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Phenomenology of the Spheres: From Ancient Spherics to Philosophical
Cosmology
Thesis · May 2018
DOI: 10.13140/RG.2.2.13317.81129
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Phenomenology of the Spheres:
From Ancient Spherics to Philosophical Cosmology
A Thesis Presented
by
Randolph Thompson Dible II
to
The Graduate School
in Partial Fulfillment of the
Requirements
For the Degree of
Masters of Arts
in
Philosophy
Stony Brook University
May 2018
Copyright by
Randolph Thompson Dible II
2018
Randolph Thompson Dible II
2018
ii
Stony Brook University
The Graduate School
Randolph Thompson Dible II
We, the thesis committee for the above candidate for the
Master of Arts degree, hereby recommend
acceptance of this thesis.
Edward S. Casey – Thesis Advisor
Distinguished Professor, Department of Philosophy, Stony Brook University
Clyde Lee Miller – Second Reader
Professor, Department of Philosophy, Stony Brook University
iii
Francesco Alfieri – Outside Reader
Professor, Department of Philosophy, Pontifica Universitas Lateranensis
This thesis is accepted by the Graduate School
Charles Taber
Dean of the Graduate School
iv
Abstract of the Thesis
Phenomenology of the Spheres:
From Ancient Spherics to Philosophical Cosmology
by
Randolph Thompson Dible II
Master of Arts
in
Philosophy
Stony Brook University
2018
Abstract: Recent developments within phenomenology have brought to light the indebtedness of phenomenological scientific philosophy to Ancient Greek philosophy. The recent trend that
builds on the ancient precedents found in the theories of forms, for example, has demonstrated the importance of the philosophy of Plato and Aristotle for contemporary manifestations of the
development of phenomenological eidetic science. This thesis builds on three parallel developments in the phenomenology of time that equally indicate the significance of the ancient
Hellenic exact mathematical science of spherical cosmology for the further propagation of phenomenological philosophy. The hypothesis of the infinite sphere gives phenomenology an
external foundation capable of accounting for the constitution of the phenomenal universe, possible worlds, and the harmonic continuum of life spanning the inner and outer cosmos.
Phenomenological cosmology offers a unified metaphysical framework for first philosophy and the special sciences, with particularly interesting implications for empirical cosmology and
theoretical physics. Phenomenology of the spheres brings these phenomenological cosmological insights together in the geometric comprehension of the infinite sphere.
v
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Dedication
This thesis is dedicated to the memory of Peter Byrne Manchester (1943—2015), who was my
professor and friend. The impetus for the line of study that became this thesis came from my
reading of his 2005 book The Syntax of Time: The Phenomenology of Time in Greek Physics and
Speculative Logic from Iamblichus to Anaximander, as an act of memorialization. His unique
position in phenomenology and Neoplatonic scholarship gave him a view of the paradigmatic
essence and original intention of philosophy. It is my intention to share this vision as I see it
articulated in the tradition that he contributes to.
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Origin and limit
Peter Manchester’s Semeion, from The Syntax of Time (Brill: 2005), p. 69. This image graphs a two-ray interpretation of Iamblichus’ Semeion of Pseudo-Archytas.
One line must be seen as being originated, the other as being terminated, at an angle to one another, i.e., each in its own dimension. - Peter Manchester, The Syntax of Time, p. 45
The κλάσις or breaking in the line comes in the act of drawing it. One must decelerate and come to a stop at the κλάσις, in order to begin in a new direction… Redirection without change of velocity ‘at an instant’ would require an instantaneously infinite acceleration; perfect breaking requires perfect breaking, passage of velocity through zero. Since this is not possible, what we really have is two rays, as amply confirmed by the oldest description, “for the κλάσις becomes of the one [ray] the origin, of the other the bound/limit (πέρας as against τέλος, end). - Peter Manchester, The Syntax of Time, p. 68-9.
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Table of Contents
Abstract of the Thesis………………………………………………………………………….…iv
Dedication……………………………………………………………………………………...…vi
Frontispiece………………………………………………………………………………………vii
Table of Contents……………………………………………………………………………..…viii
Preface: Expansion of Phenomenology to the Cosmic Scale. Peter Manchester, Anna-Teresa
Tymieniecka, and Hedwig Conrad-Martius……………………………………………………….x
Prospectus: Spencer-Brown’s Mathesis Universalis, the Calculus of Indications. A Calculus
Intended for All-Encompassing Self-Reference………………………………………..………xvii
Acknowledgments………………………………………………………………………..………xx
Chapter 1 – Introduction to the Phenomenology of the Spheres……………………….…………1
1.1 – Navigating the Academy with Geometry…………………………………...………1
1.2 – The Sphere Itself (την σφαιραν αύτήν) at the Origin of Geometry……………….2
1.3 - Ageōmétrētos mēdeìs eisítō. (ἀγεωµέτρητος µηδεὶς εἰσίτω)……………………...…5
1.4 – Philosophical Cosmology I: Plato and Aristotle…………………………………….7
1.5 – The Lost 4th Century Spherics………………………………………………………8
1.6 – Philosophical Cosmology II: From Contemporary Ancient Scholarship to Phenomenology…………………………………………………………………………………..10
1.7 – Phenomenological Cosmology…………………………………………………….12
Chapter 2 – From the Phenomenology of Time to a Phenomenology of the Spheres…………...19
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Chapter 3 – Propagation of the Spheres in the Work of Hedwig Conrad-Martius: The Two
Additional Dimensions of Aeonic Space-time and Apeiric Space-time…………...…………….45
3.1 – The Phenomenological Cosmologies of Manchester and Conrad-Martius……….48
3.2 – Peter Manchester’s The Syntax of Time………………………………..…………..49
3.3 – The Phenomenological Cosmology of Hedwig Conrad-Martius…………………..51
Bibliography………………………………………………………………………………..……55
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Preface: Expansion of Phenomenology to the Cosmic Scale. Peter Manchester, Anna-
Teresa Tymieniecka and Hedwig Conrad-Martius.
According to the current dominant tradition of philosophy, we have broken with classical
metaphysics just as classical metaphysics once broke with mythology. This tradition ties this
break to Nietzsche’s proclamation that God is dead, or in Peter Sloterdijk’s words, “the orb is
dead.”1 By this, Sloterdijk means a “philosophical cosmology”2 of metaphysical orders of reality
harmonized in a framework of spheres—in a word borrowed from Heidegger after Kant,
ontotheology—is dead. After all, what would these spheres be if not myth? Of course, they have
always been more than mythological—from the very beginning of philosophical speculation in
Ancient Greece these spheres have been present not merely as myth but as morphological
structures framing the entire paradigm of first principles, not limited to the foundations of
mathematics and the sciences. The most conspicuous vocation of the sphere paradigm has always
been the astronomy that moved equally from the astro-theology of myth and from the
navigational science of observational astronomy, to the “higher astronomy”3 of Plato and the
cosmological context of other Ancient Greek philosophers. The move from cosmogony to
cosmology with the advent of the Logos, must be repeated today at the scale of disciplines that
were once the province of philosophy. Just as myth had to give way to philosophy, now
empirical myth must give way to philosophy. With the loss of the center of orientation, the
1 Sloterdijk, Spheres II (2014), ff. 553. 2 Ibid., 113. 3 True or real astronomy is contrasted to observational astronomy in many ways in the Republic and elsewhere. Cf. 529c-530c; Mourelatos 1980; 1981. This will be seen in more detail later.
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paradigmatic sphere has been marginalized and pushed to the periphery. The naturalization of the
sciences and the secularization of philosophical speculation has emptied our ability to imagine
this situation, and changed the overall academic attitude toward Neoplatonism and its affiliated
philosophies of idealism. But the sphere motif is not myth, it is iconic, paradigmatic, and
expresses in its essential morphology an axiomatic foundation for the order of the cosmos. The
ordering principle of the sphericity of being is the guiding thought behind three
phenomenologies of time, and in this thesis I will propose that we move these insights to a new
kind of phenomenology, a phenomenology of the spheres.
