conclusions from assumed premisses, in
cases so difficult as to call for the services of a specialist,
is the sole business of the mathematician. Whether this
makes mathematics a branch of logic, or whether it cuts
off this business from logic, is a mere question of the
classification of the sciences. I adopt the latter
alternative, making the business of logic to be analysis
and theory of reasoning, but not the practice of it. [CP
4.134, The Logic of Quantity, 1893].
On the one hand, the logician is not concerned with this or that
special hypothesis, unless that in studying it, it brings him some new
information on the nature of reasoning. On the other hand, the
primordial interest of the mathematician is focused on the hypotheses
taken individually, and in how it is possible to pass necessarily from the
premises to the conclusions in each case; the interest of the
mathematician, therefore, is in the effectiveness of the methods of
reasoning, for their capacity of being extended to other unknown
instances; mathematics deals with the possible generalization of the
hypotheses, rather than with sinuosities of reasoning. For instance,
Peirce says:
The logician does not care particularly about this or that
hypothesis or its consequences, except so far as these
things may throw a light upon the nature of reasoning.
The mathematician is intensely interested in efficient
methods of reasoning, with a view to their possible
extension to new problems; but he does not, qua
mathematician, trouble himself minutely to dissect those
417
parts of this method whose correctness is a matter of
course. [CP 4.239].
This point is clarified if we look up at how each scientist considers
logical algebra:
The mathematician asks what value this algebra has as a
calculus. Can it be applied to unraveling a complicated
question? Will it, at one stroke, produce a remote
consequence? The logician does not wish the algebra to
have that character. On the contrary, the greater number
of distinct logical steps, into which the algebra breaks up
an inference, will for him constitute a superiority of it
over another which moves more swiftly to its conclusions.
He demands that the algebra shall analyze a reasoning
into its last elementary steps. Thus, that which is a merit
in a logical algebra for one of these students is a demerit
in the eyes of the other. The one studies the science of
drawing conclusions, the other the science which draws
necessary conclusions. [Id.].
So, logic seems to be interested in the “rhetorical” character of
reasoning, aiming at explicating every step – and not only the necessary
ones – of reasoning from premises to conclusions. Indeed, rhetoric is an
essential part of the Peircean conception of logic. Since the method of
science proceeds pragmatically and experientially, scientific activity
necessarily involves the adoption of methods of inquiry that are public
and dialogical. That is why it is important to define a theory of assertion
that, overcoming the difficulties of modern philosophy, allows for an
evaluation of speech as a way of attributing and claiming
responsibilities to the members of the inquiring community. And this, of
418
course, leads to an amplification of the domain of rhetoric in the context
of inquiry. Thus, logic widely conceived as semiotics would have three
orders:
All thought being performed by means of signs, logic may
be regarded as the science of the general laws of signs. It
has three branches: (1) Speculative Grammar, or the
general theory of the nature and meanings of signs,
whether they be icons, indices, or symbols; (2), Critic,
which classifies arguments and determines the validity
and degree of force of each kind; (3), Methodeutic, which
studies the methods that ought to be pursued in the
investigation, in the exposition, and in the application of
truth.127 [EP 2: 260, An Outline classification of the
Sciences].
These three divisions of logic constitute what Peirce calls the
philosophical trivium, wherein the rhetoric purport of each of them is
manifest; as in the case of speculative grammar, which studies several
other ways of uttering assertions, besides verbal expressions: "such as
algebra, arithmetical figures, emblems, gesture-language, manners,
uniforms, monuments, to mention only intentional modes of
declaration.” Speculative grammar, thus, is the study of the modes of
signifying, in general [EP 2: 19, Of Reasoning in General]. The
discipline Peirce calls speculative rhetoric is also straightly linked to
the study of the ways to be used in meaning something: ““An art of
thinking ought also to recommend such forms of thinking as will most
economically serve the purpose of Reason. […] Since this is the general
127 For a good succinct introduction to the theme of rhetoric in Peirce’s thought, see LISZKA (2000).
419
foundation of the arte of putting propositions into effective forms, it has
been called speculative rhetoric.” [id.].
Mathematics, differently, rests upon the principle of parsimony in
its procedures, what is just the application of Ockham’s razor to
reasoning. It is not the business of mathematicians to seek to evaluate
or to classify reasonings, developing all the steps, saying which is the
beautiful reasoning, or the most effective; mathematics, as an
experimental science over diagrams, seeks only to study the possible
hypothetical consequences, in a tied relation with what the pragmatical
maxim declares:
Consider what effects, which might conceivably have
practical bearings, we conceive the object of your
conception to have. Then, our conception of these effects
is the whole of our conception of the object. [W 3: 266,
How to Make Our Ideas Clear].
The definition of mathematics as the study of what is true of
hypothetical state of things is more frequent in Peirce’s writings. Such
definition justifies why the truth values of mathematical sentences do
not matter so much: the mathematician admits as object of study every
and any hypothesis, without being interested in knowing whether they
are true or not. Very often the mathematician constructs a
mathematical form following the indications given to him or her by
other scientists, who find themselves in an aporetical situation without
understanding the relations the objects entertain in a certain state of
things:
420
Now a mathematician is a man whose services are called
in when the physicist, or the engineer, or the
underwriter, etc., finds himself confronted with an
unusually complicated state of relations between facts
and is in doubt whether or not this state of things
necessarily involves a certain other relation between
facts, or wishes to know what relation of a given kind is
involved. He states the case to the mathematician. The
latter is not at all responsible for the truth of those
premises: that he is to accept. The first task before him is
to substitute for the intricate, and often confused, mass
of facts set before him, an imaginary state of things
involving a comparatively orderly system of relations,
which, while adhering as closely as possible or desirable
to the given premises, shall be within his powers as a
mathematician to deal with. This he terms his hypothesis.
That work done, he proceeds to show that the relations
explicitly affirmed in the hypothesis involve, as a part of
any imaginary state of things in which they are
embodied, certain other relations not explicitly stated.
[NEM 4: 267, On Quantity].
Hence, it makes no sense to distinguish sharply between pure and
applied mathematics.128 Once the mathematician constructs hypotheses
grounded upon a suggestion from experience, he or she has in sight
some application of the models devised. There is a demand that the
mathematician be capable to imagine models simple enough to work
with them. Then, it is his or her task to simplify the relations to the
most to try to find those that are the most elementary. There is no
metaphysical reason behind this; as the mathematical procedure is
128 TIERCELIN (1993a), pp. 41-45.
421
marked by the parsimony of reasoning, the safest way of avoiding
mistakes is also the easiest way to discover necessary relations, to wit,
to simplify and to reduce the relations to the absolutely essential. Thus,
what the mathematician does is to imagine a highly abstract model of
simplified relations, yet still capable of expressing the relations of the
facts. This high degree of abstraction allows for the generalization:
All features that have no bearing upon the relations of
the premisses to the conclusion are effaced and
obliterated. The skeletonization or diagrammatization of
the problem serves more purposes than one; but its
principal purpose is to strip the significant relations of all
disguise. [CP 3.559, The Logic of Mathematics in
Relation to Education, 1898].
The mathematician, then, makes two different things. First, he or
she imagines a hypothesis, represented in the form of a highly abstract
diagram of the state of things, representative only of its most essential
relations, without caring about whether the representation will or will
not correspond to the actual reality. Second, the mathematician begins
to draw necessary conclusions from such relations, conclusions not
explicit in the diagram. Mathematical necessity, therefore, comes from
the logical connexion settled between premises and conclusions. The
mathematician adopts hypotheses, conclusions, rules, and goes on to
verify which state of things necessarily follows from another.
Mathematics thus defined is purely formal, and concerns only the
possibility of application of its models to the actual reality:
422
Now the feature of mathematics which separates it
widely both from Philosophy and from every special
science is that the mathematician never undertakes (qua
mathematician) to make a categorical assertion from the
beginning of his scientific life to the end. He simply says
what would be the case under hypothetical
circumstances. [NEM 4: 208, Reason’s Conscience].
The hypothetical character of its assertions, besides
distinguishing it from the positive sciences that state factual truth,
warrants the very necessity of the conclusions: the interest of the
mathematician is uniquely for the form of relations. Mathematics,
consequently, opens a vast field of structural possibilities.129 The special
circumstance embodying what was mathematically ascertained is
merely contingent. To know if a given form can de facto be applied to
an actually existent state of things is a scientific question that each
scientist must resolve according to his or her needs. The mathematician
only defines the question de jure, that is, to the mathematician is due
solely the work with structures likely to be applied, which result in
certain necessary conclusions.130
It is important to notice the possibility of deducing necessary
conclusions from mathematical propositions; this is the very nature of
mathematical inquiry:
The first of these [three divisions of heuretic science]
comprises the business of finding out what might and
more especially what could not, be true under described
129 HOUSER (1990), p. 4; KERR-LAWSON (1997), p. 79.130 KERR-LAWSON (1997), id.
423
circumstances, without asking whether or not such
circumstances ever really occur. To my apprehension,
this precisely defines mathematics [...]. [MS 1338: 6, c.
1906].
The meaning of mathematical terms and propositions, in this way,
is confined to their form of expression in mathematical signs: “The
meaning of a mathematical term or sign is its expression in the kind of
signs in the imaginary or other manifestations of which the
mathematical reasoning consists. For geometry, this [expression] is [in]
a geometrical diagram.” [NEM 2.251]. However, this does not mean
that mathematical truths are defined by their use in determined
contexts, or that they are determined by some linguistic convention. It
is the importance of the modus operandi, that is, the way how
demonstrations are made and the application of the very mathematical
demonstrative procedures to the hypothetical diagrams that gives
mathematics its sureness:
I certainly think that the certainty of pure mathematics
and of all necessary reasoning is due to the circumstance
that it relates to objects which are the creations of our
own minds, and that mathematical knowledge is to be
classed along with knowledge of our own purposes. [HL
227].
The meaning of mathematical constructions is not given ab ovo,
but it is defined by demonstration: to reason is not only to use
meanings, it is not merely to operate signs, but it is also to construct
424
them, to manipulate signs in a certain way to determine them and to
suggest certain interpretations.131
The Peircean definition of mathematics, in short, has two main
characters; to wit:
1st, mathematics does not concern a special range of entities, as
every other science depending upon it in the classification of the
sciences. In other words, it is not defined neither by means of the
specificity of its objects, nor by the nature of its propositions, nor even
by the kinds of truths it may exhibit; mathematics has nothing to say
about the truth of fact because it is a science dealing with hypothesis
and abstractions; in a more traditional language, one could say that
mathematics is a science, the objects of which are entia rationis [EP 2:
352].132
2nd, according to his father Benjamin Peirce, mathematics is the
science that draws necessary conclusions. Indeed, every necessary
reasoning is mathematical reasoning [NEM 4.47]. This second
characteristic raises the problem of the definitions of a mathematical
ontology.133 What would be the nature of such entia rationis? Would they
be purely arbitrary conventions, since they do not refer to actual
reality? Or would they be purely analytical propositional systems, or
even tautological systems? If it be so, why then to insist in the practical 131 As a matter of fact, this is linked to the theme of self-controlled thinking, which is an essential subject for the definition of logic as normative science. See TIERCELIN (1993a), p. 34.132 TIERCELIN, (1993a), pp. 30-31133 For the supposed Platonism of such conception, a subject we are not able to deep here, see TIERCELIN (1993a); KERR-LAWSON (1997).
425
side of mathematics, that is, over the possibility of application of
mathematics to problems of the positive sciences?134 In short, this is
question of how to connect Peirce’s indeterminist realism with his
conception of mathematics. As a matter of fact, fallibilism in
mathematics is problematic for Peirce, who several times asserts that
error in mathematics is due only to a blunder in reasoning [CP 1.149, c.
1897; 7.108, 1892; 1.248, 1902; NEM 4: 210, 1904]. Therefore, there is
no problem for him to think of the necessity of mathematics as perfectly
compatible with an ideal system, wherein one can reason about possible
cases (and, therefore, undetermined instances), and also about actual
cases.
Finally, it is time now to justify the epigraphs. First, it seems clear
to us that Whitehead adopts a conception of mathematics that is
substantially almost the same as Peirce’s. Take, for instance, the
following statement:
The point with mathematics is that in it we have always
got rid of the particular instance, and even of any
particular sorts of entities. So that, for instance, no
mathematical truths apply merely to fish, or merely to
stones, or merely to colours. So long as you are dealing
with pure mathematics, you are in the realm of complete
and absolute abstraction. All you assert is, that reason
insists on the admission that, if any entities whatever
have any relations which satisfy such-and-such purely
134 In fact, see how TIERCELIN (1993a), p. 31, presents the problem: “If one accepts the notion of applied mathematics as something which is needed by all sciences, what is to warrant that such idealizations have the objective validity which justifies their being used by these other sciences?”
426
abstract conditions, they must have other relations which
satisfy other purely abstract conditions.135
In a very similar way Peirce also insists upon the unavoidable and
abstract character of mathematical conclusions:
The mathematician does not “rely” upon anything. He
simply states what is evident, and notes the
circumstances which make it evident. When a fact is
evident, and nobody does or can doubt it, what could
“reliance” upon anything effect? [NEM 4: 209, Reason’s
Conscience].
In this way, the evidence of the mathematical diagrams forcefully
obliges the mathematician to recognize the necessity of the
consequences. However, Peirce does not understand mathematical
relations as abstract relations of sets of things, whatever might be,
differently from Whitehead:
Thus, in considering the relations of the number ‘five’
with the number ‘three’, we are thinking of two groups of
things, one with five members and the other with three
members. But we are entirely abstracting from any
consideration of any particular entities, or even of any
particular sorts of entities, which go to make up the
membership of either of the two groups. We are merely
thinking of those relationships between those two groups
which are entirely independent of the individual essences
of any of the members of either group.136
Whitehead speaks in terms of groups of particular things. This is
an important detail, for it should be notices that Peirce does not say
that in mathematics we deal with any groups or sets of objects. In fact,
135 WHITEHEAD (1962), p. 31. 136 Our italics. WHITEHEAD (1962), p. 30.
427
the domain ot the Peircean mathematical ontology may very well go
beyond sets, for mathematical objects do not exist, but are merely
imaginary. Therefore, there is no reason why to be constrained to sets
or to relations between sets. Peirce strongly emphasizes the necessity
of mathematical conclusions; but on their applicability, the only thing
one may affirm is that they might or might not be actualized. Algebra
indeed does not want to say anything besides its own forms:
The algebraic system of symbols is a calculus; that is to
say, it is a language to reason in. Consequently, while it
is perfectly proper to define a debt as negative property,
to explain what a negative quantity is, by saying that it is
what debt is to property, is to put the cart before the
horse and to explain the more intelligible by the less
intelligible. To say that algebra means anything else than
just its own forms is to mistake an application of algebra
for the meaning of it. [CP 4.133, The Logic of Quantity,
1893].
In fact, the true mathematical objects are the very forms of
relations, or, as N. Houser says, the “relational structures” 137.
Generalizing the various relations we find in the actual world, giving
them a substantive form, the relations abstracted from all accidentality
become the objects of mathematical inquiry. Mathematics, then,
acquires the status of a formal logic of relations. Maybe the most
meaningful discovery of mathematics, from this point of view, be that
there are three fundamental forms of relation: monadic (1), dyadic (2),
and triadic (3). Here we have the famous Peircean thesis of the
137 No que segue, seguimos a interpretação de HOUSER (1990), pp. 5 seq.
428
essential irreducibility of the triad, and the reducibility of all other
higher relations ((4), (5), (6), etc.) to the triad. Triads combine both
dyads and monads, and dyads combine monads, that is, (2) and
(1) are present in (3), and (1) is present in (2). In the same way that a
triad, however, cannot be reduced to a dyad, that is, a dyad cannot
represent the same relations that a triad can; and every other relations
of higher order than three can be reduced to the triad. Thus, in (4)
there is (3) and (1), and in (5) there is (3) and (2), and in (9) there is ((3)
x (3)], and so forth. [EP 2: 364, The Basis of Pragmaticism in
Phaneroscopy].
