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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


2018


2018

ii


The Graduate School


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


Master of Arts

in

Philosophy


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.

vi

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

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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

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