In his 2005 book The Syntax of Time, Peter Byrne Manchester showed that it is possible
to land philosophical speculation in the higher dimension of eternity. This move is achieved by
opening the aperture of phenomenological disclosure space, analogous to opening the conic
section of the visual field to the full sphere of the cosmic horizon. The discovery of a movement
beyond the manifest space-time continuum of the phenomenal universe by way of a paradigmatic
framework that can be articulated in the language of philosophy and shared for the benefit of
humanity has been my hope since the beginning of my philosophical activity, and this is,
perhaps, the hope of the metaphysical speculation that characterizes philosophical activity in
general. The Syntax of Time takes the ancient precedents of Husserl’s diagrams of time-
consciousness as its subject matter, exposing the original place of phenomenological philosophy
in the history of ideas. By returning our philosophical attention to the original meditations on
phenomena, Manchester shows how contemporary phenomenology can use its own essential
structure to return our meditation on phenomenal disclosure—and our experience of the world on
its terms—to its proper place in the far sphere of the cosmic horizon. The cosmic scale and
orientation of philosophy has always been present, and the classical sources of philosophy are
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explicit enough about this presence, but the dominant metaphysical interest in the naturalization
of speculation has, especially since the end of the eighteenth century, marginalized this
orientation, and sent it to the periphery. By attending to the periphery, I hope to operationalize
the founding intuition of the infinite sphere in phenomenology.
Anna-Teresa Tymieniecka, a student of Roman Ingarden, and founder of the Analecta
Husserliana: The Yearbook of Phenomenological Research and of the World Phenomenology
Institute, has a phenomenology of time and of the world-order that is very similar to that of Peter
Manchester. Her phenomenology of life and the human condition centers on life’s intrinsic
function of the disclosure of being—a conception of life that she calls ontopoiesis. This
conception follows the development of a philosophy of life from Wilhelm Dilthey, Jose Ortega y
Gasset, and particularly Edmund Husserl. Tymieniecka’s phenomenology is a deepening of
Husserl’s last phase of phenomenology—that of the lifeworld—in the direction of the tasks he
set for phenomenology’s further development. Her phenomenology of life arises from her early
Leibnizian philosophy of a multi-spherical constitutive schema of the universe, consisting of
metaphysical world-orders as the condition of the real world. In her tireless engagement with
analytic philosophy and the special sciences, she developed a united front between
phenomenology and scientific cosmology, devoting her last decades of life to conferences on the
theme of life in the cosmos.
Tymieneicka’s own phenomenological philosophy acknowledged the influence of the
“real-ontology” and natural philosophy of an early student of Husserl named Hedwig Conrad-
Martius. Tymieniecka heroically embraced a recognition of Aristotle’s prima philosophia as
philosophia perennis, aligning her deepening of Husserlian phenomenology with the spirit of
Conrad-Martius’ profoundly mystical phenomenology that is simultaneously a rigorously
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analytic and realist metaphysical philosophy. When I first found that the later work of Conrad-
Martius, not mentioned by Tymieniecka, nor studied in the anglophone world aside from one
1972 dissertation by James G. Hart,4 had already confirmed the spherical world-view that Peter
Manchester opened up, I was certain that this motif of an ancient and perennial wisdom needed
to be shared in the contemporary world of philosophy. The hope of the unification of science in
the modern world, and the inevitability of an increasingly global metaphysical paradigm,
indicates the value of a perennial scientific philosophy. The spherical architectonic offers at least
this much.
The spherical world-view is common to the philosophies of Tymieniecka, Conrad-
Martius, and Manchester. Manchester, whose phenomenology was most closely connected to the
Ancient Greek sources of these philosophies, traces their source to the original texts of spherical
cosmology, called the spherics (sphairikē). As I researched the ancient spherics, I realized that
although the original texts are lost, the essential intuitions could be reconstructed enough to
provide the initials of a phenomenology that could synthesize the multiple phenomenological
cosmologies and open a new frontier in the exploration of the cosmos. The hypothesis of an
infinite sphere already provides a tremendous leap forward in the vision of the intercoherence of
forms and of cosmic harmony.
The three phenomenologies of time explored in this thesis are evidently
phenomenological cosmologies of space-time. The self-evidence of the given cosmos around us
4 James G. Hart’s 1972 dissertation for the Ph.D. at the University of Chicago’s Divinity School, Hedwig Conrad-Martius’ Ontological Phenomenology, is to date the only book-length work in English on her philosophy, and the only work with extensive discussion of her 1950s cosmological turn. His dissertation has been my chief source in this matter, guiding me through her original German texts. His availability for discussion has been an invaluable aid in my understanding of her sophisticated philosophy. The re-publication of his work is forthcoming.
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is sufficient for the validity of the knowledge of the external world as a phenomenal universe—
this is Husserl’s principle of all principles—but it also gives rise to more than what is merely
given. This surplus of the given is for the most part left unremarked in Husserl’s
phenomenology, but it has a history in the Neoplatonic heritage he draws his essential elements
from. Manchester, Tymieniecka, and Conrad-Martius, all take as their starting point for a
phenomenology of time the same two loci classici of Aristotle’s Physics IV and Plotinus’
Ennead III.7, “On Eternity and Time.” For Conrad-Martius, these two references show up on the
first page of her 1954 Die Zeit. The same two sources are omnipresent in Manchester’s The
Syntax of Time. In Tymieniecka’s most advanced exposition of her phenomenology, Logos and
Life, Book 4 (Tymieniecka 2000), the same Aristotelian locus classicus sets the stage for her
dialectic of Chronos and Kairos (ff. 489), while Plotinus’ treatise frames her question of eternity
(115). For all three, the Aristotelian spanned interval of the “now” of time, analogous to the point
of space, is seen to derive from the sphere of the total cosmos. Conrad-Martius calls this sphere
the “entelechial world-periphery” of “aeonic space-time,” the “eternal circular motion” of the
heavens from Aristotle’s book On the Heavens, which is elemental to his aether theory.
Tymieniecka follows Plotinus’ circular motion of the Aeon in her project of recovering the “great
vision of the All” (643), dancing in the music of the spheres (ff. 655). Manchester, finally,
develops a metrological, figured philosophy of the spanned interval of the now that is scaled
down from the cosmic context, and framed according to the full sphere of the total disclosure
space. Manchester’s philosophy expands Husserl’s schematization of the space of intentionality
into a phenomenology of the disclosure space. He calls this space of world-disclosure an “all-
encompassing self-referential equality of an intentional kind” (53), analogous to mathematical
phase space. By the extension of Husserl’s schematization, the spanned interval of the now in the
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retentional-protentional field is projected inward to the center and outward to the sphere.
Manchester identifies the lost source for this procedure in the earliest treatises of spherical
cosmology, the 4th Century spherics.5
In her earliest work, her 1913 Erscheinungslehre,6 Conrad-Martius describes the excess
of the given, the noema, in terms of the surroundings, the “given-along-with” (Hart 17), and
institutes an analysis of horizons to go along with the analysis of essences. Conrad-Martius’
early realism of the external world focused on what actually presents itself to the human being—
what is disclosed—and found, long before Heidegger, an essential relationship to the world, a
co-constitutive relation of being-in-the-world. In her final phase of philosophical work, in the
1950s, Conrad-Martius expands this thesis to the twofold cosmological limits of a being
distended between an a-cosmic sub-spatial flux, corresponding to the Aristotelian cosmological
prote hyle, and a super-spatial aetherial world-periphery, corresponding to the Aristotelian
cosmic entelechia. The earlier horizon of the surrounding world grows to include the
cosmological world-periphery. The aetherial space-time dimension is encompassed by a final
dimensionality which she calls apeiric space-time. On my interpretation this final dimensionality
is the infinite sphere. These two dimensions of space-time are the most sophisticated
developments of the philosophy of space and time, and deserve more attention. We will be in a
better position to analyze them later.
In her essay “Conjectural Inference and Phenomenological Analysis,” Tymieniecka first
outlines her program of expanding the structural analyses of her teacher Roman Ingarden from
5 Manchester 2005, ff. 49. Heath 2016, ff. 348. 6 Die erkenntnistheoretischen Grundlagen des Positivismus: Zur Ontologie Erscheinungslehre der realen Aussenwelt. Halle (Salle), Niemeyer. http://ophen.org/pers-100321 . We will follow James Hart’s convention in abbreviating this text as Erscheinungslehre.