Monads, dyads, and triads make our set of fundamental
categories of relations. The relation of one category containing another
that is exhibited is better understood as the presence of the inferior
relation in the superior one, in a structural manner, as if a part-to-whole
relation. In examining a diagram, the mathematician sees that monads
are structurally elementary, i.e., that they are firsts. Dyads,
consequently, depend on monads, i.e., they necessarily contain them;
and the same is true for triads as to dyads. The three essential forms of
relation therefore correspond to being structurally first, second or third
in mathematics. Through hypostatical abstraction, i.e., the abstraction
that permits the passage from an individual to entis rationis [CP 4.235,
The Simplest Mathematics, 1902; 4.549, Prolegomena to an Apology of
Pragmaticism], the mathematician comes to the categories of firstness,
429
secondness, and thirdness. This group of categories, because they are
extremely formal, is applicable to any triads, whether possible or
actual. Thus, we can know a priori which will be the form of experience,
once it is possible to know what will always be the relations of
dependence to be found in experience.138
“[Abstraction] may be called the principal engine of mathematical
thought.” [CP 2.364, Quantity, 1902] With such affirmation, we have
another way of defining mathematics. An abstraction is “but an object
whose being consists in facts about other things” [NEM 4: Logic of
History, c. 1901]. Mathematical notions, such as collections and
numbers, are the outcomes of abstraction, which cannot be confounded
with generalization:
[Abstraction] consists of seizing upon something which
has been conceived as a [winged word], a
meaning not dwelt upon but through which something
else is discerned, and converting it into an
[non-winged word], a meaning upon which we
rest as the principal subject of discourse. Thus, the
mathematician conceives an operation as something
itself to be operated upon.139 [CP 1: 83, Lessons on the
History of Science].
138 HOUSER (1990), p. 6.139 The image of the winged words Peirce might have borrowed from Homer, who in the Iliad, book I, lines 197-204, describes the encounter of Achilles and Pallas Athena with these words: “Rearing behind him Pallas seized his fiery hair - / only Achilles saw her, none of the other fighters - / struck with wonder he spun around, he knew her at once, / Pallas Athena! The terrible blazing of those eyes, / and his winged words went flying: “Why, why now?/ Child of Zeus with the shield of thunder, why come now?/ To witness the outrage Agamemnon just committed? / I tell you this, and so help me it’s the truth - / he’ll soon pay for his arrogance with his life!” Robert Fagles’ translation.
430
When operations are submitted to other operations in
mathematics, what is done is an abstraction. The abstractive operation
renders possible to take an object as the subject upon which
experiments are made, and from it to infer conclusions about other
objects.140 For instance: “A particle is somewhere quite definitely. It is
by abstraction that the mathematician conceives the particle as
occupying a point.” [NEM 4: 11]. Abstraction, then, defines a fixed
signification – a word without wings – to serve as bedrock for the
understanding of other objects. It is, in fact, an operation for isolating
general relations.
There are two elementary kinds of abstraction, precisive and
hypostatical141: e a hipostática:
With this preface, we may proceed to consider hypostatic
abstraction; that is, abstraction in the sense in which we
speak of abstract nouns, as contradistinguished from
precisive abstraction, which consists in concentrating
attention upon a particular feature of a supposed state of
things. [HP 2: 739, On the Logic of Drawing History].
Precisive abstraction, as it is clear, is only an act of attention, in
which certain aspects are noticed, others neglected. In hypostatical
abstraction, an individual object is taken as an ens rationis, that is, an
entity whose being consists in some other fact; its logical peculiarity is
in that the subject of the conclusion is not expressed in the premises,
140 SHORT (1997), p. 296.141 Do not confound hypostatical abstraction with the operation of prescision. See W 2: 50-51, On a New List of Categories, 1867. We will not explain the latter here; it is explained in detail in our Masters dissertation. See RODRIGUES (2001), pp. 85 ff.
431
and yet the conclusion remains necessary [CP 4.463, On Existential
Graphs, Euler’s Diagrams, and Logical Algebra, 1903]. Peirce’s
favourite illustration for hypostatical abstraction is taken from the third
intermezzo of Molière’s Le Malade Imaginaire142. Molière describes an
oral examination, wherein a doctor in medicine asks a graduate student
which are “the cause and the reason” for opium putting people to sleep.
Confident and full of certainty, the bachelor answers back in his best
Latin: “Quia est in eo virtus dormitiva”, that is, “Because there is in it a
force that makes people sleepy.” He is then applauded by the choir and
accepted in the body of doctors. Molière was satirizing, criticising the
pretension to explain everything with beautiful though empty words,
what in truth one does not know how to explain. For Peirce, even such a
declaration can provide some knowledge, since it asserts that there is
an explanation for the fact, besides the very fact: “For it does say that
there is some peculiarity in the opium to which sleep must be due; and
this is not suggested in merely saying that opium puts people to sleep.”
[CP 5.534, Pragmatism; NEM 4: 11]. In other words, hypostatical
abstraction allows for the formulation of a general conception of a
reality that even though it is manifested in the individual phenomena, it
is not neither exhausted in it nor explicit:
But hypostatic abstraction, the abstraction which
transforms ‘it is light’ into ‘there is light here,’ which is
142 O texto desse intermezzo está disponível, em francês, em hipertexto em vários sítios da Internet. Nós o acessamos em URL: [http://www.eleves.ens.fr/home/sray/moliere/maladimg.html], 18/04/2005.
432
the sense which I shall commonly attach to the word
abstraction (since prescission will do for precisive
abstraction) is a very special mode of thought. It consists
in taking a feature of a percept or percepts (after it has
already been prescinded from the other elements of the
percept), so as to take propositional form in a judgment
(indeed, it may operate upon any judgment whatsoever),
and in conceiving this fact to consist in the relation
between the subject of that judgment and another
subject, which has a mode of being that merely consists
in the truth of propositions of which the corresponding
concrete term is the predicate. Thus, we transform the
proposition, ‘honey is sweet,’ into ‘honey possesses
sweetness.’ ‘Sweetness’ might be called a fictitious thing,
in one sense. But since the mode of being attributed to it
consists in no more than the fact that some things are
sweet, and it is not pretended, or imagined, that it has
any other mode of being, there is, after all, no fiction. The
only profession made is that we consider the fact of
honey being sweet under the form of a relation; and so
we really can. [CP 4.235, The Simplest Mathematics].
Now, it is not merely to suppose entia rationis; hypostatical
abstraction leads us to see non-evident relations, leads us to discover
that the virtus dormitiva of opium must be actually real, since opium
puts us to sleep. The virtus dormitiva, therefore, taken separately from
the fact that opium makes people sleepy, is put as an entity – that is
why such abstraction is called hypostatical.143
Regarding the question of how to give content to abstract forms
and relations, this can only be answered with a minute study of Peirce’s
143 SHORT (1997), p. 296.
433
phenomenology, what will not be done in this work. We can however
briefly approach the subject. The most important point, now, is that,
while mathematics gives other sciences formal principles,
phenomenology, being an investigation of the [pháneron], must
provide empirical principles to the categories. As the study of what
seems to be, Peircean phenomenology also does not concern itself with
the precise ontological status of its object:
I propose to use the word Phaneron as a proper name to
denote the total content of any one consciousness (for
any one is substantially any other), the sum of all we
have in mind in any way whatever, regardless of its
cognitive value. This is pretty vague: I intentionally leave
it so. I will only point out that I do not limit the reference
to an instantaneous state of consciousness; for the clause
“in any way whatever” takes in memory and all habitual
cognition. [EP 2: 362].
In this way, the limitations of our metal faculties are not a
problem to phenomenology. Its business is to provide a general
description of everything that may in some way or another be present
to consciousness, inwardly or outwardly. Therefore, it is its business to
make an inventory of the most universal features of experience, i.e., to
give mental content to the abstract forms of mathematics. 144 A fuller
development of such points we reserve for a further occasion. We can
conlcusively add that the categories inform the whole natural
classification of the sciences, in a way that the division between
144 HOUSER (2000), p. 8; IBRI (1992), cap. 2
434
heuretic, retrospective and practical sciences corresponds to the
characters of being first, second and third of the phenomenon; in the
same way, purposes are defined according to the cateogries: discovery
is first regarding the organization of knowledge, for it is not possible to
organized what is unknown; and application is third, mediating between
“pure” discovery and organization. The categories also appear,
therefore, operating in the definition of the scientific method: to
abduction corresponds the category of firstness; to induction,
secondness; to deduction, thirdness. Indeed, the development of the
theory of categories appears as a decisive factor for redefining the
three kinds of reasoning as the three stages of inquiry145. A thorough
and deeper account of the matter demands a study of the manner how
phenomenological experience is organized according to the aspects of
being first, that is, possible, second, that is, having the character of
alterity, and third, that is, mediating between human beings and their
environment.146
Finally, we should notice the extremely artistic feature of
mathematics, justifying thus the first epigraph, by Murilo Mendes. As a
matter of fact, as mathematics is an activity depending largely upon
imagination, proximities with art are not few. Also the poet, for
instance, constructs possible worlds, devising imaginary hypothesis.
Take the following quotation:
145 Cf. KENT (1987); SANTAELLA (1992). 146 ROSENTHAL (1994) pp. 160 ff.
435
Modern mathematics is highly artistic. A simple theme is
chosen, some conception pretty and charming in itself.
Then it is shown that by simply holding this idea up to
one’s eye and looking trough it, a whole forest that
before seemed a thick and tangled jungle of bushes and
briers is seen to be in reality an orderly garden. [HP I:
492, The Century’s Great Men in Science].
The difference between mathematics and poetry is not in
imagination, but in the necessity obtained with mathematical
conclusions – in art, there is not and there is no need to be any
necessity in reasoning. But it seems that the most evident similarity is
not of mathematics with poesy, but – with music! Mathematics,
according to Peirce, is like music: the development of a theme, in an
unforeseen order. The reference to Bach is unequivocal: “The
intelligent listening to a fugue of Bach is certainly more like reading a
piece of higher mathematics that the lesson of the schoolboy in
elementary geometry is like the higher geometry.” [NEM 4: xiv]. Maybe
the creation of mathematical hypotheses is like writing the scores of the
divine music of the spheres.
436
10. CONCLUSION: ULRICH’S DILEMMA
believe it or notthis very if
is everything you gotPaulo Leminski
What thou lovest well remains, the rest is dross
What thou lov’st well shall not be reft from theeWhat thou lov’st well is thy true heritage
[…]The ant’s a centaur in his dragon world.
Ezra Pound, The Pisan Cantos, LXXXI
É o que eu digo, se for... Existe é homem humano. Travessia. ∞147
João Guimarães Rosa, Grande Sertão: Veredas
We can go back to the tension between the life of science that
asserts nothing as definite, and the commitment of each scientist with
the continuation of inquiry, as formerly presented: it seems the scientist
has no practical beliefs, but only theoretical beliefs. It is decisive to
know what are the aims when propositions are uttered, distinguishing
the act of merely saying from what is done in saying what is said, for
everything is resumed in knowing which are the expectations envolved
in the assertion of the truth of theories. If the truth of a hypothesis is
investigated, would the scientist be disappointed to discover its falsity?
In other words, would the scientist like to put his or her beliefs to test?
If the supreme aim of scientific inquiry is to reach the truth, even 147 Leminski’s poem was originally written in English. Guimarães Rosa’s book was translated into English with the title The Devil to Pay in the Backlands. The epigraph is the last sentence of the book, and it means: “That’s what I say, if it is… There exists human man. Traversion. ∞” Our translation.
437
though it is vague and inaccurate, the answer is: “yes”, the scientist
wants to test beliefs, even because he or she wishes for a truth less
vague and more accurate. However, it is possible that the scientist
begins to feel like Ulrich, the main character of Robert Musil’s The Man
Without Qualities148. In the novel, ambiented in the immediately pre-
First World War Europe, Musil pictures Ulrich as a “modern” man, who
living in a world dizzingly changing, in morals, in religion, in science, in
technology, in society, finds nothing permanent, the reason why Ulrich
lacks perspective; despite his good material conditions, Ulrich cannot
find a place to occupy in the world of modernity. Differently from
previous generations, in the modern world pictured by Musil, a person
cannot get or acquire “qualities”149, for all rigid certainties were
replaced by transitory truths; nothing remains the same and the sense
of a vanishing reality becomes imponent: there is no stability, but only
an acelerated process of changing takes place, impelled by the
application of scientific knowledge in the creation of new technologies
that modify ever more the way of human life. With the ever renewing of
the material aspect of society, and the simultaneous difference between
those countries that in a higher stage of economic development lead the
wordly technical progress, and those that being in a lower level of
148 For a connection between Peirce and Musil, see FINLAY (1990). The connections we propose here, however, are not exactly the same as the ones proposed by Finlay, whose main aim is to put forward a “discourse of knowledge” for contemporaneity as an alternative to what she calls the post-modern project, trying to recover the link (which was lost, according to her) between ethics, politics and the “discourse of knowledge”; such attempt, Finlay seeks to build upon Robert Musil’s literature, Peirce’s semiotics, and Werner Heisenberg’s physics.149 The German word “Eigenschaften” carries more resonances and ambiguities, and can be rendered as “characteristics”.
438
wealth try to keep up with such changes, the vital experiences –
“experience of space and time, of the self and others, of life’s
possibilities and perils” – shared by men and women all over the world
become diluted in a sensation of estrangement and vertigo:
To be modern is to find ourselves in an environment that
promises us adventure, power, joy, growth,
transformation of ourselves and the world – and, at the
same time that threatens to destroy everything we have,
everything we know everything we are. The
environmental experience of modernity can be said to
unite all mankind. But it is a paradoxical unity, a unity of
disunity; it pours us all into a maelstrom of perpetual
disintegration and renewal, of struggle and
contradiction, of ambiguity and anguish. To be modern is
to make part of a universe, wherein, As Marx said, “all
that is solid melts into air”.150
Marx and Engels statement, in the Communist Manifest, shows a
state of mind very peculiar to modernity, and sums up the disturbing
sensation of loss of references, caused by the subtle change of the
material conditions of society, in the so called “epoch of the
bourgeoisie”:
150This is taken from BERMAN (1986), p. 15. Some more from the continuing of this reasoning is interesting to what we are trying to say: “The maelstrom of modern life has been fed from many sources: great discoveries in the physical sciences, changing our images of the universe and our place within it; the industrialisation of production which transforms scientific knowledge into technology, creates new human environments and destroys old ones, speeds up the whose tempo of life, generates new forms of corporate power and class struggle; immense demographic upheavals, severing millions of people from their ancestral habitats, hurtling them halfway across the world into new lives; rapid and often cataclysmic urban growth; systems of mass-communication, dynamic in their development, enveloping and binding together the most diverse people and societies; increasingly powerful nation states, bureaucratically structured and operated, constantly striving to expand their powers; mass social movements of people, and peoples, challenging their political and economic rulers, striving to gain some control over their lives; finally, bearing and driving all these people and institutions along an ever-expanding drastically fluctuating capitalist world market. In the twentieth century, the social processes that bring this maelstrom into being and keep it in a state of perpetual becoming, have become known as ‘modernization’.” BERMAN (1982), pp. 15-16.
439
Constant revolutionising of production, uninterrupted
disturbance of all social conditions, everlasting
uncertainty and agitation distinguish the bourgeois
epoch from all earlier ones. All fixed, fast-frozen
relations, with their train of ancient and venerable
prejudices and opinions, are swept away, all new-formed
ones become antiquated before they can ossify. All that is
solid melts into air, all that is holy is profaned, and man
is at last compelled to face with sober senses his, real
conditions of life, and his relations with his kind.151
It is the velocity of such radical transformations that make Ulrich,
Robert Musil’s man without qualities, fell deep the bewilderment and
the disintegration, recognizing himself to be untimeous to the epoch he
is living in. It is the insight of such fragmentation that characteristically
distinguishes the art we call modern, for instance. Musil’s novel focus
just on these aspects. Ulrich’s world is put together as a world of
appearances that seems to be the substitute for another world also
made up of appearances:
Was ist also abhanden gekommen? Etwas Unwägbares.