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ontology to cosmology (Tymieniecka 1965, 252), by way of approaching the given (noema) not
only as an ontological structure, but as a functional pattern whose telos accords with a universal
order of indications. It is by conjectural inference that she follows the indications of the given
(noetic) intentional pattern as anticipatory evidence of a universal order, which she says is more
generally expressed by the term “pre-established harmony” (271). It is Tymieniecka’s example
that is followed in designating the field of these studies phenomenological cosmology. It is
Conrad-Martius’ cosmological turn that set the earliest post-Husserlian precedent for this
research domain, while Manchester identified its ancient doctrinal source. With these three
important developments in phenomenological cosmology, comprehended in the infinite sphere,
we can begin to see a whole system of infinite sphere variations giving horizon to all the ordered
elements of possible experience, and positioning them in relation to the dimension of the infinite
sphere. The infinite sphere as a dimension of space-time is Conrad-Martius’ apeiric space-time
(apeirische Raumzeit7), and its systematic exposition will be saved for the end of this thesis.
Under the name of a phenomenology of the spheres, these fields coalesce to the classical
philosophical economy of a geometric metaphysics, located at the origin of geometry, and
encompassing all with perfect continence.8
7 Der Raum (1958), ff. 217. 8 This Encompassing, or continens, resonates in many ways. In no special order, three such ways are the following: 1. Karl Jaspers conceived ontology, following the Parmenidean spherical ontology and Aristotelian theory of space as the surrounding, as periéchontology, and made “the encompassing” (das Umgreifende) his ultimate ontological horizon and central philosophical concept. 2. Manchester refers to the ancient spherics as a “lost continent in the history of philosophical ideas,” which he aims to recover (Manchester 56). This is a suggestive phrasing because it brings up the Atlantean myths of the Republic, as well as the connections of philosophical ground of reference and cosmological firmament. 3. As in Euclid’s Elements, which Bertrand Russell compares it to, George Spencer-Brown’s mathematical text Laws of Form, which we will hear more about shortly, generates forms a posteriori on forms given a priori, which all depend on the definition of the first term, distinction: “distinction is perfect continence” (1).
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Prospectus: Spencer-Brown’s Mathesis Universalis, the Calculus of Indications. A Calculus
Intended for the All-Encompassing Self-Reference of the Sphere.
This course of study all began in the Fall semester of 2015, shortly after Peter Manchester had
passed away. At the most personal level, this course of study initiated by Professor Manchester’s
work has been a return to my original interest in the intersection of the philosophy of mysticism
and the cybernetic metaphysics initiated by my long-time friend and mentor, George Spencer-
Brown. Spencer-Brown’s 1969 book Laws of Form marked a new age for systems theory and
cybernetics, and it did this by way of a philosophy of the act of making a mark—the indication
of the first distinction—in an otherwise unmarked space. For me, the central idea of this
ubiquitous act marked a paradigmatic revolution that oriented my mental space according to the
logical context of space itself—a syntax of space! I first found this strain of semiotic
metaphysics in the work of John Cunningham Lilly, who used Spencer-Brown’s calculus to
traverse mathematical phase space in his pioneering consciousness studies in his own invention
of the flotation tank. John Lilly had interpreted the marked state of Spencer-Brown’s calculus as
a way of traveling into other universes. This interpretation, of course is far out, to employ the
nomenclature of these pioneering psychedelic scientists of the mind.
Spencer-Brown’s response to Lilly’s other-worlds interpretation reverses it to the point of
a strong positivity of the indexical universe, clearing the way for an equally far-out mathematical
realism. In 1973, Lilly organized what would become an historical conference in the history of
cybernetics. On the final day of the conference, Lilly confronted Spencer-Brown with this
interpretation of his calculus, and Spencer-Brown corrected him by reversing it, telling Lilly that
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in fact it was the way to get back to this universe.9 I have gradually come to understand this
admittedly far-out exchange to be about the function of the imagination in a phenomenology of
possible worlds grounded in the principle of the reality of the indexical universe. This is a
general interpretative schema that only years later found confirmation in the philosophy of the
phenomenologists described in this thesis. The mathematical calculus of Spencer-Brown came
from his work in the algebras of logic, but belongs to the philosophical tradition of mathematical
developments running through Euclid, Leibniz, and the Cambridge Neoplatonists. This tradition
emerges in his era as an axiomatic, formal deductive instance of the classical mathesis
universalis. Its phenomenological interpretation had been apparent to me for some time, but I
had not yet known that the early modern articulation of the mathesis universalis, whose
philosophical roots ultimately lie in the philosophy of the Pythagoreans, was so significant for
the phenomenology of Husserl. Spencer-Brown’s calculus of indications has important
implications for the developing thesis of a phenomenology of the spheres initiated by my more
recent researches. These implications will be explored in part in this thesis, but the further
development of the cosmology of iconic logic and void-based algebra for the phenomenology of
9 The transcripts for this encounter are available online, via Kurt von Meier’s webpage: https://www.kurtvonmeier.com/the-aum-conference/ My own allusion to the historical significance of this conference recalls to those in the cybernetic community the famous Macy conferences that took place in New York City after the second World War. The constituents of the second-order cybernetics that began with this 1973 conference—and who, for example, comprise the population of the American Society for Cybernetics—might agree with this allusion. Spencer-Brown work in pure mathematics marks the transition from first-order to second-order cybernetics, in the history of this contemporary science.
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the spheres is beyond the scope of the thesis.10 The figured philosophy presented in what follows
is preliminary to these developments.
10 For an application of the calculus of indications as mathesis universalis to Tymieniecka’s phenomenology of life as ontopoiesis, see my forthcoming (2019) article in Analecta Husserliana, “Ontopoiesis, Autopoiesis, and a Calculus Intended for Self-Reference.”
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Acknowledgments
The research for this thesis began as a tribute to Professor Peter Manchester in the early Fall of
2015. This thesis synthesizes my own philosophy to date, and therefore brings in earlier
influences, but the influences on this more recent research are more tightly concentrated than the
discours fleuve of previous years. Before I embarked on an academic life of philosophy, I found
my pre-philosophical roots in a pattern of metaphysical development that led me to the peak
insights of a 1969 work in pure mathematics, which sparked a revolution in cybernetics and
systems theory. This work is Laws of Form by Professor George Spencer-Brown, who was my
early tutor and friend. Since his revolutionary development is also present in the programming of
the spherical paradigm that I’ll argue for in this thesis, his influences remained to this day
operational in my thinking. I visited Spencer-Brown in England a year before he died, and on
that trip I received word that Professor Manchester had passed away. I had not yet opened my
mind to the spherical perspective of Professor Manchester’s work. But already the mere
coincidence unconsciously suggested a confluence of their respective philosophical
developments. By one year later I had discovered, but not yet synthesized, the few foundational
elements of this thesis, and was happy share with Professor Spencer-Brown in person the fact
that I was applying his calculus to phenomenological scientific philosophy through the work
prepared by a few “mystical logicians,” which was to his liking. By this I meant the constellation
of phenomenological philosophers (who are also logico-ontologists committed to the philosophia
perennis and mathesis universalis) I had recently discovered, such as Tymieniecka, Mahnke, and
Conrad-Martius. Anna-Teresa Tymieniecka passed on one year before Manchester, so I never
did meet her, but these three—Anna-Teresa Tymieniecka, Peter Manchester, and George
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Spencer-Brown—all deserve special acknowledgment as guiding lights for me. Hedwig Conrad-
Martius is perhaps in another category altogether, belong to the immediately preceding
generation of philosophers, but is also grouped, in my mind, with these completed lives, who
represent for me the most exalted extant doctrines of philosophy.
I am abundantly grateful to the community of students, faculty, and staff at Stony Brook
University’s Department of Philosophy who have participated in the lively philosophical energy
that nourished my research and philosophical development. Stony Brook has an important legacy
in the American philosophical academy, and being a part of this department over so many years
has been a real joy and definite privilege. The changing student and faculty body has always
done well to support the spirit of philosophical pursuit. Professor David Dilworth was my first
advisor at Stony Brook. By teaching such synoptic philosophers as C. S. Peirce and Kitaro
Nishida, Professor Dilworth gave me ample opportunity to meditate on the history of
philosophical ideas, from my first semester to my last. Professor Peter Manchester’s teaching of
hermeneutic method preceded the arrival of his positive phenomenological philosophy in my
life. His example has been the paradigm case of a comprehensive precision that is reflected in the
form of his positive contributions to phenomenological philosophy. The administrative care and
generosity of Alissa Betz, Assistant to the Chair, has made this thesis possible. Her
administrative wisdom and diligence keeps the department running smoothly, and has kept me
employed, freeing time for this work. I am honored and pleased to have had Professor Clyde Lee
Miller join my committee on short notice. His work on Nicholas de Cusa has been important to
me, and I sincerely appreciate his vantage on my particular topic.