Ein Vorzeichen. Eine Illusion. Wie wenn ein Magnet die
Eisenspäne losläßt und sie wieder durcheinandergeraten.
Wie wenn Fäden aus einem Knäuel herausfallen. Wie
wenn ein Zug sich gelockert hat. Wie wenn ein Orchester
zu spielen anfängt. Es würden sich schlechterdings keine
Einzelheiten haben nachweisen lassen, die nicht auch
früher möglich gewesen wären, aber alle Verhältnisse
hatten sich ein wenig verschoben. Vorstellungen, deren
Geltung früher mager gewesen war, wurden dick.
Personen ernteten Ruhm, die man früher nicht für voll
151 MARX; ENGELS (1848), p. 5 of the S. Moore translation.
440
genommen hätte. Schroffes milderte sich, Getrenntes lief
wieder zusammen, Unabhängige zollten dem Beifall
Zugeständnisse, der schon gebildete Geschmack erlitt
von neuem Unsicherheiten. Die scharfen Grenzen hatten
sich allenthalben verwischt, und irgendeine neue, nicht
zu beschreibende Fähigkeit, sich zu versippen, hob neue
Menschen und Vorstellungen empor. Die waren nicht
schlecht, gewiß nicht; nein, es war nur ein wenig zu viel
Schlechtes ins Gute gemengt, Irrtum in die Wahrheit,
Anpassung in die Bedeutung. Es schien geradezu einen
bevorzugten Prozentsatz dieser Mischung zu geben, der
in der Welt am weitesten kam; eine kleine, eben
ausreichende Bemeingung von Surrogat, die das Genie
erst genial und das talent als Hoffnung erscheinen ließ,
so wie ein gewisser Zusatsz von Feigen- oder
Zichorienkaffe nach Ansicht mancher Leute mit
einemmal waren alle bevorzugten und wichtigen
Stellungen des Geistes von solchen Menschen besetzt,
und alle Entscheidungen fielen in ihrem Sinne. Man kann
nichts dafür verantwortlich machen. Man kann auch
nicht sagen, wie alles so geworden ist. Man kann weder
gegen Personen noch gegen Ideen oder bestimmte
erscheinungen kämpfen. Es fehlt nicht an Begabung noch
an gutem Willen, já nicht es ist, als ob sich das Blut oder
die Luft verandert hätte, eine geheimnisvolle Krankheit
hat den Kleinen Ansatz zu Genialem der früheren Zeit
verzehrt, aber alles funkelt von Neuheit, und zum Schluß
weiß man nicht mehr, ob wirklich die Welt schlechter
geworden sei oder man selbst bloß älter. Dann ist
endgültig eine neue Zeit gekommen.152
152 MUSIL (1999), chapter 16: “Eine geheimnisvolle Zeitkrankheit”, pp. 57-58.
441
Ulrich, then, seeking a life directed by values minimally constant,
turns to science, and exactly to the most abstract of them, mathematics.
Let us see:
Und so hat es auch schon damals, als Ulrich
Mathematiker wurde, Leute gegeben, die den
Zuzammenbruch der eupäischen Kultur voraussagten,
weil kein Glaube, keine Liebe, keine Einfalt, keine Güte
mehr im Menschen wohne, und bezeichnenderweise sind
sie alle in ihrer Jugend- und Schulzeit schlechte
Mathematiker gewesen. Damit war später für sie
bewiesen, daß die Mathematik, Mutter der exakten
Naturwissenschaft, Großmutter der Technik, auch
Erzmutter jenes Geistes ist, aus dem schließlich Giftgase
und Kampfflieger aufgestiegen sind.
In Unkenntnis dieser Gefahren lebten eigentlich nur die
Mathematiker selbst und ihre Schüler, die Naturforscher,
die von allendem so wenig in ihrer Seele verspürten wie
Rennfahrer, die fleissig darauf los treten und nichts in
der Welt bemerken wie das Hinterrad ihres
Vordermanns. Von Ulrich dagegen konnte man mit
Sicherheit das eine sagen, dass er die Mathematik liebte,
wegen der Menschen, die sie nicht ausstehen mochten.
Er war weniger wissenschaftlich aus menschlich verliebt
in die Wissenschaft.153
Ulrich seeks for science. First, by the passage above, we see he
does not share the belief that science (mathematics, in this case)
necessarily leads to the production of technical means for anihilating
life. He does not either thinks of science as an actiity closed in itself,
narrow sighted, without any concern regarding the wider horizon of the
153 Idem, chapter 11: “Der wichtigste Versuch“, p. 40.
442
cultural and historical context of human life. Ulrich, in this sense,
neither was a scientist like a ciclist, who only had eyes for the whell of
the runner ahead; nor he was a fake humanist, denouncing the crimes
of technique: he was someone “humanly in love with science”, someone
who had become a mathematician because he was in love with it, and
took the decision to oppose the demonizing image of mathematics as
the cause for all the bad thing in the world, opposing in this way its
obscurantist adversaries:
Man braucht wirklich nicht viel darüber zu reden, es ist
den meisten Menschen heute ohnehim klar, daß die
Mathematik wie ein Dämon in alle Anwendungen unseres
Lebens gefahren ist. Vielleicht glauben nicht alle diese
Menschen an die Geschichte vom Teufel, dem man seine
Seele verkaufen kann; aber alle Leute, die von der Seele
etwas verstehen müssen, weil sie als Geistliche,
Historiker und Künstler gute Einkünfte daraus beziehen,
beseugen es, daß sie von der Mathematik ruiniert bilde,
der den Menschen zwar zum Hernn der Erde, aber zum
Sklaven der Maschine mache.154
This image causes the impression that “all the evils of our time” –
“evilness, the incredible coldness of hear, greed, cruelty, and violence”
(to name just a few) – would result from the increasing influence of
mathematics in practical life, through technology produced according
to the rules of capitalist industrial production. This judgment seems to
Ulrich as quite mistaken, for it leads to the idea of the nature of science
as a cold specialized activity, unconnected from the wider context of
154 Id.,ibidem, p. 39-40.
443
human life – as if the scientist was a bicicle runner. In truth,
apassionate dedication is needed in science, it is needed to make it a
form of life. If this idea is put aside all the transformative and
sublimatory power of science is lost. Ulrich muses:
Wenn man statt wissenschaftlicher Anschauungen
Lebensanschauung setzen würde, statt Hypothese
Versuch und statt Wahrheit Tat, so gäbe es kein
Lebenswerk eines ansehnlichen Naturforschers oder
Mathematikers, das na Mut und Umsturzkraft nicht die
größten Taten der Geschichte weit übertreffen würde.155
Ulrich is successful in science, and not just a little, if we trust
what the narrator tells us. Talented, he becomes a hope, and gets some
acknowledgment. However, he soons perceives that the life of science
will not bring him what he hopes for. Signs of his delusion appear when
he faces difficulties in obtaining recognition for his efforts, due to the
hierarchical bureaucracy of the scientific academy; Ulrich then sees
that “even in the kingdom of truth only older wises are admired, upon
whom the obtaining of a masters or of the chair in the unversity
depends.”156 But the last drop to convince him to give up one more
attempt to become a man with qualities comes from the news on a
genial horse in the races:
Und eines Tag hörte Ulrich auch auf, eine Hoffnung sein
zu vollen. Es hatte damals schon die Zeit begonnen, wo
man von Genies des Fußballrasens oder des Boxrings zu
sprechen anhub, aber auf mindestens zehn geniale
155 Id., ibid., p. 40. 156 Ibid., p. 33, chapter 8.
444
Entdecker, Tenöre oder Schriftsteller entfiel in den
Zeitungsberichten noch nicht mehr als höchstens ein
genialer Centerhalf oder großer taktiker des
Tennissports. Der neue Geist fühlte sich noch nicht ganz
sicher. Aber gerade da las Ulrich irgendwo, wie eine
vorverwehte Sommerreife, plötzlich das Wort “das
geniale Rennpferd”. Es stand in einem Bericht über einen
aufsehenerregenden Rennbahnerfolg, und der Schreiber
war sich der ganzen Größe des Einfalls vielleicht gar
nicht bewußt gewesen, den ihm der Geist der
Gemeinschaft in die Feder geschoben hatte. Ulrich aber
begriff mit einemmal, in welchem unentrinnbaren
Zusammenhang seine ganze Laufbahn mit diesem Genie
der Rennpferd stehe. Denn das Pferd ist seit je das
heilige Tier der Kavallerie gewesen, und in seiner
Kasernenjugend hatter Ulrich kaum von anderem
sprechen hören als vonPferden und Weibern und war
dem entflohn, um ein bedeutender Mensch zu werden,
und als er sich nun nach wechselvollen Anstrengungen
der Höhe seiner Bestrebungen vielleicht hätte
nahefühlen können, begrüßte ihn von dort das Pferd, das
ihm zuvorgekommen war.157
Now, how is it possible to have some quality in a world where
horses for races are genial? The ideal of “genius and greatness” of the
“antique” world one day Ulrich knew was replaced, in the scale of
modern values, by the quantifiable and measurable objectivity of a
horse race – or a boxing fight: “the sport and the objectivity deservingly
advanced” 158. The hurry, the “impetus”, the “velocity” and the “frauds”
of the modern world fatally hit Ulrich’s image of the world. That
157 Ibid., p. 44, chapter 13.158 Id., ibid.
445
induces him to conclude that also the scientific life, to which he
dedicated himself with sincere perseverance, leads to nowhere in the
modern world. The “pleasure in the power of mind”, the “expectation”
that is as “a kind of undefined imperious right on the future” is worthy
of nothing in this world; as a matter of fact, “he did not know very well
whereto he would be led with such strength; one could do everything or
nothing at all with it, to be a savior of the world or a criminal.” 159 The
spiritual preparation offered by science was substituted for the
preparation of muscles; and this appears to Ulrich as decadence, and
even as a useless and stupid illusion, once no adventure comes to make
such athletic preparation useful. Ulrich’s disenchantment is then
expressed by the narrator:
Seine Meinung war, man befinde sich in diesem
Jahrhundert mit allem Menschlichen auf einer
Expedition, der Stolz verlange, daß man allem unnützen
Fragen ein “Noch nicht“ entgegensetze und ein Leben
mit Interimsgrundsätzen, aber im Bewußtsein eines Ziels
führe, das später Kommende erreichen werden. Die
Wahrheit ist, daß die Wissenschaft einen Begriff der
harten, nüchternen geistigen Kraft entwickelt hat, der
die alten metaphysischen und moralischen Vorstellungen
des Menschengeschlechtes einfach unerträglich macht,
obgleich er an ihre Stelle nur die Hoffnung setzen kann,
daß ein ferner Tag kommen wird, wo eine Rasse geistiger
Eroberer in die Täler der seelischen Fruchtbarkeit
niedersteigt.
159 Ibid.
446
Das geht aber nur so lange gut, wie man nicht
gezwungen wird, den Blick aus seherischer Ferne auf
gegenwärtige Nähe zu richten, und den Satz lesen muß,
daß inzwishcen ein Rennpferd genial geworden ist.160
Now, it seems clear to us that Ulrich’s image of science resembles
in several respects Peirce’s concept of science. We focus the following
contact points:
1) Science is an activity that has to be sincerely practiced. In
effect, just as Musil links Ulrich’s passion to mathematics, we can think
that the revolutionary power of science comes exactly from its being
practiced with the wholehearted frame of mind of sincerity and honest
attitude. Science practice sincerely allows for a synoptic view of the
whole of human life, making it possible a better grasp of the particular
and the individual.
2) Hence, opposed to the idea of specialization and individuation
of knowledge and reason, scientific life would be an alternative to the
“dryness of inward life, the monstrous mix of sensitiveness to the
details and indifference to the whole.”161
3) The life of science, transforming all beliefs and old habits,
builds an upward pathway, “as a stairway to heaven”. Its wildest
dreams allow us to think differently, rendering scientists (and all
present mankind, we could say) accountable as to the future. Science,
then, is a prospective activity.
160 Ibid., p. 46.161 Ibid. p. 40-41, chapter 11.
447
4) This prospective character of science renders all present
certainties instable and provisional; in their places it sets up the hope
that, in future, in the long run, truth shall be discovered, and the
present effort of inquiry will be waged.
Now, to know if the life of science is worthy of living is to answer
to the question about the conformation of means to ends. Science
viewed as a projective activity, as an open inquiry, has not an
immediate end, a practical objective given beforehand; judging by the
status of mathematics in the classification of the sciences, the supreme
aim aimed at appears in such a way that science may be understood as
a practice of inventing possibilities, distinguished from technique, to
which the ends are ab ovo defined. Examining the image of science
conveyed by Ulrich’s metaphors, we see that the similitude to Peirce’s
concept of science is not so big as it may seem.
Musil pictures the spirit of an age quite according to the
diagnosis made by Max Weber. In his writing Wissenschaft als Beruf,
Weber points out to the fact that, in the 20th century, science is brought
about as a vocation through specialization. The technical-scientific
process of rationalization reached by humanity puts the question on the
possibility of the scientist being conscious about his or her own activity,
within the context of the industrialist capitalism of the early 20th
century. Weber states Ulrich’s dilemma in an exemplary way, in terms
of the opposition between the ever more specialized scientific work and
448
the sense of science, as the projective activity towards the universal. In
effect, to Weber, the “sense” of the scientific work is opposed to the
artistic. While in art the artist’s realizations remain without ever aging,
science is directed to its own overcoming:
Jeder von uns dagegen in der Wissenschaft weiß, dass
das, was er gearbeitet hat, in 10, 20, 50 Jahren veraltet
ist. Das ist das Schicksal, ja: das ist der Sinn der Arbeit
der Wissenschaft, dem sie, in ganz spezifischem Sinne
gegenüber allen anderen Kulturelementen, für die es
sonst noch gilt, unterworfen und hingegeben ist: jede
wissenschaftliche »Erfüllung« bedeutet neue »Fragen«
und will »überboten« werden und veralten. Damit hat
sich jeder abzufinden, der der Wissenschaft dienen will.
[...] Wir können nicht arbeiten, ohne zu hoffen, dass
andere weiter kommen werden als wir. Prinzipiell geht
dieser Fortschritt in das Unendliche. Und damit kommen
wir zu dem Sinnproblem der Wissenschaft.162
It could not be made more explicit: the end of all is to walk
towards the overcoming [Überholung] of the actual stage, and it is
towards this surpassing that science is also directed. More: one could
say that science drives such overcoming.
Apparently, nothing Weber says is foreign to what we have
already seen Peirce saying. And, as a matter of fact, the idea that
science is directed to the future, that its conclusions are mere probable
hypotheses, that everything can be changed all of a sudden, are dear
ideas to both authors. However, there is an essential difference.163 To
162 WEBER (1995a), p. 17.163 Besides several others we will not try to unfold in this work, as for instance, the difference in the treatment each one gives of scientific progress, an expression Weber uses more characteristically than Peirce, one
449
Weber, science is an activity unconnected from the world of value – the
scientific work, in contradistinction to every other elements of culture,
is conceived by Weber as the accomplishment of western Reason in its
highest degree of technological development; in the capitalist world of
the 20th century, science for Weber is settled in a domain of axiological
neutrality, what results in the demystifying of the world, to the
elimination of “magic”, effected through the “increasing rationalization
and intellectualization”:
The growing intellectualization and rationalization do not
mean therefore a growing general knowledge of the
general conditions of our life. Their meaning is quite
different: they mean that it is known or believed that at
any moment that it is wanted it is possible to know; that,
therefore, there are not occult and unpredictable powers
around our lives, but rather that on the contrary
everything can be dominated through calculus and
prediction. This means only that the magic is excluded
from the world. On the contrary to the savage, to whom
there are such powers, we do not nave anymore to use
magical means to control or to make spirits peaceful.
This is accomplished due to technical means and to
prediction. Such is in essence the meaning of
intellectualization. 164
The separation between to be and must be, as H. Marcuse says,
leads to the weberian conception of science showing just the opposite
of what Weber intended: “an attempt to ‘freed’ science, in order to put
should notice. For an account in more detail of Max Weber’s thoughts, see for instance, HABERMAS (1991), cap. II: “Max Weber’s Theory of Rationalization”.164 WEBER (1995a), p. 19.