Above all, my wife, Jennifer Carter, has in many ways nourished the wonder behind my
philosophizing. Not only is she also a philosopher, she was a philosopher before I was, and she
xxii
encouraged and motivated me to pursue philosophy academically. Philosophizing whole-
heartedly is a necessity for engaging life as a whole, and our sym-philosophein pervades our life
together. The spiritual dimension of the philosophical life opens in the intimate sphere, and
meeting a philosopher there is an indescribable joy. Her gifts of insight and language have also
touched my techniques, teaching me to express in the most appropriate way whatever wisdom I
might generate. Her own philosophy of touch and the caress has shaped our relationship in the
most wonderful ways. While inspiring my sphere of philosophy in my own way, hers reaches out
and structures our lives to make them more open to the fund of wonder, and more productive of a
shared world of living together in sexuate difference. My gratefulness to her continues to grow.
Sharing in that growth and joy of the life behind the work, are the children, whose influence may
not have yet reached the technique of the letter, but pervades the spirit and the meaning of the
expression. While they may grow to work outside the academy, their cortical reticuli will always
have a store of philosophical curricula. Between me writing my thesis and Jennifer writing her
dissertation, and both of us defending in the same week, special thinks are due to our childcare
provider, Felisa Mahabal. I hope that our academic accomplishments whilst raising five small
children serves some as motivation to proceed with life uninhibited by the demands of graduate
school.
Many philosophy professors at Stony Brook encouraged my early speculative system of
metaphysics, but the most supportive has been Distinguished Professor Edward Casey, who
served as my thesis advisor. Professor Casey was a close friend of Professor Manchester, and a
collaborator in joint phenomenologizing. Professor Casey’s enterprising and distinctively
American style of making his own unique contributions to phenomenology, and proceeding to
think the material through along the lines he established for this purpose, led him to uncover ever
xxiii
new places, new worlds, for philosophy. This style has certainly influenced by methods in the
generalizing of Professor Manchester’s position. Professor Casey’s peri-phenomenology, from
The World at a Glance and The World on Edge, kept cropping up for me—for example, in my
studies of Paul Ricoeur, who was impacted by Jaspers’ metaphysical Encompassment
(Umgreifende); in my studies of Derrida, whose early focus on indication and arche-writing
described the limits of phenomena—until I found it to hold in my own way at the periphery of
the spherical paradigm I picked up from Professor Manchester. This cosmological peri-
phenomenology of my own attends to edges and outsides of phenomena as does that of Professor
Casey, but also stands on the apeiron-ontology of Hedwig Conrad-Martius, and returns to the old
peras-kentron (limit-center) equation of periéchontology. Above all the individual contributions,
Professor Casey’s style in philosophizing has been a tremendous gift of my studies here at Stony
Brook. I am indebted to his leading example in philosophy and altruistic spirit in daily life.
In the adventure of discovery, numerous people have been able to evaluate my work as
worthy of their time and attention, which always brings me the dumbfounded joy of frontier
exploration. Leon Conrad, who I met at George Spencer-Brown’s funeral, generously applied the
rhetorical skill of his school, The Academy of Oratory, in extensively editing a draft of my
second chapter, nearly as soon as it was handy for him. I owe him a debt of warm gratitude for
this gift. Our scholarly exchanges afforded stimulating engagement with themes relevant to both
of our interests, which happen to be aligned with the themes of this thesis. Paul St. Denis is
another friend who shared the sense of urgency that emerges in the jubilation of philosophical
conversation. St. Denis also invited me to work in his laboratory for employment during the time
of writing this thesis. His flexibility in accommodating my student schedule—and appreciation
of the tangential philosophical consideration of computer science—has been invaluable in the
xxiv
weaving together of this gossamer. Paul St. Denis also introduced me to a Stony Brook graduate
student, Sushank Chibber, who is a willing collaborator in the translation of Hedwig Conrad-
Martius’ works that are most relevant to my studies. Chibber has been invaluable in providing
me access to Conrad-Martius’ thought, and has done so selflessly, at my direction.
The community and legacy of Professor Tymieneicka’s society, the World
Phenomenology Institute (WPI), under the direction of Professors Jadwiga and William Smith,
has provided a place for scholars working in Professor Tymieneicka’s spirit of higher order
phenomenological philosophy to meet and share ideas. I owe a heartfelt thanks to them for this
service to the phenomenological community, and especially to such a unique interest as mine in
the phenomenology of Professor Tymieniecka herself. The North American Society for Early
Phenomenology (NASEP), presided by Professor Kimberly Baltzer-Jaray, and organized by
Professors Rodney Parker, vice-president, and Charlene Elsby, treasurer, has been another
philosophical organization that hosted my work. Professor Parker also runs a course on early
women phenomenologists at the Paderborn University Center for the Study of Women
Philosophers and Scientists, which has been an important gathering together of scholars working
on the philosophy of Hedwig Conrad-Martius from around the world. There I was happy to meet
Professor Ronny Miron, whose works on Conrad-Martius I have appreciated from the start of my
studies. My participation in the Libori Summer School in Paderborn has been formative of my
appreciation for Conrad-Martius’ career and development of her own unique ontological
phenomenology. In pursuing the things I learned there, my continuing research led me to contact
Hans Rainer Sepp, of the Central European Institute of Philosophy (Mitteleuropäisches Institute
fur Philosophie), who responded to my questions and gave me more things to consider in my
studies, and who generously invited me to collaborate further. Finally, in seeking out an outside
xxv
reader for this thesis, Professor Francisco Alfieri, who is both a secretary of the World
Phenomenology Institute and the scientific editor of the Italian Opera Omnia of Hedwig Conrad-
Martius, agreed to read my work at the last minute. His kind spirit shows itself in such an
undertaking, in the midst of his very demanding work on Heidegger with Professor von
Herrmann. His encouragement in such circumstances testifies as much to his attitude as to the
quality of my thesis. I am truly fortunate to have him see my work.
Conversations over email with members of the organization Professor Manchester once
presided over provided some of the missing elements I needed to fill out his thought in the area
of Neoplatonic studies. These philosophers of the International Society for Neoplatonic Studies
(ISNS) include Marilynn Lawrence, Emilie Kutash, and Michael Wagner. Daniele De Santis,
who has written extensively on early phenomenology and ancient philosophy, has also been
wonderfully generous with his willingness to engage me philosophically.
Dietrich Gottstein of the Forum Münchener Phänomenologie International e.V. (FMPI)
has not only been instrumental in providing material from Conrad-Martius’ nachlass, but has also
hosted me at his home in Deggendorf. Conversations with Professor James Hart on Hedwig
Conrad-Martius’ philosophy have supplemented my reading of his 1972 book on Hedwig
Conrad-Martius (Hedwig Conrad-Martius’ Ontological Phenomenology, 1972; re-publication
forthcoming), which has been my key to understanding Conrad-Martius’ philosophy. I am
grateful to him for making himself available for extensive conversations.
1
Chapter 1: Initial Explorations of the Sphere
ἀγεωµέτρητος µηδεὶς εἰσίτω Ageōmétrētos mēdeìs eisítō. “Let no one untrained in geometry enter.” Inscription over the entrance to Plato’s Academy (quoted in Elias’ commentary on Aristotle’s Categories).11
1.1 Navigating the Academy with Geometry
Above the entrance to Plato’s Academy, there was an inscription that read “Let no one untrained
in geometry enter.” As we reach into the darkness of lost history, what lights the way is our own
living thought. Thought floats in the space of the imagination, and by its assumption of the forms
of the possibilities available for realization, it experiments with the intrinsic possibilities of its
being in that space—possibilities of configuration. That some possibilities are intrinsic it
discovers by means of the agglomeration of evidence that builds the case for the worlds it
inhabits, which it finds itself located in, yet still within the greater sphere of the imagination.