450
it into conditions of accepting obligatory values, the origin of which
rests precisely outside it.”165 In such way, two dimensions of human life
are isolated one from another: the one of the questions of value and the
one of the questions of technique. Scientific rationality is seen from a
very individualistic and deterministic point of view, according to the
pattern of a technical rationality oriented towards specific aims,
characterized by a distinct “purposive rational action”, in Habermas’
famous expression166. And such ends, we may add, are particular and
directed towards immediate accomplishments, justifying the idea that
the only certainty or scientific belief is the one of the certain knowledge
and of the domination through calculus and prediction. Scientific
neutrality, contrary to Weber’s pretension, cannot be sustained, given
Weber’s own account of the development of the worldly capitalism:
The pure philosophical and sociological conception
established outside the circle of values is converted in
the course of its own development into a criticism of
those same values. And the inverse is equally valid: pure
and value-void scientific concepts reveal their own
system of tacit values. They are converted into a criticism
of data, in the light of what such data impose to the man
and to the world. “What ought to be” reveals as “what
is”. It is the inexhaustible dynamics of the concept that
uncovers it.167
165 Marcuse’s text “Industrialization and capitalism in the work of Max Weber”, was used in the Portuguese edition of Wissenschaft als Beruf: O Político e o Cientista, pp. 9-44; this quotation is from p. 10. See bibliography for complete references.166 HABERMAS (1991), p.145-146.167 MARCUSE, op. supra cit., pp. 11-12.
451
Now, according to our judgment, Ulrich’s dilemma is valid within
this context of industrial capitalism of the early 20th century, such as
describe by Weber. The world Musil pictures in The Man Without
Qualities is such that, on the one hand, the Weberian description of the
process of scientific rationalization is valid and brought about by the
development of the capitalism; on the other hand, the criticisms made
to it cannot offer in alternative to this model of technical rationality
another conception of science. No wonder Ulrich feels lost, fascinated
as he was for science.
The establishment of science as a market business, technique and
science as ideology, so to say, are dear themes to the 20th century. For
instance, to sum up, remember the words of the Brazilian geographer
Josué de Castro:
It happens that these scientists can find payment only
when their works are interesting to someone, whether
the industry, the private initiative or the State. Now, in
this last century of western culture, the State, the
institutions and the bosses have deviated their interests
to the problems of economic exploration, problems of
production and wealth creation, becoming in general
disinterested of human problems. Almost only seeing
man as a machine for production, as a gear of their
technical economicism.168
168 CASTRO (1968), p. 143. Our translation; see the original: “Acontece que estes cientistas só encontram pagamento quando os seus trabalhos são do interesse de alguém, seja este alguém a indústria, o particular ou o Estado. Ora, neste último século de cultura ocidental, o Estado, as instituições e os patrões desviaram os seus interesses para os problemas de exploração econômica, problemas de produção e de criação de riquezas, desinteressando-se em geral pelos problemas humanos. Quase que só vendo o homem como máquina de produção, como uma engrenagem de seu economismo técnico.”
452
According to Josué de Castro, the “mechanicist and utilitarist”
western civilization, because of its “eager desire for dominating the
powers of nature through technique to enslave them”, in truth, “ended
in enslaving man to this technique”169. Notice there is not, to Josué de
Castro, as there was to Max Weber, an idea of strictly separating the
world of values and the world of technique, for the fact that there is not
a condemnation of all science and all technique. The Brazilian
geographer in fact urges for a change in perspective, a better
application of the scientific knowledge, according to the historical
perspective:
The discoveries in the field of atomic energy are rapidly
employed in the destruction of the world, but the
discoveries that are conductive to the salvation are
crawling in marasmus for which there is no explanation…
Something has to change, so that we can steadily affirm
we live in a scientific age. Meanwhile, science has been
only a myth – the new myth in which the most ardent
hopes of a great part of mankind are concentrated.170
Now, according to our account, such statements go very well
along Peirce’s, showing the back door of a myth of science: a door that
opens to the utilitarianism of profits disguised in the highest human
aims. Remember Peirce’s criticisms to Karl Pearson, who claimed that
science should serve society. In the way we understand, there is no
169 Id., p. 141. Our italics.170 Id., ibid., our translation; cf. the original: “As descobertas no campo da energia atômica são rapidamente aplicadas na destruição do mundo, mas as descobertas que conduzem à salvação, se arrastam num marasmo sem explicação... Alguma coisa precisa mudar, para que possamos afirmar com convicção que vivemos numa era científica. Por enquanto, a ciência tem sido apenas um mito – o novo mito no qual se concentram as mais ardentes esperanças de uma grande parte da humanidade.”
453
substantial difference between Peirce’s claims and the idea of the
redirection scientific applications defended by Josué de Castro. Not that
our geographer had read Peirce. And, more that showing Peirce as a
precursor – as if he was only one more precursor – we want to show the
historical persistence of certain problems, to make the critical value of
Peirce’s thought come to the surface; problems of today that he, in the
19th century, was already well aware of.
We have already pointed out some connexions between ethics and
pragmatism; this latter understood as a definition of a horizon of ends.
The idea of horizon in Kantian philosophy has to do with the illuminist
ideal of the possibility of self-determination of mankind. The pragmatic
horizon is defined by Kant in terms of the influence of a given
knowledge on our moral conducts [Sittlichkeiten], indicating that the
convergence between human knowledge and ends depends on a
determination of the will: for what ends we want to converge? 171 The
answer to this question, according to Kant, involves the answer to the
three questions of essential interest for human reason: what can I
know? What should I do? What could I licitly wait? [KrV A 805/ B 833].
This three questions define de domains of metaphysical speculation, of
morals, and of religion, respectively, and can be resumed in one
anthropological question: what is man? 172
171 KANT (1799-1800), Ak. 40-41.172 Id., Ak 25.
454
As a matter of fact, a more detailed account of the connexions
between pragmatism and Kantian morals would have to deal more
thoroughly with Kant’s anthropology, what it is impossible for us to
accomplish here, as just now mentioned. However, some comments can
be done, in order to get a more light upon the issue. It is in the
Anthropology that the ideas of horizon and pragmatic imperative
appear in a more defined way, linked to the idea that the human being
is simultaneously a sensitive natural being [sinnlichen oder
Naturwesens] and a rational being endowed with freedom [eines
vernünftigen, mit Freiheit begabten Wesens]. What makes an
anthropology characteristically pragmatic is the fact that the reflection
“on what man makes, can, or should make of himself as a freely acting
being [frei handelndes Wesen]”.173 The anthropology from a pragmatic
point of view, in this way, is “knowledge of the world” with the purpose
of understanding the human being as a natural being and as “citizen of
the world” 174. It is interesting that human freedom is seen as the ability
to actually interact within a context of play:
Let it be remarked that such anthropology, understood as
knowledge of the world, that has to be continued after
school, is not yet properly called pragmatic so long as it
contains extended knowledge of the things in the world,
such as animals, plants, and minerals in various lands
and climates. It is properly pragmatic only when it
incorporates knowledge of Man as a citizen of the world.
173 KANT (1798), Ak. 119, Vorwort.174 Id., ibid., Ak 120.
455
– Hence even knowledge of the races of man, which are
regarded as products of the play of Nature, is not yet
pragmatic, but only theoretical knowledge of the world.175
For such reason, there are two distinct senses of the human
situation in the world, that are knowing the world, in which situation
human beings are as simply spectators, and having the world, in which
situation human beings enter into play.176 Human freedom for acting in
this play is so plain that they get to exert power over nature,
dominating; and the radical character of human freedom conduces to
the manifestation of a tendency to overwin the freedom of other human
beings, taking them as means to attain private particular ends:
“Controlling the inclinations of other people in order to direct and
manage them according to one’s own intentions, almost amounts to
being in possession of them as mere instruments of one’s own will.”177
Because of such radical aspect of human freedom, Kant even defines a
notion of semiotica universalis, that is, a general and natural theory of
signs, opposed to the civil theory of signs, with the purpose of studying
the character [Charakter] of human beings in their interactive play with
nature and other human beings.178 Human freedom is defined in the
175 Id., ibid. Translation slightly modified; see the original: „Eine solche Anthropologie, als Weltkenntnis, welche auf die Schule folgen muß, betrachetet, wird eigentlich alsdann noch nicht pragmatisch gennant, wenn sie ein ausgebreitetes Erkenntnis der Sachen in der Welt, z. B., der Tiere, Pflanzen und Mineralien in vershciedenen Ländern und Klimaten, sondern wenn sie Erkenntnis des Menschen als Weltbürgers enthält.. – Daher wird selbst die Kenntnis der Menschenrassen als zum Spiel der Natur gehörender Produkte noch nicht zur pragmatischen, sondern nur zur theoretischen Weltkenntnis gezählt.“176 Id., ibid.177 id., ibid., § 84, Ak. 271. Nossa tradução: „Denn anderer Menschen Neigungen in seine Gewalt zu bekommen, um sie nach seinen Absichten lenken und bestimmen zu können, ist beinahe ebensoviel als im Besitz anderer, als blößer Werkzeuge seines Willens, zu sein.“178 Ibid., § 89, Ak. 285.
456
Anthropology, then, as the capacity to pass from the state of nature to
the state of freedom, and critical philosophy seeks to explain this
passage.
Let us go back to Ulrich. Where is his dilemma after all?
According to our account, it is possible to understand it as a lack of
horizon, or better as the lack of understanding his horizon:
Ganz das gleiche ist mit der Liebe der Fall, auf die der
Mensch in der ungeheuerlichsten Weise vorbereitet wird,
und schileßlich entdeckte Ulrich noch, daß er auch in der
Wissenschaft einem Manne glich, der eine Bergkette
nach der anderen überstiegen hat, ohne ein Ziel zu
sehen. Er besaß Bruchstücke einer neuen Art zu denken
wie zu fühlen, aber der anfänglich so starke Anblick des
Neuen hatte sich in immer zahlreicher wervdende
Einzelheiten verloren, und wenn er geglaubt hatte, von
der Lebensquelle zu trinken, so hatte er jetzt fast alle
seine Erwartung ausgetrunken.179
As a matter of fact, the dilemma appears now even more clearly,
when Ulrich perceives he is “more distant from what he wished to be
than he felt when he was young, if he ever knew what he wished.” 180
The character’s perplexity is well described by the narrator: Ulrich
recognizes in himself “all the capacities and qualities that his time high-
praised”, but, at the same time, he is completely unable to apply
them.181 Ulrich’s dilemma, therefore, such as we understand it, is in his
incapacity to define a pragmatic horizon to allow, in a general way,
179 MUSIL (1999), p. 46-47, chapter 13.180 Id., p. 47.181 Id., ibid.
457
shaping present conduct, having in sight the aimed ends, which can be
then seen as regulative ideals.
It seems to us also that the proximity of pragmatism with certain
respects of the ideal of the Kantian philosophy is plain. The difference
would be, on our account, in that Peirce, grounded in his semiotic
theory of the thought-sign, abandons the distinction among the
different uses of reason (the speculative and the practical), unifying all
the interests in one single horizon. In fact, the schematism of the
categories in the first Critic sought to solve the problem of how to
understand the scission between the grounding of the conditions of
validity of knowledge and the question of the rational validation of
knowledge; in other words, the schematism was concerned with how to
explain the application of the categories to the experience, and then
completing the transcendental deduction.
Peirce is quite aware of such problems. With his philosophy of
mathematics, it is clear that he abandons the way Kant deals with the
issue of the schematism. There being no further separation between the
faculty of imagination, which produces the schemes, and the rational
faculty of judgment, which applies the schematized concepts to
experience, there is no more the separation between distinct uses of
reason, the practical and the speculative, as there was for the
philosopher from Königsberg. In Kantian terms, one could say that the
sign’s function of meaning forces the understanding to translate and
458
interpret experience remittently, involving the recognition of the
regularities and the functioning of thought in the semiosis of the
interpretants, unifying the uses of reason, subject and object, in one
domain of meaning, continuous creation, and interpretation of signs.182
In this way, as the supreme ends of morality, metaphysics and
religion are not anymore distinct one from another, the answer to the
problem of defining horizons depends upon the logical coherence of the
thought of all mankind, such coherence being obtained only with the
adhesion and the trust of each individual in the collective inferences, in
a thoroughly and always self correctable process of induction, as we
have seen. Thus, as in Leminski’s poem, everything one has is an if, a
mere if – a hypothetical imperative, like a precept of prudence
[Ratschläge der Klugheit] to guide the conduct in the definition of
means to attain a supreme finality of all rational beings, such as Kant
says in the Groundworkings of the Metaphysics of Morals183. Now,
pragmatism could only be guided indeed by a hypothetical manner of
putting the ends, since the criticism to Kant’s logic showed it was
impossible to distinguish between categorical and hypothetical
propositions. Besides, the attunement of pragmatism with the idea of
the agreement of individual interests with the interests of the
community of inquiry demands that there is no a priori determination of
182 ROSENTHAL (1990), pp. 197.183 KANT (1785), Ak. 415-416. In the Anthropology, the maxims of prudence are identified with the techno-practical reason [technisch-praktischen Vernunft]. Cf. KANT (1798), § 84, Ak. 271. We do not intend with such brief remarks to exhaust the theme of the relations of Peirce’s pragmatism and Kant’s pragmatic anthropology, but only to suggest it, opening the way for a a possible recollection of it in a further occasion.
459
the domain of ought to be, once the ideally aimed truth would be
fallible, because it is semiotically mediated.184
In such way, a consideration on politics from a Peircean
perspective has to embrace the idea of the communicative activity of
science, so that possible to privilege public and collective means for
questioning the assertions and the results of inquiry. In this way, it
cannot deal with the relation between theory and practice privileging
the role to the first over the second, or vice-versa, for that would mean
to submit one to the authority of the other, blocking the way of inquiry.
In his criticisms to Karl Pearson’s ideas, as well as to what he used to
call the Gospel of Greed [EP 1: 357, Evolutionary Love, 1893], we see
that Peirce’s clear concern on the insubordination of theory to practice
is unfolded in two directions: first, theory should not be submitted to
practice because the immediate (and imediaticist) concerns of the
individual or of a finite community are not ultimate, in the widest sense
of such word; they may be vital for the individual, but that does not
mean that they are ultimate and final to the collectivity; second, inquiry
(and not the application of its results) is teleonomically oriented to the
future, and it does not need always follow the aims and objectives
defined by present society, whatever it is.185 That is, then, how the ideas
of truth as a regulative ideal and the idea of the definition of a
pragmatic horizon converge.
184 SILVEIRA (1980) and (2000).185 ANDERSON (1997), p. 227.
460
The idea of truth, as a sign of a general nature to which inquiry
would converge in the long run, is not an affirmation that the
affirmations of a finite group of research will be true, in case this group,
which is indeed competent, follow its investigations for a certain span
of time. Truth in Peirce’s philosophy is defined in terms of the
correspondence between sign and its object, independently of any
sociologically or ideologically limited opinion, since such
correspondence is not actualized, because it is defined in terms of its
possibility of actualization, if inquiry is carried indefinitely, by the right
methods.
The correlation between the conceptions of reality and truth is
central. Take the following passage:
A figment is a product of somebody's imagination; it has
such characters as his thought impresses upon it. That
whose characters are independent of how you or I think
is an external reality. There are, however, phenomena
within our own minds, dependent upon our thought,
which are at the same time real in the sense that we
really think them. But though their characters depend on
how we think, they do not depend on what we think those
characters to be. Thus, a dream has a real existence as a
mental phenomenon, if somebody has really dreamt it;
that he dreamt so and so, does not depend on what
anybody thinks was dreamt, but is completely
independent of all opinion on the subject. On the other
hand, considering, not the fact of dreaming, but the thing
dreamt, it retains its peculiarities by virtue of no other
fact than that it was dreamt to possess them. Thus we
461
may define the real as that whose characters are
independent of what anybody may think them to be. [W
3: 136-137, How to Make Our Ideas Clear].
The difference between fiction and reality is confirmed in the
absence of an objecting object in fiction. Reality has the character of
alterity, of being an opposite to thought, what settles the conditions
minimally necessary of the criteria by means of which to define what is
a true representation, from the point of view of the conformity with
facts. Effectively, the difference between fiction and reality is entirely
understood by the fact that, in objecting to consciousness, reality has
the power of shaping conduct and fixing belief: “The only effect which
real things have is to cause belief, for all the sensations which they
excite emerge into consciousness in the form of beliefs.” [id.] Fiction
does not settle beliefs, for it is lacking the being permanent of alterity,
which is an essential characteristic of the exterior object to the
representation:
The being of a sign is merely being represented. Now
really being and being represented are very different.
Giving to the word sign the full scope that reasonably
belongs to it for logical purposes, a whole book is a sign;
and a translation of it is a replica of the same sign. A
whole literature is a sign. The sentence “Roxana was the
queen of Alexander” is a sign of Roxana and of
Alexander, and though there is a grammatical emphasis
on the former, logically the name “Alexander” is as much
a subject as is the name “Roxana”; and the real persons
Roxana and Alexander are real objects of the sign. Every
sign that is sufficiently complete refers to sundry real
462
objects. All these objects, even if we are talking of
Hamlet’s madness, are parts of one and the same
Universe of being, the “Truth”. [EP 2: 304, ].
As fictional objects are constructed by the sign, that which is said
of the object is not different from the way how it is said; form of
presentation and form of representation are therefore confounded. In
the representations of reality it is otherwise, for such amalgam does not
exist: the way how to say is defined by the object of what something is
said. Thus, science, whose truth depends on the real, is as a matter of
fact an activity that tries to discover the behaviour of the object, so that
inquiry is continuous with reality, and in its limit-horizon, in the long
run, the permanence of the real will lead us to think that the object is in
such way, and not otherwise. In other words, the object is a
determining subject of our representations, so that the continuation of
inquiry will arrive at a representation of a general nature, which is
structurally isomorphic to the conduct of the object, representing it
independently of whatever particular and subjective idiosyncrasies in
an icon. In other words, experience, because it objects, is also subject
of thought; it is experience that makes us think, that conduces us to
think in the existence of things because things react against us, shaping
our conduct, making us conscious of ourselves:
We are continually bumping up against hard fact. We
expected one thing, or passively took it for granted, and
had the image of it in our minds, but experience forces
that idea into the background, and compels us to think
463
quite differently. You get this kind of consciousness in
some approach to purity when you put your shoulder
against a door and try to force it open. You have a sense
of resistance and at the same time a sense of effort.
There can be no resistance without effort; there can be
no effort without resistance. They are only two ways of
describing the same experience. It is a double
consciousness. We become aware of ourself in becoming
aware of the not-self. The waking state is a consciousness
of reaction; and as the consciousness itself is two-sided,
so it has also two varieties; namely, action, where our
modification of other things is more prominent than their
reaction on us, and perception, where their effect on us
is overwhelmingly greater than our effect on them.186 [CP
1.324, Lowell Lecture III, 1903].
As we can see by the passage above, there are no absolute
dichotomies between subject and object, since experience appears as
architect of its own representation. In fact, it is experience that allows
us to give the step from appearing to being, and vice-versa, also the
step that goes from the recognition of an existence different from ours
to the representation of such existence:
When we say that a thing exists, what we mean is that it
reacts upon other things. That we are transferring to it
our direct experience of reaction is shown by our saying
that one thing acts upon another. It is our hypothesis to
explain the phenomena, – a hypothesis, which like the
working hypothesis of a scientific inquiry, we may not
believe to be altogether true, but which is useful in
enabling us to conceive of what takes place. [CP 7.534,
On Topical Geometry, in General].
186 Cf. IBRI (1992), pp. 27-28 e (1999).
464
[And yet:] Whatever exists, ex-sists, that is, really acts
upon other existents, so obtains a self-identity, and is
definitely individual.187 [EP 2: 343, What Pragmatism Is].
The application of the pragmatic maxim to the metaphysical
debate on the nature of truth and reality fortifies the connexion
between the effective practice of science and its orientation to the
general future truth. If, as Peirce claimed in 1878, the method of
science is the best to fix beliefs, it is needed to conciliate the idea that
the practice of science is essentially revolutionary with the adoption of
a living belief, and at the same time, a belief which is regulative of
conduct, even though it is only provisional. In other words, we cannot
take science as an ideology, for this would justify the Weberian image
of technical rationality, making us remain in the perplexity of Ulrich’s
dilemma. The philosopher should look to our quotidian practices and to
attempt at discovering which account of truth would be more adequate:
“We must not begin by talking of pure ideas, – vagabond thoughts that
tramp the public roads without any human habitation, – but must begin
with men and their conversation.” [CP 8.112, Josiah Royce’s The World
and the Individual, 1900]. This anchorage in common experience of
human beings refuses all and any possible axiological neutrality of
science – as a matter of fact, all and any possible inquiry, in so far as it
is a collective effort having its start interhomines should take into
187 On the issue of experience as subject causing representations, see IBRI (1992), pp. 27-28; (1999), passim; (2003b), passim.
465
account all presuppositions, principles, hypotheses, sentiments,
emotions, prejudices, and instincts, from the beginning:
Although inquiry is to be an inquiry into truth, whatever
the truth may turn out to be, and therefore of course is
not to be influenced by any liking for pragmatism or any
pride in it as an American doctrine, yet still we do not
come to this inquiry any more than anybody comes to any
inquiry in that blank state that the lawyers pretend to
insist upon as desirable, though I give them credit for
enough common-sense to know better. [HL 118].
Thus, every form of thought brings with itself historical and social
presuppositions that are unavoidable, and it is the duty of inquiry to put
them to test, and if it is the case of a requirement of the experience of
reality, to refute them. The contrast showed is circumscribed between a
sincere attitude and a fake attitude. Two postures are compared: first, it
is needed to know which responsibilities can be assumed in the
execution of an illocutionary assertive act; second, as the quotation
above makes it clear, which are the responsibilities de facto assumed,
when someone engages in an inquiry. In other words, it is needed to
remember that there is no place so profound or sublime enough where
from we could look to the inquiry without ideological assumptions, as if
reality under questioning was not also our reality; because it is, it is
fundamental that there are various ways to make the communicative
interaction of science possible with every other spheres of life. The
continuity between common-sense and science in Peirce’s philosophy
teaches us that the assumptions and beliefs of common-sense make up
466
the only bedrock upon which it is possible to question assertions,
theories, and taking conscience. Thus, the definition of truth that does
not refer to belief, to doubt, to experience, is a void definition of truth –
a mere transcendental figment, with no relation to whatever human
effective practice.188
Nor even because of this it is necessary to assume any relativism
or historicism, whose results would equally lead to the presupposition
of a Weberian Wertfrei Wissenschaftliche Theorie. Let us get back to
the experience of inquirers that seem to be the more relevant to the
problem – the proofs they have pro and contra hypotheses. On the one
hand, if we stay with the Weberian idea of scientific rationality, the
chasm between theories of which we can have some evidence of being
truth and reality becomes insurmountable and unbearable. On the other
hand, the theory of truth as correspondence also does not reveal to us
what we can expect from a true hypothesis, and therefore it also would
not be capable to guide us in our actions and inquiries. We could have
all proofs and evidences for a hypothesis, and yet it would not be true.
If truth is the aim of inquiry, then, according to the correspondence
between being and being represented, the inquirers do not have any
rule to follow for conducting theur inquiries. The aim, Peurce says, is
not “readily comprehensible” 189 [CP 1.578, Minute Logic, c. 1902]. How
could one aim at a kind of truth that transcends and transforms
188 MISAK (1994a), pp. 360 ff. 189 Cf. MISAK, idem, p. 362.
467
experience? How could an inquirer develop means to attain such aim?
Peirce states:
Yet the logician will never be scientifically or safely
equipped for his explorations until he knows precisely
what it is that he is seeking. The whole doctrine of logic
depends upon that to a degree one could hardly foresee.
The best way will be to go back to the beginning and
inquire what it is that we can be content to wish for
independently of any ulterior result. [id.].
With such statements, Peirce intends to establish the link
between truth and inquiry that, as we can see, was lost of sight by
transcendental philosophy. The pragmatic interpretation of assertions
that aim at truth concerns the common and collective experience that
informs the beginning of inquiry, and thus offers a conception of truth
that can be a regulative ideal for inquiry. The separation between the
sphere of public morals and private morals disappears, once ethics has
to be based on the most basic practical life. Peirce says:
Ethics as a positive science must rest on observed facts.
But it is quite a different thing to make it rest on special
scientific observation, and still more so to base it upon
scientific conclusions. The only solid foundation for ethics
lies in those facts of every-day life which no skeptical
philosopher ever yet really called in question. [N 3: 51,
Ethics: Descriptive and Explanatory, 1901].
The enrooting in the facts of everyday life involves that every
knowledge that intends to say something about our present historical
reality cannot assume beforehand any critical detachment, but rather it
should recognize that it is a part of this historical moment. That does
468
not prevent to attain some minimally degree of autonomous criticism.
Moreover, since inquiry begins, it is possible and often desirable to give
up was already done in face of empirical requirements and constraints.
Obviously, it is not that all accumulated experience is to be abandoned;
even we come to discover that we are not on the right track, the
experience of error leads us to change and to seek to correct ourselves;
in more Peircean terms, the error causes a doubt that requires its own
annihilation.
From Peirce’s philosophy, we can say that every collective project
of constructing an axiological regulative horizon presupposes the
openness of all ways of inquiry, for truth is seen as a human value to be
semiotically developed and worked up ad infinitum. It equally
presupposes the identification of the individual values with the
collective values, as we have previously emphasized. Even knowing to
be accomplishing small, little fragments without apparent relation one
with another, just like Pound’s ant, the individual can trust the
collective work of all other ants of the colony, for they also confront
dragons.
According to Peirce, “To say that a proposition is true is to say
that every interpretation of it is true.” [CP 5.569, c. 1906]. This is, in
fact, another way of saying that the interpretation of a proposition
enables us to define, yet in a uncertain and provisional way, what it is
possible to expect from a true belief: if we begin to inquiry into p, we
469
would discover that p would not find any sort of negative experience
against it, continuing to be permanently true. Then, we could predict
that, if inquiry was carried on further enough, the object represented in
the proposition p would lead us unavoidably to believe that p. In other
words, there would be no doubts as to the veracity of p. A true belief,
therefore, is such that it resists doubt, even with the continuation of
inquiry and investigations. The pragmatic view is that reality is the
“object” of true beliefs – it is what true beliefs Express, it is that about
which they concern. Reality is that over which beliefs would be fixed, in
the final opinion reached in the long run.
Thus, it makes no sense to suppose, as Karl Pearson did, that the
truth value of a proposition would lie in its conformity or contrariety to
the norms and interests of the accepted society. Such affirmation would
have as result only the closure of ways of inquiry, even because it would
be rather difficult to ascertain what is or what is not the true interest of
society [EP 2: 60-61]. Peirce then can say what is the hope that should
guide the actions of the individuals, in the present:
Our hope, however, in endeavoring to make a
measurement extremely precise, is that there is a certain
value toward which the resultant of all the experiments
would approximate more and more, without limitation.
Having that hope, the Berkeleyan theory is, that
whenever we endeavor to state the distance, all that we
aim at is to state as nearly as possible what that ultimate
result of experience would be. We do not aim at anything
quite beyond experience, but only at the limiting result
470
toward which all experience will approximate, – or, at
any rate, would approximate, were the inquiry to be
prosecuted without cessation. [CP 8.112, Josiah Royce’s
The World and the Individual]
Such affirmation is linked to the idea that it not needed to regard
the life of common-sense as the only and inescapable bedrock for
critical action and reflection. The continuity between sentiments and
inquiry, such as it is configured in the critical common-sensism, does
not impose contingent determinations to inquiry. Even the provisional
beliefs of science have the power to guide conduct. The defense of
freedom to inquiry, relative to the social and historic pressures of the
present, has as a possible consequence the outcome that inquiry
purports not only the knowledge of truth such as it would be in the long
run, but that it might come to be applied, in a way that a true belief
would have practical conceivable bearings to the conduct, even tough
these bearings are not necessary and intrinsic to the definition of
truth.190 Thus, yet provisionally, the genuine spirit to learn can take the
individual inquirer to the right way to eliminate his or her doubts – it
can take, but one does not know if in fact it will lead. However, it is
certain that inquiry leans to the future, not being limited to the actual
present.
Remember that Peirce’s critical common-sensism can be
criticized, what does not contradicts the idea that science can refuse,
all of a sudden, all its beliefs, in function of a revolution in experience.
190 ANDERSON (1997), p. 233.
471
As a matter of fact, the starting condition of enrooting in common-sense
does not prevent that science be – science! The knowledge that results
from scientific inquiry can be always partial, limited, provisional,
because it is semiotically mediated, incomplete – but for the same token
it will always be a knowledge turned to possible interpretation and to
possible communication. The way inquiry turns back over its own
presuppositions necessarily implies the recognition of the fallible and
incomplete character of its assumptions.191 Finally, we want to indicate,
for a further development, the idea that the continuity between
instincts and rationality is the key to the discovery of the fundaments of
abduction:
Every concept, doubtless, first arises when upon a
strong, but more or less vague, sense of need is
superinduced some involuntary experience of a
suggestive nature; that being suggestive which has a
certain occult relation to the build of the mind. We may
assume that it is the same with the instinctive ideas of
animals; and man's ideas are quite as miraculous as
those of the bird, the beaver, and the ant. [CP 5.480, A
Survey of Pragmaticism].
The abductive suggestions are of an instinctive nature, and come
to human mind as the lume naturale Peirce praised so much. It is this
continuity between human mind and nature that grounds the refusal of
the substantial duality between matter and mind, subject and object,
theory and practice.192 This continuity, however, does not warrant that
191 Id., ibid.192 ANDERSON (1997), p. 232; IBRI (1999), p. 287-288.
472
we obtain truth, but it is only the first step of inquiry, as we have seen,
for instinctive suggestions must be experientially tested [RLT 112].
Now, what interests us here is that such continuity leads to the
continuous reformulation of the terms in which experience happens, at
the same time that it is adopted as norm for action that guides conduct.
If it is the task of inquiry to test the hypotheses suggested by instinct, it
is necessary to begin to experiment, practicing inquiry in an effective
way. And such infinite process always recommences, leading to the
necessity of abandoning the ideas of absolute necessity, mechanicism,
and determination.193
Ulrich’s dilemma appears because he cannot in the beginning of
the novel unify the various dimensions of his experience. And, in truth,
the view of this unity characterizes the beginning of scientific activity.
It is in the Play of Musement that we envisage a peculiar harmony
between the universe of possibility, the universe of actual fact, and the
universe of mediation, in straight connexion with the categories of
firstness, secondness, and thirdness, that the view of the universal
leads us to inquiry on the hypothesis of its reality: “Let the Muser, for
example, after well appreciating, in its breadth and depth, the
unspeakable variety of each Universe, turn to those phenomena that
are of the nature of homogeneities of connectedness in each; and what
a spectable will unroll itself!” [EP 2: 438, A Neglected Argument for the
Reality of God]. The Play of Musement, in sum, makes it possible the 193 Id.; Ibri (1992), cap. 4: “Idealismo Objetivo e Continuum”.