When it finds among the meaningful forms of this evidence an evidence for the possibility of
certain definite limits, it gains a foothold in the imagination and can begin to see that its world
stands in relief against this greater background of possibilities that do not cohere in the same way
as the evidence for the world. These limits are certainties that transcend the world of the forms
which cohere in the same way the case made for the world coheres. Phenomenology has a
11 Eliae in Porphyrii Isagogen et Aristotelis categorias commentaria, CAG XVIII 1: (Berlin) 1900, 118, 13-19. Cf. Henri-Dominique Saffrey, “ἀγεωµέτρητος µηδεὶς εἰσίτω. Une inscription légendaire.” Revue des études grecques. Vol. 81 (1968, 67-87), 81.
2
concise name for this world of experience: the lifeworld. These limits cohere as a realm of
objective validities that can serve to confirm, cancel, condense, or compensate, for the case made
for the lifeworld. They are generally known as to us as the mathematical world of objective
truths, and its intrinsic forms are known to phenomenology as essences. But far from only being
mathematical in the conventional sense, this natural realm of transcendental objectivities is
ubiquitous in the special sciences, and constitutes the proper subject of philosophy instituted by
Plato and Aristotle. Sedimented in the Ancient Greek beginning of philosophy, specifically at the
origin of geometry, lies a paradigmatically foundational intuition of the whole far sphere of the
encompassing world of the transcendental imagination, indicated by the highest forms of certain
intuition, the telos that Plato calls the form of the good, but which we will understand as the
sphere itself—the paradigm for all possible spheres, which are its copies or images, but precisely
put, its icons (eikones) or ectypes. The point of this thesis is the positing of a kind of description
of phenomena that is at the same time the positioning of the phenomenal universe according to
the origin of space, the origin of geometry, the center of the sphere itself, and its comprehension
in the sphere. Intentionality, in the phenomenology of the spheres, is intentionality-as-
directionality, locating phenomena in the kosmos noetos.
1.2 The Sphere Itself (την σφαιραν αύτήν) at the Origin of Geometry: Center and Periphery
The center of the sphere itself is the ubiquitous self-referentiality of every point of reference we
bump up against in our experience of the world, as in our narrative (here, an eikos mythos) of
thought floating in the space of the imagination. Points of reference are openings, infinitesimal
apertures, or breaking-points, in the continuity of a self-referentially closed continuum. Points
3
are mere indications of ontological closure, they have indefinite plurality in the manifold worlds
of experience, and that is why the absolute certainty of being forever escapes the definition of a
point of reference—there is always an element of difference, allo-reference—and that is why
they are indications, points. They are never difference itself, only differences. The things in the
world, in contrast to the things in themselves, participate in this indefinite allocation of
difference and sameness, which will be raised to the cosmic context when we understand what
Plato’s meant by the identification of the cosmic equator with the circle of the same, and of the
ecliptic with the circle of the different. These circles are “great circles” of the infinite sphere, the
sphere itself (την σφαιραν αύτήν), which the Stoics called the Sphere of the All. As such,
because the sphere is infinite, its great circles are straight lines. Rays of particles which tend to
travel in a straight line only do so relatively to the space they occupy in the phenomenal
universe, not in the greater space of the imagination, where their indicational referents of
straightness and curvature and other mathematical descriptions lie. We can demonstrate a
particle’s mathematically precise position or momentum (kinesis), but never both
simultaneously. Demonstration, or the construction of a proof, is a matter of experience, which is
a distended form because it is in process, it is living with us, it is operational, and it is with us in
time. All this involvement is not the case with the things in themselves, and so with the form
itself, after the sphere itself. The realm of the form—its frame of reference, its case, its logical
syntax—is in the mathematical realm of objective validities, essences, eide. Experience is an
ecstatic de-centering, and therefore always involves the natural course of the becoming of a
particle of position as a point along a course, a path, a line. The validity of experience lies within
its distension, in its essence, where the sufficiency of its evidence lies. This is what Husserl
called the principle of all principles. The form itself, in contrast to its distended, spaghettified
4
form, is had through intuition, realization, noesis. Experience derives etymologically from the
very Greek which concerns us here: peras, limit. The realm of eide is the realm of the kosmos
noetos, ubiquitous, but properly peripheral to the phenomenal universe, constituting its horizons.
These horizons are horizons of the space of the greater sphere of the imagination as a disclosure
space. The emanations which define these horizons are not physical, but intentional rays, which
in turn define the physical space. They are intentionalities-as-directionalities which define the
realm of possibilities as a continuum of extended space-time. The dimensionality of phenomena,
which gives it its ecstatic quality of indefinite multiplicity, is in a very precise sense its order of
being, its degree of separation from the dimensionless peras and the far realm of mathematical
objective validities about the peras.
The periphery of the sphere itself is as equally ubiquitous as the center, but as the
invisible frame of reference for all the forms of indication of the center, it is the radically far
sphere, the infinite sphere itself, identifies with its periphery as much as its center is identified
with the center. We can imagine the center at the center of our every imaginative act—even
though this would not be the real center, which is the peras beyond ex-peri-ence—but the
infinite sphere itself and its periphery escapes becoming a content of our imagination, because it
can only be approached by conjectural inference, speculation, extrapolation from our geometrical
experience with the essential properties of spheres. It is instead the continens, the all-
encompassing outermost layer of the heavens. But we will, with Plato, “let the things in the
heavens alone,” and concern ourselves with their patterns, a ‘higher’ or ‘true’ astronomy
(Republic, VII).
5
1.3 Ageōmétrētos mēdeìs eisítō. (ἀγεωµέτρητος µηδεὶς εἰσίτω)
So let us return to the motto framing Plato’s Academy. For Plato, the highest aim of philosophy
is to lead the soul through the hierarchy of levels of being to the form of the good (agathon), so
what kind of geometry must we be in touch with if we wish to enter the academy? There is a
tradition of interpretation available to answer this question. Plato’s theory of forms posits the
forms as arithmetical in a specific sense; eidetic number (arithmos eidetikos). Each essence is
numerically a unit, one, a monad. The unity of a multiplicity is what is common to it (koinon),
and this is the basis for understanding how the essence of a thing is known on the Platonic
account. The immediate successor to the monad (monas) is the Indefinite Dyad (aoristos dyas),
whose geometrical expression is the line (gramme). In the description we can see the meaning of
indefinite as horizonless (a-horizmos). This Platonic “arithmological” account of the eide has its
proper context in the Pythagorean doctrine of the tetractys, the tetrad of the decad. On this
account the relationship between the one as limit (peras) to the unbounded (apeiron) holds in the
relations of the numbers to each other. The subject of arithmetic is the individuality of the
cardinal numbers, so of course a more complete account would go into the meaning of these first
ten numbers, and explain how they interrelate in the world of combinations of these elements.
Suffice it for now to say that the Pythagorean motivation for phenomenological eidetic science,
by way of Plato’s account, requires the explication of not only the arithmological interpretation
of the eide, but the equally general mathematical doctrine of geometry upheld by the
Pythagoreans as a paradigm for natural science. This will give us the sense of geometry
appropriate for the appreciation of the Platonic inscription, and the understanding of the sphere
proper to the phenomenology of the spheres.
6
Corresponding to the arithmetical unit or monad is the geometrical unit or metron.
Metrology and monadology are intimately related, but the difference is fundamental. There are
of course many fascinating courses to take here, but of particular interest for a phenomenological
cosmology is the interpretation of the metron itself as incorporating aspects of both the monad
and the dyad. The metron is conceived as the spanned interval between two horizons, or at the
limit case, between the limit (peras) and the unlimited (apeiron), which applies to the first
principle (arche) and founding cosmological notion of Anaximander, the apeiron.
We will see in the discussion of Peter Manchester’s phenomenology of the disclosure
space, the development of a metrology in the phenomenology of time that is a schematic
phenomenology of the cosmos—a figured philosophy. Anna-Teresa Tymieniecka’s
phenomenology of life’s intrinsic timing and spacing, framed by her phenomenology of possible
worlds and world-orders, adds to this framework a functional paradigm that is calibrated for the
application to scientific domains, capable of operationalizing the phenomenology of the spheres
by linking up with special sciences such as cybernetics and science of consciousness. The
advanced concept of “apeiric space-time” as the foundational dimension of an omnipresent
constitutive ontological dynamism in the thought of Hedwig Conrad-Martius is the primary
model for the paradigm of the phenomenology of the spheres. This sophisticated idea of a
dimension of the infinite gives us the fundamental concept of a general theory of extension, a
science of order and measure, elucidating the syntactical or liminal conception of dimensionality.
What we hope to find in future research is a development of this metrology in the direction of a
phenomenology of the spheres that elucidates a new framework for the transcendentally pure
cosmology that gives us the laws governing the constitution of dimensional continuua from first
7
principles, their relationships to phenomenal contents, and thereby the possibility of expanding
the lifeworld to the higher dimensions of the far sphere of the imagination.
1.4 Philosophical Cosmology I: Plato and Aristotle
After the famous triptych of the Sun, Line, and Cave, in the Seventh Book of the Republic, we
find Plato’s discussion of the training of philosophers in the mathematical sciences propaedeutic
to dialectic. Here, the sciences are organized to show the way to the highest teaching, showing
the soul the way to the highest end and aim of philosophy, the form of the good. The science of
astronomy appears multiple times in the short list of five sciences: first is arithmetic, second is
geometry, third is stereometric astronomy, fourth is what he calls real or true astronomy (ta onti
de astronomikon, 530A3)—a general and pure kinematics—and finally, fifth, harmonics. The
astronomy discussed here can also be seen in the Tenth Book of the Republic, the Tenth and
Twelfth Books of the Laws, in the Timaeus, and in the Epinomis. In the Epinomis, the Athenian
identifies astronomy as the highest teaching, which he admits is perhaps a surprise, and so asks
Clinias, “Are you unaware that the true astronomer must be a man of great wisdom?” (990a).
The topic of this thesis is the definite idea of that very wisdom indicated by Plato, marked by a
clear Pythagorean influence, and returned to its role of cosmological framework for philosophy.
In the Posterior Analytics, Aristotle develops his architectonic of the sciences in terms of
a distinction between “fact” and “reasoned fact,” regarding the investigations of different
sciences into problems related to one another as subordinate and superior. “As when” he writes,
“optical problems are subordinated to geometry, mechanical problems to stereometry, harmonic
problems to arithmetic, the data of observation to astronomy” (McKeon 1941, 130). The choice
8
of superior sciences, in the context of the distinction of mathematics from empirical sciences, is
an echo of Plato’s short list of sciences propaedeutic to dialectic, but in the form of Aristotle’s
distinctively empirical scientific philosophy. The “facts” of astronomy are the data of
observation, i.e. the phenomena. The “reasoned facts” of astronomy are the first principles of
spherical cosmology, which, according to the tradition starting with Eudemus, are designed to
“save the phenomena.”12 With the emergence of Logos from Mythos, the justification of
phenomena is mediated through the law (nomos) and order (kosmos) of the sphere. According to
Aetius, the first to describe the universe as a kosmos was Pythagoras,13 and Aristotle attributes
the identification of air-psyche-life (aer), the eternity of their motion, and the discovery of the
order (kosmos) of their movements to the Pythagorean Alcmaeon (De Anima, 1.405a).14 Like the
other exact mathematical sciences, contemporary astronomy is still, despite all its differences,
indebted to certain definite paradigmatic foundations formulated by the Greeks, and treated by
the philosophers. Today’s sciences are shaped by a naturalistic attitude very different from the
astrological vision of the ancients, but the definitions and paradigmatic theorems of Euclid’s
Elements and Diophantus’ Arithmetic, for example, are still the standard today.
1.5 The Lost 4th Century Spherics
The astronomy of Plato has as its standard the lost pre-Euclidean astronomical texts of the 4th
Century, but echoes of this lost work can be seen in the surviving texts of Autolycus, Euclid,
12 “What hypotheses of smooth and regular motions must we posit to save the phenomena of the wandering motions of the planetary bodies?” (Mourelatos, 1980, 34). 13 Peters, 1967, 108: Kosmos. 14 Ibid, 146: Ouranos.
9
Theodosius, and Aristarchus, which were collected and passed down by Pappus of Alexandria.
These surviving texts have in common a description of mathematical astronomy that builds on
the insights of observational astronomy, but distinguishes itself from the latter by positing the
full spherical context of the apparent motions of heavenly phenomena. We can call this the
hypothesis of the sphere. These ancient texts describe their subject with the convention of
distinguishing a science of phenomena from a science of the first principles supporting
phenomena, in this case a science of the sphere. This can be seen already in their titles:
Autolycus’ On Risings and Settings (observational astronomy), Autolycus’ On the moving
Sphere (spherics), Eudoxus’ kindred researches in spherics (lost; mentioned by Dietrich
Mahnke’s student Joseph Ehrenfried Hofmann15) Euclid’s Phenomena (spherics; made use of
Eudoxus’ lost text), Theodosius’ On days and nights (observational astronomy), and Theodosius’
Sphaerica (spherics). Sir Thomas Heath devotes six pages of his A History of Greek
Mathematics, Volume I, to making the case for a lost 4th Century textbook on spherics by
comparing similar propositions from Autolycus’ On the moving Sphere and Euclid’s
Phenomena.16 The object of Euclid’s Elements Book XIII is to “comprehend in a sphere” each of
the five regular solids, by the construction of the circumscribing sphere involving the relation of
an edge of the solid to the radius of the sphere.17 Archimedes extended the method of exhaustion,
which measures a figure from the inside, combining it with an approximation from the outside.
One can imagine that these methods of comprehension in a sphere and approximation from the
outside horizon could proceed from the intuition of the infinite sphere, giving us a metrology
based in synthesis. Heath’s description of the spherics is more historical than his adjacent
15 The History of Mathematics (1957), 25. 16 Heath 1921, ff. 348. 17 Ibid, 415.
10
description of Plato’s mathematical philosophy, which in turn contextualizes the mathematics of
Euclid, so we are left to speculate about the philosophical spherics Manchester alludes to.
I.6 Philosophical Cosmology II: From Contemporary Scholarship to Phenomenology
The five sciences mentioned in Plato’s list have a different outward form today, but their
axiomatic foundations and first principles are the same. Plato intended certain formulations
familiar in his time—for example, by arithmetic we can imagine he intended the doctrines of
number centered on principles of the one (monas) and the two (aoristos dyas) in the traditional
context deriving from the Pythagoreans and treated by the Presocratics, given his own synopsis
and orientation. His student Philippus of Opus, who edited the Laws after Plato’s death, and who
may be the author of the Epinomis, gives a synopsis of the mathematical sciences that delves
more deeply into the philosophical meaning of Plato’s mathematical sciences.18 Modern scholars
of Ancient Greek philosophy who have contributed comprehensive studies to the philosophical
cosmology in Plato’s dialogues include Alexander P. D. Mourelatos, Alan C. Bowen, J. L.
Berggren, and Ernst G. McClain, perhaps all indebted to the Sir Thomas Heath’s early 20th
Century translations and analyses. McClain, for one, brings Pythagorean musicological
scholarship into the mix, discovering in the work of Ernst Levy the astonishing discovery that the
music of the spheres were in fact coded into the composition of the written dialogues. Antonio T.
de Nicolás finds these encoded musical structures in Vedas as well. The Tübingen school of
Platonic scholarship that stands with the reconstruction of Plato’s unwritten doctrines (agrapha
dogmata) passed on orally within the academy holds that Plato’s inner-academic teachings were
18 Cf. Konrad Gaiser’s essay in The Other Plato (2012), ed. Dmitri Nikulin, ff. 83.
11
perhaps more direct and sophisticated than the exoteric teachings of the dialogues. Hans Joachim
Kramer and Konrad Gaiser, the main constituents of this school, emphasize a deep structure of
Platonic doctrine, based on the theory of two principles; the monas and aoristos dyas. This
formulation is also thematized by the American phenomenologist Robert Sokolowski in a
number of his works, where he emphasizes the relevance of the indefinite dyad for both
Husserlian and Heideggerian phenomenology.19 The formulation of the philosophical cosmology
emphasized in this thesis agrees with this di-pole structure for a theory of principles behind a
doctrine of elements, but refers to them as peras and apeiron, which include this arithmetical
This is all operational in the longitudinal tradition of Platonism and Neoplatonism,
including Aristotelian Platonism. The continuity of the doctrines of Plato and Aristotle, for all
their breaking, could be said to be the specific doctrine behind classical metaphysics, and in its
last manifestations is tied to the tradition of mystical Christian Neoplatonism. But the sphere
theosophy was a pre-Christological proto-monotheism. Apeiron is the Greek equivalent for the
later Latin infinite, and is more precisely the Absolute Infinite, to avoid misunderstanding.