473
view of the reality of thirdness, understood as a harmonic congruence
of the three universes of experience, such a congruence appearing so
perfect that it would seem to us supremely admirable.194
The inextricability in science of the three stages of inquiry
provides a “solution” for Ulrich’s dilemma, a solution that does not
solve all the tensions, but incorporates them to it. 195 Remember that
abduction is characterized by the opening of new possibilities of
experience; in other words, abduction gives us the suggestion of
horizons in possible experience, horizons that will be always
overwhelmed, given the nature of scientific activity proper. There is no
more, as there was for Kant, a sharp distinction between what is
outside our horizon and what is beyond the horizon196; in fact, we can
say that for Peirce there is not what is outside human horizons, since
the incognizable is impossible, and therefore it does not exist:
[…] all our conceptions are obtained by abstractions and
combinations of cognitions first occurring in judgments
of experience. Accordingly, there can be no conception of
the absolutely incognizable, since nothing of that sort
occurs in experience. But the meaning of a term is the
conception it conveys. Hence, a term can have no such
194 On the subject of esthetics in Peirce’s thought, as science of the ascertainment of the conditions of possibility of what is de per se admirable, cf. BARNOUW (1988) and (1994); SANTAELLA (2000); SILVEIRA (2003).195 We remember that Musil’s novel is an unfinished work. Not even because of this Ulrich remains all the time in the aporetical situation we have described. The way the dilemma is resolve in the novel, we will not say it here, inviting the reader to the experience or the ecstasy of such discovery.196 KANT (1799-1800), Ak. 42.
474
meaning. [W 2: 208, Questions Concerning Certain
Faculties Claimed for Man].
Peirce can say, then, that there is a cognizable reality behind
every human conception; nothing therefore can be outside or beyond
the reach of knowledge, what does not mean that it is possible to
exhaust knowledge. The identification of being and cognoscibility
assures only the possibility of constructing knowledge, without
determining its necessity, completeness or absolute certainty. In fact,
from the Peircean account of scientific method, we have reasons to
affirm that nothing is outside or beyond human horizons, for nothing is
outside the range of possible experience, even thought the possibility of
transforming experience, overcoming horizons and going beyond them,
is in a certain sense unavoidable. At least this tension remains.
After all this way, it appears it is possible to conclude that the
task of philosophy, as the inquiry of human life and its forms of life, will
always be unfinished, as long as there is human life. There is the
famous passage where Peirce says that human beings actually are
signs:
Without fatiguing the reader by stretching this
parallelism too far, it is sufficient to say that there is no
element whatever of man's consciousness which has not
something corresponding to it in the word; and the
reason is obvious. It is that the word or sign which man
uses is the man himself. For, as the fact that every
thought is a sign, taken in conjunction with the fact that
life is a train of thought, proves that man is a sign; so,
475
that every thought is an external sign, proves that man is
an external sign. That is to say, the man and the external
sign are identical, in the same sense in which the words
homo and man are identical. Thus my language is the
sum total of myself; for the man is the thought. [EP 1: 54,
Some Consequences of Four Incapacities].
In the quotation, Peirce says that human beings do not exist in a
determinate way, for if a human being is a sign, its truth depends upon
how it is going to be interpreted from now on. The complete and
definite actualization of the human being, therefore, is merely a
possibility, for it depends on an esse in futuro. For the same reason,
man is a sign, as Peirce says, it is “a symbol [that] is an embryonic
reality endowed with power of growth into the very truth, the very
entelechy of reality.” [EP 2: 324, ]. Entelechy is not
[enérgueia], it is not exhausted hic et nunc in the present, but it is the
perfect realization of a process whose end is inherent to the process
itself. The affirmation that man is an end in itself is, in this way,
reformulated to make human ends coincide with the self-development
of reality itself. But this end in itself is unattainable by the individual
alone; as all symbols, human beings mutually depend on each other to
affirm themselves as such – human beings are altogether projected to
the experience of the world:
We can now see what judgment and assertion are. The
man is a symbol. Different men, so far as they can have
any ideas in common, are the same symbol. Judgment is
the determination of the man-symbol to have whatever
476
interpretant the judged proposition has. Assertion is the
determination of the man-symbol to determining the
interpreter, so far as he is interpreter, in the same way.
[id.].
Human beings, therefore, cannot live isolated one from another,
for their nature is oriented to the mutual interpretation and sharing of
common experiences. In truth, if a human being is not affirmed and
interpreted within a defined practical context such as it is with the
proposition, a human being then is little more than a mere empty form,
lacking realization. As symbols are the only signs capable of growing,
also human beings are conjointly projected into a collective endeavour
of undefined limits, oriented towards the asymptotical approach of
reality. Now, human truth, however, is not fixed or delimited.
An equally interesting less known affirmation is that a human
being is not a vortex, but a wave: “A man is a wave, but not a vortex.”
[EP 2: 124, On Science and Natural Classes]. A vortex is a fluid in
continuous rotation, a whirlpool with a defined center, in constant and
stable velocity. A wave is otherwise a form assumed by the parts of a
body that are out of equilibrium, always in movement and changing
places, in a constant and chaotic tension, so to propagate this tension to
all parts of the body, “while preserving more or less the same form and
other characteristics”. The human being in consequence never is
perfectly stable, and it always changing, always tensioned and
intentioned outwards, to the other, to the future.
477
Just as for Guimarães Rosa, the human being according to Peirce
is movement and instability, a continuous signifying – crossing-
prophecy: “Man is nature’s first essay towards the production of an
intellectual animal. He is not that, but is a prophecy of it, perhaps.” [W
1: 9, Private Thoughts principally on the conduct of life, 18 June 1867].
478
BIBLIOGRAPHY OF CONSULTED OR QUOTED WORKS
ANDERSON, Douglas R. (1995). Strands of System: The philosophy of
Charles Peirce. West Lafayette, IN: Purdue University Press.
____________________. (1997). A political dimension of fixing belief. In:
BRUNNING, Jacqueline; FORSTER, Paul (ed(s).). (1997). Sub cit., pp.
223-240.
APEL, Karl-Otto. (1995a). Charles S. Peirce: From Pragmatism to
Pragmaticism. Trad.: John Michael Krois. Atlantic Highlands, NJ:
Humanities Press.
______________. (1995b). De Kant à Peirce: la transformation sémiotique
de la logique transcendantale. In: Philosophie. Paris, nº 48, dez.
1995, pp. 49-70.
ARISTÓTELES. (1925). Analytica Posteriora. In: The Works of Aristotle
translated in to English. Oxford: Oxford University Press, v. 1. Ed.
by W. D. Ross. Edição eletrônica do texto original em grego na
URL:
[http://www.fh-augsburg.de/~harsch/graeca/Chronologia/S_ante0
4/Aristoteles/ari_a200.html]. Acessado em 18 de julho de 2004.
___________. (1966). Aristotle’s Physics. A revised text with introduction
and commentary by W. D. Ross. Oxford: Clarendon Press.
Tradução consultada: R. P. Hardie e R. K. Gaye, in: The Complete
Works of Aristotle – The Revised Oxford Translation. Vol. 1. Ed. by
Jonathan Barnes. Princeton, NJ; Oxford: Princeton University
Press, 1984.
___________. (1987). Metafísica de Aristóteles. Edición trilingüe por
Valentín García Yebra. 2ª ed. revisada. Madrid: Editorial Gredos.
___________. (2001a). Ética a Nicômaco. Trad.: Mário da Gama Kury. 4ª
ed. Brasília: Editora da Universidade de Brasília. Edição
479
eletrônica do texto original na URL:
[http://www.perseus.tufts.edu/]. Acessado em 18 de julho de 2004.
___________. (2001b). Metafísica. Ensaio introdutório, texto grego com
tradução e comentário de Giovanni Reale. Trad.: Marcelo Perine.
3 v. São Paulo: Edições Loyola.
BACHA, Maria de Lourdes. (1999). Peirce Crítico de Mill: sobre os
contextos nominalista e realista da indução. Tese de
doutoramento apresentada à Pontifícia Universidade Católica de
São Paulo como exigênca parcial para a obtenção do título de
doutor em comunicação e semiótica.
_______________________. (2003). Realismo e Verdade: Temas de Peirce.
São Paulo: Legnar Informática & Editora Ltda
BACHELARD, Gaston. (1984). A Filosofia do Não: Filosofia do Novo
Espírito Científico. Trad.: Joaquim José Moura Ramos. Lisboa:
Editorial Presença.
BAKHTIN, Michail. (1997). Marxism and Philosophy of Language.
Translation used: Marxismo e Filosofia da Linguagem: Problemas
fundamentais do método sociológico na ciência da linguagem.
Prefácio de Roman Jakobson; apresentação de Marina Yaguello;
trad.: Michel Lahud e Yara Frateschi Vieira, com a colaboração de
Lúcia Teixeira Wisnik e Carlos Henrique D. Chagas Cruz. 8ª ed.
São Paulo: HUCITEC.
BANDEIRA, Manuel. (1974). Poesia Completa e Prosa. Rio de Janeiro:
Companhia José Aguilar Editora.
BARNOUW, Jeffrey. (1988). “Aesthetic” for Schiller and Peirce: a
neglected origin of pragmatism. In: Journal of the History of
Ideas. Baltimore, v. XLIX, nº 4, out. / dez. 1988, pp. 607-632
______________. (1994). The place of Peirce’s ‘esthetic’ in his thought and
in the tradition of aesthetics. In: PARRET, Herman (ed.). (1994) sub
cit., pp. 155-178.
480
BERMAN, Marshall. (1982). All that Is Solid Melts into Air. Translation
used: Tudo que é Sólido Desmancha no Ar. Trad.: Carlos Felipe
Moisés e Ana Maria L. Ioriatti. 1ª ed. 8ª reimpressão. São Paulo:
Companhia das Letras.
BÍBLIA: Tradução Ecumênica. (1994). São Paulo: Edições Loyola.
BLACK, Max. (1971). A Companion to Wittgenstein’s ‘Tractatus’.
Cambridge: Cambridge University Press.
BOCHEŃSKI, Innocentius M. (1970). A History of Formal Logic.
Translated and edited by Ivo Thomas. 2ª ed. New York; Notre
Dame, IN: Chelsea Publishing Company; University of Notre
Dame Press.
BOGHOSSIAN, Peter G.; DREWNIAK, Erik. (1995). Wittgenstein and Peirce
on meaning: the evolution from absolutism to fallibilism. In:
Dialogos – Revista del Departamento de Filosofia – Universidad de
Puerto Rico. Puerto Rico, ano XXX, nº 65, jan. 1995, pp. 173-188.
BORGES, Jorge L. (1993). El Aleph. Madrid: Alianza Editorial.
BOURDEAU, Michel. (1995). Vague pragmatique et quantification.
Resenha crítica de CHAUVIRÉ (1995) sub cit. In: Critique – Revue
générale des publications françaises et étrangères. Paris, tomo LI,
nº 583, dez. 1995, pp. 953-963.
BOURDIEU, Pierre. (2004). Os Usos Sociais da Ciência: Por uma
sociologia clínica do campo científico. Texto revisto pelo autor
com a colaboração de Patrik Champagne e Etienne Landais.
Trad.: Denice Bárbara Catani. São Paulo: Editora UNESP.
BOUVERESSE, Jacques. (1976). Le Mythe de l’Interiorité: Expérience,
signification et langage privé chez Wittgenstein. Paris: Éditions
du Minuit.
BRADY, Geraldine. (1997). From the algebra of relations to the logic of
quantifiers. In: HOUSER, Nathan; ROBERTS, Don D.; VAN EVRA,
James (ed(s).). (1997), sub cit., pp. 173-192.
481
________________. (2000). From Peirce to Skolem: A neglected chapter in
the history of mathematical logic. 1ª ed. Amsterdam: Elsevier
Science B.V.
BRENT, Joseph. (1998). Charles Sanders Peirce: A life. Revised and
enlarged edition. Bloomington e Indianapolis: Indiana University
Press.
BROCK, Jarret E. (1981). An Introduction to Peirce’s Theory of Speech
Acts. In: Transactions of the Charles S. Peirce Society – A
quarterly journal in American philosophy. Buffalo, v. XVII, nº 4,
Spring, 1987, pp. 319-326.
BRUNNING, Jacqueline; FORSTER, Paul (ed(s).). (1997). The Rule of
Reason: The Philosophy of Charles Sanders Peirce. Toronto;
Buffalo, NY; London: University of Toronto Press.
BUNGE, Mario. (1985). Seudociência e ideología. 1ª ed. 4ª reimpressão:
1989. Madrid: Alianza Editorial.
CALLAWAY, Howard G. (2002). Schelling and the background of
American philosophy. Resenha crítica de Franz Josef Wetz,
Friedrich W. J. Schelling, zur Einführung (Hamburg: Junius
Verlag, 1996). In:
[http://members.door.net/arisbe/menu/library/aboutcsp/callaway/s
chelling.htm]. Acessado em 03 de Maio de 2004.
CARNOIS, Bernard. (1983). La sémiotique de C. S. Peirce et ses
limitations épistémologiques. In: Les Études Philosophiques.
Paris, nº 3, 1983, pp. 299-316.
_________________. (1985). La philosophie pragmatique de Peirce et son
ouverture métacritique. In: Revue de Metaphysique et de Morale.
Paris, 90e année, nº 4, out./ dez. 1985, pp. 505-531.
CASTRO, Josué de. (1968). Ensaios de Biologia Social. 4ª ed. São Paulo :
Editora Brasiliense.
482
CHAUVIRÉ, Christiane. (1979). Peirce, le langage et l’action – sur la
théorie peircienne de l’assertion. In: Les Études Philosophiques.
Paris, nº 1, 1979, pp. 3-17.
___________________. (1984). Peirce, logicien, mathématicien: recherches
récentes. In: Revue de Synthèse. Paris, 3e série, nº 115, jul./ set.
1984, pp. 352-359.
___________________. (1995). Peirce et la Signification: Introduction à la
logique du vague. Paris: Presses Universitaires de France.
COSTA, Newton Carneiro A. da. (1993). Lógica Indutiva e Probabilidade.
São Paulo: HUCITEC; Editora da Universidade de São Paulo.
DAUBEN, Joseph W. (1995). Peirce and History of Science. In: KETNER,
Kenneth L. (ed.). (1995), sub cit., pp. 146-195.
DEBROCK, Guy; HULSWIT, Menno (ed(s).). (1994). The Living Doubt:
Essays concerning the epistemology of Charles Sanders Peirce.
Dordrecht, The Netherlands: Kluwer Academic Publishers.
DELANEY, Cornelius F. (1993a). Peirce on the conditions of possibility of
science. In: MOORE, Edward C. (ed.) (1993a). Sub cit., pp. 17-29.
___________________. (1993b). Science, Knowledge, and the Mind: A
study in the philosophy of C. S. Peirce. Notre Dame, IN; London:
University of Notre Dame Press.
___________________. (1995). Peirce on the reliability of science: a
response to Rescher. In: KETNER, Kenneth L. (ed.). (1995). Sub
cit., pp. 113-119.
___________________. (2002). Peirce on science and metaphysics:
overview of a synoptic vision. In: Cognitio – Revista de Filosofia.
São Paulo, nº 3, nov. 2002, pp. 11-21.
DELEUZE, Gilles. (1969). Logique du Sens. Paris: Éditions du Minuit.
Translation used: Lógica do Sentido. Trad.: Luiz Roberto Salinas
Fortes. 4ª ed. São Paulo: Editora Perspectiva, 2000.
483
______________. (1974). Hume. In: História da Filosofia – Idéias,
Doutrinas; v. 4: O Iluminismo: O século XVIII. Sob a direção de
François Châtelet. Rio de Janeiro: Zahar Editores, pp. 59-70.
DE TIENNE, André. (1996). L’Analytique de la Representation chez
Peirce: La genèse de la théorie des categories. Bruxelles: Facultés
Universitaires Saint-Louis.
DICKSON, David. (1988). The New Politics of Science. Chicago; London:
The University of Chicago Press.
EISELE, Carolyn. (1979). Studies in the Scientific and Mathematical
Philosophy of Charles S. Peirce: Essays by Carolyn Eisele. Ed. by
R. M. Martin. Haia; Paris; New York: Mouton Publishers.
______________. (1995). Charles S. Peirce, mathematician. In: KETNER,
Kenneth L. (ed.). (1995). Sub cit., pp. 120-131.
ESPOSITO, Joseph L. (1977). Peirce and Naturphilosophie. In:
Transactions of the Charles S. Peirce Society – A quarterly journal
in American philosophy. Buffalo, v. XIII, nº 2, Spring, 1977, pp.
122-141.