Mystical sources are considered in my own analyses, just as they were important for the German
idealist tradition and other influences on philosophy. Another important line of tradition in the
history of philosophical ideas leading back to the sphere paradigm for the three
phenomenologists we will be focusing on, is that line from Aristotle to Leibniz. Phenomenology
is indebted to Aristotle’s scientific philosophy in many ways, but there is a deficiency in the
ingression of the fullness of the Aristotelian worldview bluntly because it is antiquated. But here
there is a covert convention of anti-Platonism, especially when it comes to Aristotle’s “aether
theory,” so-called as if it were an extrinsic addition to his cosmology and his physics. Rudolf
19 Cf. Sokolowski 1974, 1976, 1978.
12
Steiner reported that Husserl’s teacher Franz Brentano, the authority on Aristotle at the time (just
like his own teacher Adolf Trendelenberg), so disdained Christian Neoplatonism that he would
fly into a fit of rage at the very mention of Plotinus.20 But by-passing Neoplatonism in the
secular spirit of a naturalized scientific first philosophy still lets in the motif of entelecheia,
Aristotle’s term for actualization as being-at-work-staying-the-itself, or being-at-an-end. This is
the process of the maintenance of a living form, but applied to all material substances in a world
where everything is in process.
I.7 Phenomenological Cosmology
In what follows I will be engaging the phenomenology of time and the cosmos in the philosophy
of Peter Manchester, Anna-Teresa Tymieniecka, and Hedwig Conrad-Martius. Having found
their roots in a Neoplatonic tradition that understands time as originally emerging from eternity
as a sphere, these phenomenologists recognize how this origination operates in their philosophy
of time by seeing the phenomena of time as a part of the total sphere. The relation of Chronos to
Aion finds in phenomenology a figured philosophy of a phenomenological counterpart to
mathematical phase space; a disclosure space. In The Syntax of Time, Manchester defines the
disclosure space as “an all-encompassing, self-referential unity of an intentional kind” (53). It is
worth seeing now how this framework is figured, so we shall immediately look to the key
concepts in Peter Manchester’s philosophy. For Manchester, whose phenomenology of time is
the more diagrammatic of the three, the geometry of timelike phenomena is propagated beyond
the Husserlian diagram of inner time-consciousness into the logical space of formal syntax which
20 Moran 2014, 607.
13
Husserl leaves unmarked in the corner of his parallelogram diagram. The syntax of time turns out
to be the intentional structure of a relation between dimensions of space-time, and its mark of
indication is a particular Pythagorean definition of the geometrical point: the Semeion of
Archytas. The Semeion figure is a line broken at a point. On Manchester’s interpretation,
following the double-intentional structure of inner time-consciousness, the two lines are rays of
intentionality, and each exists at an angle to one another, each “in its own dimension” (45). Thus
we have our key figure, which I’m calling Manchester’s figura paradigmatica, after the
precedent for a figured philosophy of the cosmos set by Cusanus. It looks like an angle. We
don’t yet concern ourselves with whether it is acute, obtuse, or square, nor even with the truth of
its two-dimensionality, although these do bear on the noetic framework on the phenomenal
content in its range. Variations on the presentation of this figure could describe conic sections, as
in the mathematical astronomy of Apollonius of Perga, or perhaps this is a way of understanding
the Platonic solids described in the cosmogonic myth of the elements of stereometric form in the
cosmogonic myth of the Timaeus, or perhaps it is a way of reading the definition of the point in
the First Book of Euclid’s Elements into the geometrical algebra of the Second Book, where we
see most clearly the definition of elements a priori by way of the gnomon. In any case the
constant parameters of the figure are only the relation of center to periphery. The parallelogram
of Husserl’s inner time-consciousness diagram is thus extended to include the point of the
triangle in the corner, and to recognize this point as the center of an encompassing sphere. This
center, analogous to transcendentally pure subjectivity or intersubjectivity in Husserl’s
transcendental phenomenology, positions phenomena in the total harmony of its manifold logical
possibilities, that is, as the center of its sphere. Since every phenomena has its sphere, it is part of
a universal harmony of spheres.
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A final point should be noted about this figura paradigmatica. Manchester comprehends
phenomenology in a sphere that is all-encompassing—the disclosure space—yet is also multiply
encompassing of multiple concentric spheres. This spherical worldview has ancient precedents,
the Pythagorean “harmony of the spheres” influence is clear enough, but some others may be
noted: the Pythagorean and Parmenidean identification of time with the Sphere of the Whole
comes to shape the tradition of Neoplatonic speculation about time so much that Philip Merlan
has proposed that the doctrine of a plurality of spheres of being is the first characteristic of
Neoplatonism to be noted21. The ancient doctrine of four classical elements—earth, air, fire and
water—was originally ordered by Empedocles according to the relative heaviness of these
elements, with earth being the heaviest and thus occupying the center, fire lightest and thus sent
to the periphery, called empyrean; for Empedocles the elements were held together by the
cosmic force he named Love (philotes), which was a sphere. In The Syntax of Time, Manchester
adopts the Stoic Neoplatonic formulation “Sphere of the All,” but it is the same concept as the
later Latin tradition of the “infinite sphere” that builds on the famous third proposition of the
Book of the 24 Philosophers, “God is a sphere whose center is everywhere and periphery
nowhere.” The Greek ancestor of the concept of infinity is the apeiron, literally the limit-less
(limit is peras), the boundless nature which traditionally belongs to Anaximander in the capacity
of a first concept of cosmology. The very word ‘syntax’ in Manchester’s title is a development
upon Anaximander’s famous fragment on the cosmic dike, justice:
The first principle is neither water nor any of the so-called elements, but some different,
boundless nature, from which the heavens arise and the cosmos within them; out of those
21 This characteristic is the first of a list in the first footnote on the first page of his study From Platonism to Neoplatonism (1960).
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things whence is the generation for the beings, into these again does their destruction take
place, according to what needs must be; for they make amends and give reparation to one
another for their offense, according to the syntax of time (150, emphasis added).
To round off a final point about Manchester’s figura paradigmatica, I want to suggest that this
ancient apeiron principle can be approached by way of a simple thought experiment that leads
the thinker to the precise idea of the sphere that is foundational for a ‘philosophy of the spheres’
in the sense of a deductive system, a metaphysica more geometrico demonstrato. It is well
known that for Plato the final aim of philosophy is to lead the soul to the idea of the good
(agathon). In the Sixth Book of the Republic this goal is famously said to be beyond being
(epekeina tes ousias; 509b), leading Plato sometimes to call it meon (non-being: me-on). A
modern meontology building on this Platonic precedent can be seen in the philosophy of
Levinas, for example. Of course something that is first of all not a thing in the usual sense, but
moreover somehow is nothing is a bizarre predication, but we philosophers pretend to at least
negatively know what Plato intended by this term. In the comparative philosophy of religion,
mysticism is sometimes identified with metaphysical belief systems in which something like
nothingness is the ultimate reality. In Buddhism, for instance, there is sunyata, the state of being
that is non-being and nothing, sometimes not even nothingness. In a logically strict sense—to
start with a simple approach to this idea—the idea of ‘the beyond of being’ can have two
possible valencies: either it is, we might say, (1) ‘pure and radical’ nothingness, which admits of
nothing, issues nothing, and is completely disconnected to anything, everything and even from
the being of empty space in a continuum, or alternatively, (2) it is the overwhelming positivity of
the surplus concept of the infinite—specifically the absolute infinite. If it were pure and radical
nothingness it would annihilate us, any way you try to construe it. If it were a supreme surplus it
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would be beyond being, but in this latter case there would be enough room for all the things that
are to be, together with all of their possible combinations.
The ‘one’ of Neoplatonic speculation, like apeiron, should be approached by thought
experiment too. The monad goes by many names, including peras. In Plotinus we find the
formulation ‘center of all centers’ (Ennead VI.2), and it is in this direction that we find the image
of limit (peras) relevant to the apeiron we have conceived previously. This experiment is that of
radical oneness, and its apparent alternative, like that of Parmenides’, is really just one. Maybe
it’s not an experiment at all, perhaps it is mere peri-mentation. The point is to conceive a oneness
so radical that it is numerically one and experientially only once. It is the ubiquitous center from
the Book of the 24 Philosophers mentioned earlier. The conception of the one occupies a place in
the Neoplatonic threefold schema of participation as the ‘unparticipated one,’ and it is the
unmoving center of our ancient cosmogonies.