EVES, Howard. (2004). Introdução à História da Matemática. Trad.:
Hygino H. Domingues. Campinas, SP: Editora da UNICAMP.
FARIA, Ernesto. (org.). (1956). Dicionário Escolar Latino-Português. 2ª
ed. Rio de Janeiro: Ministério da Educação e Cultura;
Departamento Nacional de Educação.
FERRARA, Lucrécia D’Alessio. (1986/1987). Ciência do olhar atento. In:
Trans/ Form/ Ação: Revista de Filosofia. Marília, SP, nº 9-10,
1986-1987, pp.1-7.
FINLAY, Marike. (1990). The Potential of Modern Discourse: Musil,
Peirce, and Perturbation. Bloomington: Indiana University Press.
FISCH, Max H. (1986). Peirce, Semeiotic, and Pragmatism: Essays by
Max H. Fisch. Ed. by Kenneth L. Ketner and Christian J. W.
Kloesel. Bloomington: Indiana University Press.
484
FREGE, Gottlob. (1970). Translations from the Philosophical Writings of
Gottlob Frege. Ed. by Peter Geach and Max Black. Oxford: Basil
Blackwell.
GALBRAITH, John K. (1977). The Age of Uncertainty : A history of
economic ideas and their consequences. Boston: Houghton Mifflin
Company.
GORLÉE, Dinda L. (1989). Wittgenstein et Peirce: le jeu de langage. In :
Semiotica – Journal of the International Association for Semiotic
Studies/ Revue de l’Association Internationale de Sémiotique.
Haia; Paris; New York, v. 73, nºs. 3/4, 1989, pp. 219-231.
GRANGER, Gilles G. (1979). Langages et Épistémologies. Paris: Éditions
Klincksieck.
_________________. (1994). A Ciência e as Ciências. Trad.: Roberto Leal
Ferreira. São Paulo: Editora da Universidade Estadual Paulista.
HAACK, Susan. (1996). Between scientism and conversationalism. In:
Philosophy and Literature. Baltimore, v. 20, nº 2, out. 1996, pp.
455-474.
_____________. (1997). The first rule of reason. In: BRUNNING, Jacqueline;
FORSTER, Paul (ed(s).) (1997). Supra cit., pp. 241-261.
_____________. (1998). Quanto àquela frase “estudando com um espírito
literário...”. In: PINTO, Paulo Roberto M. et all. (org(s).). (1998).
Sub cit., pp. 40-70.
HABERMAS, Jürgen. (1982). Conhecimento e Interesse. Introdução e
tradução de José N. Heck. Revisão de texto de Gustavo Bayer. Rio
de Janeiro: Zahar Editores.
_________________. (1991). The Theory of Communicative Action. V. 1:
Reason and the rationalization of society. Translated by Thomas
McCarthy. 1ª ed. 1984. London: Polity Press.
_________________. (1995). Peirce and Communication. In: KETNER,
Kenneth L. (ed.). (1995). Sub cit., pp. 243-266.
485
HANTZIS, Catherine W. (1987). Peirce’s conception of philosophy: its
method and its program. In: Transactions of the Charles S. Peirce
Society – A quarterly journal in American philosophy. Buffalo, v.
XXIII, nº 2, Spring, 1987, pp. 289-307.
HAUSMAN, Carl R. (1993). Charles S. Peirce’s Evolutionary Philosophy.
Cambridge; New York; Victoria, Austrália: Cambridge University
Press.
HAWKINS, JR., Benjamin S. (1997). Peirce and Russell: The history of a
neglected ‘controversy’. In: HOUSER, Nathan; ROBERTS, Don D.;
VAN EVRA, James (ed(s).). (1997). Sub cit., pp. 111-146.
HEIDEGGER, Martin. (1993). Sein und Zeit. 7. Auflage. Tübingen: Max
Niemeyer Verlag. Tradução utilizada: Being and Time. Translated
by John Macquarrie and Edward Robinson. San Francisco, CA:
Harper & Row, 1962.
HILPINEN, Risto. (1982). On C. S. Peirce’s theory of the proposition:
Peirce as a precursor of game-theoretical semantics. In: The
Monist – An International Journal of General Philosophical
Inquiry. La Salle, IL, v. 65, nº 2, April, 1982, pp. 182-187.
HOMER. (1990). The Iliad. Translated by Robert Fagles; introduction and
notes by Bernard Knox. New York: Viking Penguin.
HOOKWAY, Christopher. (1992). Peirce. Paperback edition. London and
New York: Routledge.
_____________________. (1998). Peirce, Charles Sanders. In: Routledge
Encyclopedia of Philosophy. Ed. By Edward Craig. London:
Routledge. URL: [http://www.rep.routledge.com/article/DC059].
Acessado em 23 de Novembro de 2004.
_____________________. (2002). Truth, Rationality, and Pragmatism:
Themes from Peirce. Oxford, RU; New York: Oxford University
Press through Clarendon Press.
HOUSER, Nathan. (1990). The form of experience. Reviewed and
unpublished English version, kindly provided by the author, of the
486
following article: La structure formelle de l’expérience selon
Peirce. In: Études Phénoménologiques. Louvain-la-Neuve, tome V,
nºs. 9-10, 1989, pp. 77-111.
_______________. (1994). Algebraic Logic from Boole to Schröder, 1840-
1900. In: Companion Encyploedia of the History and Philosophy of
the Mathematical Sciences. Vol. I. Edited by Ivor Grattan-
Guinness. London; New York: Routledge, 1994, pp. 601-616.
HOUSER, Nathan; ROBERTS, Don D.; VAN EVRA, James (ed(s).). (1997).
Studies in the Logic of Charles Sanders Peirce. Bloomington;
Indianapolis: Indiana University Press.
HULSWIT, Menno. (2002). From Cause to Causation: A Peircean
Perspective. Dordrecht; Boston; London: Kluwer Academic
Publishers.
HUME, David. (1739-1740). A Treatise of Human Nature. Edited, with an
analytical index, by L. A. Selby-Bigge. 2nd edition, with text
revised and variant readings by P. H. Nidditch. Oxford: Clarendon
Press, 1978.
IBRI, Ivo A. (1992). Kósmos Noētós: A arquitetura metafísica de Charles
S. Peirce. São Paulo: Perspectiva; Hólon.
__________. (1994). Kósmos Poietikós: Criação e Descoberta na Filosofia
de Charles S. Peirce. Tese de Doutoramento. São Paulo:
Universidade de São Paulo; Departamento de filosofia.
__________. (1996). A física da physis. In: Hypnos. São Paulo, ano 1, nº 2,
2º sem. 1996, pp. 23-32.
__________. (1998). Pragmatismo e técnica. In: Hypnos. São Paulo, ano 3,
nº 4, 2º sem. 1998, pp. 149-155.
__________. (1999). Verdade e continuum. In: Hypnos. São Paulo, ano 4,
nº 5, 2º sem. 1999, pp. 280-289.
__________. (2000a). As conseqüências de conseqüências práticas no
pragmatismo de Peirce. In: Cognitio – Revista de Filosofia. São
Paulo, ano 1, nº 1, nov. 2000, pp. 30-37.
487
__________. (2000b). Sobre a identidade ideal-real na filosofia de Peirce.
In: Cognitio – Revista de Filosofia. São Paulo, ano 1, nº 1, nov.
200, pp. 38-450.
__________. (2003a). Pragmatismo e a possibilidade da metafísica. In:
Cognitio – Revista de Filosofia. São Paulo, v. 4, nº 1, jan. / jun.
2003, pp. 09-14.
__________. (2003b). Tópicos para uma poética da alteridade. In:
Cadernos Bispo do Rosário, São Paulo: Centro Cultural Banco do
Brasil.
__________. (2004). Semiótica e pragmatismo: interfaces teóricas. In:
Cognitio – Revista de Filosofia. São Paulo, v. 5, nº 2, jul. / dez.
2004, pp. 168-179.
JOSWICK, Hugh. (1988). Peirce’s mathematical model of interpretation.
In: Transactions of the Charles S. Peirce Society – A quarterly
journal in American philosophy. Buffalo, v. XXIV, nº 1, Winter,
1988, pp. 107-121.
KANT, Immanuel. (1786). Metaphysische Anfangsgründe der
Naturwissenschaft. Edição eletrônica. URL: [http://www-user.uni-
bremen.de/~kr538/kantnat.html]. Acessado em 25 de maio de
2004. Translation used: Metaphysical Foundations of Natural
Science. Trad.: James Ellington. Indianapolis; New York: The
Bobbs-Merrill Company, INC., 1970.
_______________. (1785). Grundlegung der Metaphysik der Sitten. Edição
eletrônica: URL
[http://www.fb12.uni-dortmund.de/wtheorie/JPEG/KANT2_1.HTM]
. Acessada em 18 de abril de 2005. Tradução utilizada:
Fundamentação da Metafísica dos Costumes. Introdução de
Viriato Soromenho-Marques. Tradução de Paulo Quintela. Porto:
Porto Editora, 1995.
_______________. (1787). Kritik der reinen Vernunft. Eletronic editons:
edition A, 1781, URL:
488
[http://gutenberg.aol.de/kant/krva/krva.htm]; edition B, 1787,
URL: [http://gutenberg.aol.de/kant/krvb/krvb.htm]. Acessed: 25
March 2003. Translations used: Crítica da Razão Pura. Trad.:
Valério Rohden e Udo Baldo Moosburger. 3ª ed. 2 v. Col. Os
Pensadores. São Paulo: Nova Cultural, 1987; Crítica da Razão
Pura. Trad.: Manuela Pinto dos Santos e Alexandre Fradique
Morujão. 3ª ed., contendo as edições de 1781 e a de 1787. Lisboa:
Fundação Calouste Gulbenkian, 1994; Norman Kemp-Smith’s
translation, available on-line at URL:
[http://www.hkbu.edu.hk/~ppp/cpr/toc.html]. Acessed: 25 March
2004.
_______________. (1798). Anthropologie in pragmatischer Hinsicht.
Herausgegeben und eingeleitet von Wolfgang Becker; mit einem
Nachwort von Hans Ebeling. Sttutgart: Philip Reclam jun.
Translations used: Anthropologie du point de vue pragmatique.
Trad.: Michel Foucault. 7éme. tirage augmenté d’une table des
matières détaillée. Paris: Libraire Philosophique J. Vrin, 1994;
Anthropology from a Pragmatic Point of View. Translated by
Victor Lyle Dowdell; revised and edited by Hans H. Rudnick, with
an introduction by Frederick P. Van De Pitte. Carbondale &
Edwardsville: Southern Illinois University Press, 1977.
_______________. (1799-1800). Logik – ein Handbuch zu Vorlesung.
Translations used: Manual dos Cursos de Lógica Geral. Tradução,
apresentação e guia de leitura de Fausto Castilho. Uberlândia;
Campinas: EDUFU; IFCH-UNICAMP, 1998; Lectures on Logic.
Translated and edited by J. Michael Young. Cambridge:
Cambridge University Press, 1992.
KENT, Beverley. (1987). Charles Sanders Peirce: Logic and the
Classification of the Sciences. Kingston, CA; Montréal: McGill-
Queen’s University Press.
489
______________. (1997). The Interconnectedness of Peirce’s
Diagrammatic Thought. In: HOUSER, Nathan; ROBERTS, Don D.;
VAN EVRA, James (ed(s).). (1997). Supra cit., pp. 445-459.
KERR-LAWSON, Angus. (1997). Peirce’s pre-logistic account of
mathematics. In: HOUSER; ROBERTS; VAN EVRA (ed(s).). (1997).
Supra cit., pp. 77-84.
KETNER, Kenneth L. (ed.) (1995). Peirce and Contemporary Thought:
Philosophical Inquiries. New York: Fordham University Press.
LEIBNIZ, Gottfried W. (1880). La Monadologie. Edition anotée, et
précédée d’une Exposition du Système de Leibnitz par Émile
Boutroux; note terminale sur les principes de la Mécanique dans
Descartes et dans Leibnitz par Henri Poincaré. Reedição: Paris:
Delagrave, s/d. Tradução consultada: Os Princípios da Filosofia
ditos a Monadologia. Trad.: Marilena Chauí. São Paulo: Abril
Cultural, 1979.
__________________. (2001). The Labyrinth of the Continuum: Writings on
the Continuum Problem, 1672-1686. Translated, edited, and with
an Introduction by Richard T. W. Arthur. New Haven and London:
Yale University Press.
LEMINSKI, Paulo. (1991). La Vie en Close. 2ª ed. São Paulo: Brasiliense.
LEO, Rossella F. (2001). Continuità e Vaghezza: Leibniz Goethe Peirce
Wittgenstein. 1ª ed. Milano: CUEM s.c.r.l.
_____________. (2002). Cosa Significa Dirsi Pragmatisti – Peirce e
Wittgenstein a confronto. 1ª ed. Milano: CUEM s.c.r.l.
LEVY, Stephen H. (1997). Peirce’s theoremic / corollarial distinction and
the interconnections between mathematics and logic. In: HOUSER,
Nathan; ROBERTS, Don D.; VAN EVRA, James (ed(s).). (1997). Supra
cit., pp. 85-110.
LISZKA, James J. (1978). Community in C. S. Peirce: science
as a means and as an end. In: Transactions of the Charles S.
490
Peirce Society – A quarterly journal in American philosophy.
Buffalo, v. XIV, nº 4, Fall, 1978, pp. 305-321.
__________________. (2000). Logic and Peirce’s New Rhetoric. In:
Semiotica – Journal of the International Association for Semiotic
Studies/ Revue de l’Association Internationale de Sémiotique.
Berlim, v. 131, nºs. 3/4, 2000, pp. 289-311.
LOHR, Charles H. (1982). The medieval interpretation of Aristotle. In:
The Cambridge History of Later Medieval Philosophy: From the
rediscovery of Aristotle to the disintegration of scholasticism,
1100-1600. Ed. by Norman Kretzmann, Anthony Kenny, J Pinborg.
Cambridge, RU: Cambridge University Press, pp. 80-98.
LUCAS, Sofia Isabel M. (2003). A Classificação das Ciências de Charles
Sanders Peirce. Dissertação de Mestrado. Pontifícia Universidade
Católica de São Paulo.
MAGALHÃES, Teresa C. de. (1981). Signe ou Symbole: Introduction à la
théorie sémiotique de C. S. Peirce. Louvain-la-Neuve ; Madrid :
CABAY.
________________________. (1984). Pragmatismo e pragmática – aspectos
da filosofia contemporânea da linguagem. In: Revista de Filosofia
e Epistemologia. Lisboa, nº 5, 1984, pp. 181-197.
MARTIN, Robert M. (1980). Peirce’s Logic of Relations and Other
Studies. Dordrecht, Holanda; Cinnaminson, NJ: Foris
Publications.
MARX, Karl; ENGELS, Friedrich. (1848). Manifest der Kommunistischen
Partei. Translations used: Manifesto Comunista. Organização e
introdução: Osvaldo Coggiola. Trad.: Álvaro Pina. 1ª ed. São
Paulo: Boitempo Editorial; Jinkings Editores Associados, 1998;
Manifesto of the Communist Party. Translation by Samuel Moore,
in collaboration with Friedrich Engels (1888). Availlable on-line at
URL: [http://www.marxists.org/archive/marx/works/1848/
communist-manifesto/index.htm] Acessed: 25 April 2004.
491
MCCARTHY, Jeremiah E. (1980). Peirce’s Normative Science. A
dissertation submitted to the faculty of the university of North
Carolina at Chapel Hill in partial fulfillment of the requirements
for the degree of Doctor in Philosophy in the Department of
Philosophy.
MENDES, Murilo. (1994). Poesia Completa e Prosa. Volume único.
Organização e preparação do texto: Luciana Stegagno Picchio. 1ª
ed. Rio de Janeiro: Nova Aguilar.
MERRILL, Daniel D. (1984). The 1870 Logic of Relatives Memoir.
Introdução, parte 3, a Writings of Charles Sanders Peirce – A
Chronological Edition, v. 2: 1867-1871, pp. xlii-xlviii.