Putting these two radicalizations (peras and apeiron) together, we can see the genesis of
the cosmic sphere: apeiron appears to peras in its initial ecstasis outward in all directions as an
equality in the form of sphericity. This is the sense of equality that for the Pythagoreans was the
arithmetical element of the ‘even,’ and for Manchester, the equality of the disclosure space that
gives horizon to phenomena and lets them appear in its transparency as static, stable entities in a
universal horizon. Apeiron appears to peras as sphere. It is the symmetriai of celestial bodies in
the Republic, as well as the eternal circular motion of Aristotle’s aetheric physical cosmology.
The idea of the infinite sphere encapsulates these thought experiments, and caps the
phenomenology of the disclosure space in The Syntax of Time with a final frame of reference.
The higher astronomy of Plato is developed further in Aristotle’s theory of the aether,
which Hedwig Conrad-Martius already transformed into phenomenological cosmology in the
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1950s. The entelechial aspect of Aristotle’s scientific philosophy that inspired Conrad-Martius
came through a Leibnizian route of development to a Polish-American student of Roman
Ingarden, Anna-Teresa Tymieniecka, in whose hands it became a monadological cosmology, and
finally a vision of the total cosmos. For both Tymieniecka and Conrad-Martius, it was the cosmic
aspect of the entelechial potencies of the things themselves that bloomed into phenomenological
cosmology. This development was already laid down in her 1964 Leibniz’ Cosmological
Synthesis, where she outlines her “multi-spherical constitutive pattern of the universe” (5),
characterized according to Leibniz’ essay “Double Infinité chez Pascal et Monade” (1695), as a
double infinity of the infinitely great and the infinitely small, which recalls the ancient
arithmetical context of the monad, the indefinite dyad (aoristos dyas) of the great and the small
(mikros kai megas), which she quotes from at length (162-3). In his 1960 L’homme Falllible,
Paul Ricoeur employs this Pascalian framework of the great and the small for his philosophical
anthropology. In her 1966 Why Is There Something Rather Than Nothing?, Tymieniecka
develops her Leibnizian framework of the 1964 book into a philosophical cosmology also along
these lines of the “two infinities” (ff. 2). Her multi-sphere model becomes a philosophy of the
relation of cognitive constitution to cosmo-ontological constitution, according to “the regulatory
function of transcendent ideas” (5). The central idea of this philosophy is that of the world-order
playing a limited role “within the vast scheme of universal constitution” (ibid.), within an order
of orders at the highest scale.
Like Manchester, her central concern is the flux and stability of the structural patterns of
phenomenal form. These forms are ideal structures, following the phenomenological ontology of
her teacher, Roman Ingarden, but she explains that this eidetic method as a cognitive device is
not sufficient “to restore the completeness of being to the abstract skeletons” (ibid.). For this she
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saw the individual being not only according to its essentialities, but as an ingrown being of the
whole totality of being, including all the concentric spheres of its participation with other beings.
Thus she understood beings themselves as intrinsic patterns of beings presupposing the world-
context and its ultimate infinite horizon. This multi-sphere model describes the ideal structures as
constant patterns, structurally rooted indications of the world-order in its superior architectonic
plan of totality, as holograms or echoes of the whole. The move from ontology to cosmology is
marked by the conjectural inference based on anticipatory evidence characteristic of the
speculative logic operant in the teleological functional systems that steer their course according
to a final aim, the “intrinsically purposive orientation of natural processes” which have been, she
writes, “established by Hedwig Conrad-Martius in Der Selbstaufbau der Natur, Entelechien und
Energien, H. Goverts Verlag, Hamburg, 1944” (52, n. 2). This footnote makes it clear where she
departs from Conrad-Martius, but focusing on the development of philosophical cosmology, we
are interested in the inheritances. My hope is that this brief introduction to her style of thinking
makes the Greek themes evident, up to the teleology of Conrad-Martius, a phenomenologist
whose cosmology begins with this Aristotelian inheritance of entelechia, and blooms in her
1950s cosmological turn. It is not clear whether Tymieniecka was familiar with Conrad-Martius’
1950s development. The next chapter will look at the resonances of Tymieneicka’s and
Manchester’s philosophical cosmologies, and a final chapter will continue this theme with the
exploration of Conrad-Martius’ cosmological turn.
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Chapter 2: From the Phenomenology of Time to a Phenomenology of the Spheres
Peter Byrne Manchester's The Syntax of Time (Brill, 2005) presents a phenomenology of
time extending from Husserl to the Ancients. By establishing that time has a syntax, Manchester
reorients the paradigm according to which we think about time, and establishes a contrast with an
ancient way of thinking. The goal of his study is to recover the ability to imagine eternity, a
capability that our tradition has largely forgotten. He argues that the lived experience of a “now”
is nothing like the domain of the variable 't' in Cartesian analytic geometry, to which it has more
recently been compared. The logical abstraction of time is qualitatively unlike real time. Through
philosophical reconstruction of an ancient worldview, Peter Manchester uncovers a lost doctrine
called the spherics (ta sphairike), which has deep implications not only for time but for all the
dimensions of experience. He names his guiding figure the Sphere of the All, a formulation
belonging to his ancient sources. Anna-Teresa Tymieniecka's phenomenology of life also
recognizes a previously unnoticed syntax, this time in the intrinsic functioning of life. Her
extensive philosophy of life’s inner-workings yields a phenomenological cosmology of multiple
spheres of being grounded in a “great vision of the All” (Tymieniecka 2000, 643), much like
Manchester’s spherics. The convergence to similar frameworks arrived at independently by these
two philosophers is an occurrence rare enough in phenomenology, but what is even more
surprising is the convergence of their specific functional systems and metrological terms. This
convergence arises from the pursuit of a phenomenological cosmology entailing a synthesis of
order and measure. The ancient intuition that the language of God is the language of mathematics
plays a special role in classical phenomenology, and the recovery of the doctrine of the spheres
represents a new contribution to this intuition. By arriving at the most fundamental ontological
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units of analysis, a new speculative cosmology and transcendental logic emerges from the model
of the sphere.
It is often the case that different but related regions of philosophical inquiry can enhance
one another, and when this happens we sometimes achieve new perspectives on old ideas. This is
certainly the case with the two phenomenological undertakings explored here. Two
phenomenologies, one of time and one of life, have each independently reached a level of
analysis that reactivates ancient categories of thought that were operative at the origins of the
Western metaphysical world-view, and that have since gone dormant but have not disappeared.
Both Anna-Teresa Tymieniecka, a student of Roman Ingarden and the founder of the Analecta
Husserliana and the World Phenomenology Institute, and Peter Byrne Manchester—a professor
of philosophy and speculative theology at Stony Brook University in New York and a student of
Hubert Dreyfus, Hillary Armstrong, and Hans Jonas—seek to open up transcendental
phenomenology, beyond the tendency to logical abstraction, and in effect, open the
dimensionality of thought up to the fullness of life. Each thinker strives towards a holistic vision
of the way the total cosmos makes its mark in every ordered and measured part. Manchester
conceives of his framework of the Sphere of the All as "an all-encompassing self-referential
equality of an intentional kind—a disclosure space" (Manchester 2005, 53). Tymieniecka's key
concept of phenomenological disclosure is the unity of apperception, extending the meaning of
this Kantian and Husserlian concept to include in its compass the ontopoietic functions of life's
essential individualization (Tymieniecka 2000, 265-80). Tymieniecka's modal thematization of
life in its elementary operations presents in relief the place of life's inner-workings within the big
picture of ‘the All’ of possible fulfillments, and develops outward into a phenomenology of
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possible worlds (Tymieniecka 1974, 3-41). It could be stated that in large part what the modal
realism of her cosmic architectonic gives us is a visualization of individualization. Manchester's
phenomenology of time and Tymieniecka's phenomenology of life will be shown to have
sufficient structural and methodological convergences to frame a phenomenological exploration
of the ancient doctrine of the spheres, Pythagorean and otherwise.
The manifold nature of life's self-disclosure in extended space and time is the systematic
background of the original Husserlian phenomenological methodology, and this too often
neglected framework is what is reactivated in the phenomenological work of both Manchester
and Tymieniecka. Tymieniecka's cosmic ar