________________. (1997). Relations and Quantification in Peirce’s Logic,
1870-1885. In: HOUSER, Nathan; ROBERTS, Don D.; VAN EVRA,
James (ed(s).). (1997). Supra cit., pp. 158-172.
MISAK, Cheryl. (1994a). American Pragmatism: Peirce. In: Routledge
History of Philosophy. Volume VII: The Nineteenth Century.
Edited by C. L. Ten. London and New York: Routledge, 1994, pp.
357-380.
_____________. (1994b). Pragmatism and the transcendental turn in truth
and ethics. In: Transactions of the Charles S. Peirce Society – A
quarterly journal in American philosophy. Buffalo, v. XXX, nº 4,
Fall, 1994, pp. 739-775.
_____________. (2002). C. S. Peirce on vital matters. In: Cognitio –
Revista de Filosofia. São Paulo, nº 3, nov. 2002, pp. 64-82.
MOORE, Edward C. (1961). American Pragmatism: Peirce, James, and
Dewey. New York: Columbia University Press.
__________________. (ed.). (1993a). Charles S. Peirce and the Philosophy
of Science: Papers from the Harvard Sesquicentennial Congress.
Tuscaloosa, AL; London: The University of Alabama Press.
492
__________________. (1993b). Introduction: Charles S. Peirce and the
Philosophy of Science. In: MOORE, Edward C. (ed.). (1993a). Supra
cit., pp. 1-13.
MURACHCO, Henrique G. (1998). Apresentação do tema Téchne: Eidos-
Téchne-Tektón. In: Hypnos. Publicação do Centro de Estudos da
Antigüidade Grega; Departamento de Filosofia da PUC-SP. São
Paulo, ano 3, nº 4, pp. 09-17.
MURPHEY, Murray G. (1993). The Development of Peirce’s Philosophy.
Indianapolis; Cambridge, MA: Hackett Publishing Company, Inc.
1ª ed.: Cambridge, MA: Cambridge University Press, 1961.
MUSIL, Robert. (1999). Der Mann ohne Eigenschaften. Neu
durchgesehene und verbesserte Ausgabe 1978. Reinbeck bei
Hamburg: Rowohlt Taschenbuch Verlag GmbH. Translation used:
O Homem sem Qualidades. Trad.: Lya Luft e Carlos Abbenseth.
Rio de Janeiro: Nova Fronteira, 1989.
NEWMAN, Lex. (1997). Descartes' Epistemology. In: The Stanford
Encyclopedia of Philosophy (Fall 2000 Edition). Ed. by Edward N.
Zalta. Acessado em 21/01/1998. URL:
[http://plato.stanford.edu/archives/fall2000/entries/descartes-
epistemologie].
NIETZSCHE, Friedrich W. (1967). Kritische Gesamtausgabe.
Herausgegeben von Giorgio Colli und Mazzino Montinari. Berlim:
Walter de Gruyter. Tradução consultada: A Gaia Ciência.
Tradução, notas e posfácio de Paulo César Souza. São Paulo:
Companhia das Letras, 2001.
OXFORD ENGLISH DICTIONARY, THE. (1971). Compact edition. 2 v. 21st
printing in the U. S., June 1981. Oxford: Oxford University Press.
OEHLER, Klaus. (1995). A Response to Habermas. In: KETNER, Kenneth
L. (ed.). (1995). Supra cit., pp. 267-271.
PAPE, Helmut. (1993). Final causality in Peirce’s semiotics and his
classification of the sciences. In: Transactions of the Charles S.
493
Peirce Society – A quarterly journal in American philosophy.
Buffalo, v. XXIX, nº 4, Fall, 1993, pp. 581-607.
PARKER, Kelly. (1998). The Continuity of Peirce’s Thought. Nashville;
London: Vanderbilt University Press.
_____________. (2003). Reconstructing the normative sciences. In:
Cognitio – Revista de Filosofia. São Paulo, v. 4, nº 1, jan. / jun.
2003, pp. 27-45.
PARRET, Herman (ed.). (1994). Peirce and Value Theory: On Peircean
ethics and aesthetics. Amsterdam; Philadelphia: John Benjamins
Publishing Company.
PERELMAN, Chaïm; OLBRECHTS-TYTECA, Lucie. (1971). Traité de
l’Argumentation: La Nouvelle Rhetorique. Paris: Gallimard.
Translation used: Tratado da Argumentação: A nova retórica.
Trad.: Maria Ermantina Galvão G. Pereira. São Paulo: Martins
Fontes, 1996.
PINTO, Paulo Roberto M. et all. (org(s).). (1998). Filosofia Analítica,
Pragmatismo e Ciência. Belo Horizonte: Ed. UFMG.
POTTER, Vincent G. (1967). Charles S. Peirce on Norms and Ideals.
Cambridge, MA: The University of Massachusetts Press.
_________________. (1996). Peirce’s Philosophical Perspectives. Ed. by
Vincent M. Colapietro. New York: Fordham University Press.
POUND, Ezra. (1970). The Cantos of Ezra Pound. 9th printing (1983).
New York: New Directions Books.
PUTNAM, Hillary. (1982). Peirce the logician. In: Historia Mathematica –
Journal of the International Commission on the History of
Mathematics, v. 9, pp. 290-301, August, 1982.
PYCIOR, Helena W. (1995). Peirce at the intersection of mathematics and
philosophy: a response to Eisele. In: KETNER, Kenneth L. (ed.)
(1995). Supra cit., pp. 132-145.
494
RANSDELL, Joseph. (1977). Some leading ideas of Peirce’s semiotic. In:
Semiotica – Journal of the International Association for Semiotic
Studies/ Revue de l’Association Internationale de Sémiotique.
Haia; Paris; New York, v. 19, nºs. 3/4, 1977, pp. 157-178.
RAPOSA, Michael L. (1989). Peirce’s Philosophy of Religion.
Bloomington; Indianapolis: Indiana University Press.
RESCHER, Nicholas. (1978). Peirce’s Philosophy of Science: Critical
studies in his theory of induction and scientific method.
NotreDame, IN; London: University of Notre Dame Press.
________________. (1995). Peirce on the validation of science. In: KETNER,
Kenneth L. (ed.) (1995). Supra cit., pp. 103-112.
ROBIN, Richard S. (1967). Annotated Catalogue of the Papers of Charles
S. Peirce. Amherst, MA: University of Massachusetts Press.
Available in electronic edition at URL:
[http://www.iupui.edu/~peirce/robin/robin.htm]. Acessed in 20
March 2004.
RODRIGUES, Cassiano T. (2001). Lógica e Investigação: Uma
interpretação da gênese dos principais temas do pensamento de
Charles S. Peirce. Dissertation presented to the Departament de
Philosophy of the Universidade Estadual de Campinas, under the
direction of Prof. Dr. Arley Ramos Moreno, as a partial
requirement for the obtaining of the title of Master in Philosophy.
____________________. (2003). O encantamento da musa: apresentação à
tradução de “Um Argumento Negligenciado para a Realidade de
Deus”. In: Cognitio – Revista de Filosofia. São Paulo, v. 4, nº 1,
jan. / jun. 2003, pp. 87-97.
ROSA, João Guimarães. (1986). Grande Sertão: Veredas. Rio de Janeiro:
Nova Fronteira.
ROSENTHAL, Sandra B. (1990). Peirce’s ultimate logical interpretant and
dynamical object: a pragmatic perspective. In: Transactions of the
495
Charles S. Peirce Society – A quarterly journal in American
philosophy. Buffalo, v. XXVI, nº 2, Spring, 1997, pp. 195-210.
___________________. (1994). Charles Peirce’s Pragmatic Pluralism.
Albany, NY: State University of New York Press.
RUSSELL, Bertrand. (1956). Logic and Knowledge. Essays 1901-1950.
Ed. by Robert Charles Marsh. London: George Allen & Unwin ltd.
SANTAELLA, Maria Lúcia. (1992). A Assinatura das Coisas: Peirce e a
Literatura. Rio de Janeiro: Imago Editora.
______________________. (1995). A Teoria Geral dos Signos: Semiose e
Autogeração. São Paulo: Editora Ática.
______________________. (1999). A new causality for the understanding of
the living. In: Semiotica – Journal of the International Association
for Semiotic Studies/ Revue de l’Association Internationale de
Sémiotique. (separata/ offprint). Berlin; New York, nº 127, v. 1,
1999, pp. 497-519.
______________________. (2000). Chaves do pragmatismo peirciano nas
ciências normativas. In: Cognitio – Revista de Filosofia. São Paulo,
ano 1, nº 1, segundo semestre de 2000, pp. 94-101.
______________________. (2004). O Método Anticartesiano de C. S. Peirce.
São Paulo: Editora da UNESP.
SAVAN, David. (1977). Questions concerning certain classifications
claimed for signs. In: Semiotica – Journal of the International
Association for Semiotic Studies/ Revue de l’Association
Internationale de Sémiotique. Haia; Paris; New York, v. 19, nºs.
3/4, 1977, pp. 179-195.
SFENDONI-MENTZOU, Demetra. (1995). A response to Savan. In: KETNER,
Kenneth L. (ed.). (1995). Supra cit., pp. 329-338.
SHERIFF, John K. (1994). Charles Peirce’s Guess at the Riddle: Grounds
for human significance. Bloomington and Indianapolis: Indiana
University Press.
496
SHORT, Thomas L. (1997). Hypostatic abstraction in self-consciousness.
In: BRUNNING, Jacqueline; FORSTER, Paul (ed(s).) (1997). Supra
cit., pp. 289-308.
SILVEIRA, Lauro Frederico B. da. (1980). A produção dos signos numa
estrutura social antagônica. In: Trans/Form/Ação – Revista de
Filosofia. São Paulo, v. 3, pp. 81-90.
_____________________________. (1983). Semiótica peirciana e produção
poética. In: Trans/Form/Ação – Revista de Filosofia. São Paulo, v.
6, pp. 13-23.
_____________________________. (1984). Pensamento, fenômeno
experimental e experimento na proposta pragmaticista. In:
Trans/Form/Ação – Revista de Filosofia. São Paulo, v. 7, pp. 49-59.
____________________________. (1991). Na origem está o signo. In:
Trans/Form/Ação – Revista de Filosofia. Marília, SP, v. 14, pp. 45-
52.
____________________________. (2000). Em busca dos fundamentos da
universalidade e da necessidade da semiótica e do pragmatismo
de C. S. Peirce. In: Cognitio – Revista de Filosofia. São Paulo, ano
1, nº. 1, nov. 2000, pp. 117-137.
____________________________. (2001). A comunicação de um ponto de
vista pragmatiscista. In: Cognitio – Revista de Filosofia. São
Paulo, nº 2, nov. 2001, pp. 203-212.
____________________________. (2003). Três espécies de bem. In: Cognitio
– Revista de Filosofia. São Paulo, v. 4, nº 1, jan. / jun. 2003, pp.
60-79.
____________________________. (2004). Observe-se o fenômeno: forma e
realidade na semiótica de Peirce. In: Cognitio – Revista de
Filosofia. São Paulo, v. 5, nº 2, jul. / dez. 2004, pp. 194-199.
SMYTH, Richard A. (1994). What logic can learn from ethics. In: PARRET,
Herman (ed.) (1994). Supra cit., pp. 49-60.
497
STUHR, John J. (1994). Rendering the world more reasonable: the
practical significance of Peirce’s normative science. In: PARRET,
Herman (ed.) (1994). Supra cit., pp. 03-15.
TANI, Ruben M. (1987). Peirce’s Semiotic-Pragmatism on Saying/ Doing.
In: Manuscrito – Revista Internacional de Filosofia. Campinas, v.
X, nº 1, Abril de 1987, pp. 95-103.
THIBAUD, Pierre. (1997). Between saying and doing: Peirce’s
propositional space. In: Transactions of the Charles S. Peirce
Society – A quarterly journal in American philosophy. Buffalo, v.
XXXIII, nº 2, Spring, 1997, pp. 270-327.
TIDMAN, Paul; KAHANE, Howard. (2003). Logic and Philosophy: A
modern introduction. Belmont, CA: Wadsworth/ Thomson
Learning.
TIERCELIN, Claudine. (1993a). Peirce’s realistic approach to
mathematics: or, can one be a realist without being a Platonist?
In: MOORE, Edward C. (ed.) (1993a), supra cit., pp. 30-48.
_________________. (1993b). La Pensée-Signe: Études sur Peirce. Nîmes:
Éditions Jacqueline Chambon.
_________________. (1994). Un pragmatisme conséquent? In: Critique –
Revue générale des publications françaises et étrangères. Paris,
tomo L, nº 567-568, ago./ set. 1994, pp. 642-660.
TRAMMELL, Richard L. (1972). Religion, instinct and reason in the
thought of Charles S. Peirce. In: Transactions of the Charles S.
Peirce Society – A quarterly journal in American philosophy.
Buffalo, v. VIII, nº 1, Winter, 1972, pp. 3-25.
WEBER, Max. (1995a). Wissenschaft als Beruf. Sttutgart: Philipp Reclam
jun. Translation used: O Político e o Cientista. Introdução de
Herbert Marcuse. Trad.: Carlos Grifo. 2ª ed. Lisboa: Editorial
Presença, 1973.
____________. (1995b). Politik als Beruf. Sttutgart: Philipp Reclam jun.
Translation used: O Político e o Cientista. Introdução de Herbert
498
Marcuse. Trad.: Carlos Grifo. 2ª ed. Lisboa: Editorial Presença,
1973.
WELLS, Rulon S. (1977). Peirce’s notion of the symbol. In: Semiotica –
Journal of the International Association for Semiotic Studies/
Revue de l’Association Internationale de Sémiotique. Haia; Paris;
New York, v. 19, nºs. 3/4, 1977, pp. 197-208.
WHITEHEAD, Alfred N. (1962). Science and the Modern World: Lowell
Lectures, 1925. New York: The Macmillan Company.
___________________. (1978). Process and Reality: An Essay in Cosmology.
Corrected edition. Ed. by David Ray Griffin and Donald W.
Sherburne. New York: The Free Press.
WHITEHEAD, Alfred N.; RUSSELL, Bertrand. (1927). Principia
Mathematica. Volume 1. 2ª ed. Cambridge: Cambridge University
Press.
WITTGENSTEIN, Ludwig J. J. (1921). Logische-Philosophische
Abhandlung. Translation used: Tractatus Logico-Philosophicus.
Tradução, apresentação e estudo introdutório de Luiz Henrique
Lopes dos Santos. Introdução de Bertrand Russell. São Paulo:
Editora da Universidade de São Paulo, 1993.
________________________. (1977). Vermischte Bemerkungen. Frankfurt-
am-Main: Suhrkamp Verlag. Edition used: Culture and Value. Ed.
by G. H. von Wright in collaboration with Heikki Nyman.
Translation by Peter Winch. Oxford: Basil Blackwell, 1980.
________________________. (1998). Philosophische Untersuchungen /
Philosophical Investigations. 2ª ed. Translated by G. E. M.
Anscombe. Oxford; Malden, MA: Blackwell Publishers.
WOLFF, Christian. (1728). Discursus Praeliminaris de Philosophia In
Genere. Tradução utilizada: Preliminary Discourse on Philosophy
in General. Translated, with an introduction and notes by Richard
J. Blackwell. Indianapolis; New York: The Bobbs-Merrill Company,
Inc, 1963.
499
_______________. (1729). Philosophia Prima, sive Ontologia. Edidit et
curavit Joannes Ecole e consortibus laborum C.N.R.S.
Metaphysicae. In: Gesammelte Werke. Herausgegeben und
bearbeitet von J. École, J. E. Hoffmann, M. Thomann, H. W. Arndt.
2. Abteilung. Lateinische Schriften, Bd. 3. Hildesheim; New York:
Georg Olms Verlag, 1977.
_______________. (1731). Cosmologia Generalis. In: Gesammelte Werke.
Herausgegeben von J. École. 2. Abteilung. Lateinische Schriften,
Bd. 4. Hildesheim; New York: Georg Olms Verlag, 1964.
ZINN, Howard. (2003). A People’s History of the United States: 1492-
Present. New York: HarperCollins Publishers Inc.
500