Table Of ContentParmenides’ Grand Deduction
Parmenides’ Grand
Deduction
A Logical Reconstruction
of the Way of Truth
Michael V. Wedin
1
1
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To my wife
Janet Kovak
and
our steadfast companion
Charlie
Preface
Shortly after arriving at Davis I began teaching, almost on a yearly basis, a lower
division course in ancient Greek philosophy. I began with what I considered the
chief Presocratics and worked my way through the main themes in Plato and
Aristotle. This was my first systematic encounter with the Presocratics, and the
cast of characters could not have been more engaging. Whether described as cos-
mologists, natural scientists, or philosophers, I found myself facing an array of
theories of astonishing originality and brilliance. Almost without exception, the
major players backed their theories and claims with arguments that were recog-
nizably philosophical. As an impenitent analytical philosopher, I was more than a
little intrigued. Still, if I harbored any notion of publishing on Presocratic topics, it
was buried deep in my unconscious. This was due largely to the fact that my agenda
was filled with projects in Plato and, especially, Aristotle, but, in some measure, it
was also a function of the introductory nature of the course.
The situation changed dramatically when, over a decade ago, I inherited from
John Malcolm a more advanced course devoted exclusively to Presocratic philos-
ophy. Now I had license and leisure to pursue detailed interpretation and indulge
my penchant for logical reconstruction. The chief beneficiary was Parmenides,
and I found myself devoting large chunks of class-time to the deductions of the
Way of Truth (WT). From these sessions emerged the outlines of the present
monograph, both the general shape of Parmenides’ deductive arguments and a
keen appreciation for the logical problems facing them, especially the problems
facing the fundamental deductions in Fragments 2, 3, and 6—deductions which
comprise Parmenides’ Master Argument, as I shall call it in the balance of the
monograph. So it is no surprise that my first obligation lies with the students
in my Presocratic philosophy classes over the span of a decade, for fearlessly
voicing worries and objections, and, most of all, for patiently enduring multi-
ple versions of my reconstructions of Parmenides’ deductions. I am especially
indebted to Mr. Erik Johnson for ongoing and engaging conversation. Jan Szaif
and John Malcolm joined me for a series of basement colloquies on Parmenides’
arguments, and Malcolm additionally provided helpful comments on the earli-
est incarnation of the monograph. A third Davis colleague, Michael Glanzberg,
cheerfully endured hours of forced conversation on logical and semantical topics
of Eleatic stamp. Less local debts are owed to Alex Mourelatos for a wealth of
detailed comments and suggestions, most of which now grace the pages of the
viii preface
finished product, and to Brad Inwood who pressed a set of concerns that altered,
for the better, the overall strategy of Part I. Indeed, an earlier version of Part I has
appeared under his imprimatur at Oxford Studies in Ancient Philosophy. Finally,
Peter Momtchiloff, editor nonpareil, assembled a suite of readers whose astute
criticisms and apt advice raised the bar for the final product. I am deeply grateful
to all these individuals.
This monograph has been long in the writing. I began the project as a relative
tyro in the field and there was much to absorb. As I continued apace with analysis
and logical reconstruction, the extensive secondary literature eventually reared
its head and demanded a place at the table. I yielded and the result is a robust
discussion of contending views. However, the principal impediment to timely
completion of the monograph resists scholarly measure. For better than a decade
I have devoted significant hours in attempting to lessen my wife’s physical distress.
Matters have worsened over the past two years. Some weeks I could find only a few
hours for writing, other weeks none. And this at all hours of the day and night (the
key insight in Section 3, for instance, fell to me one night just before dawn). More
than once I considered leaving the field, but Janet unfailingly urged me to con-
tinue. So to my wife, Janet Kovak, I wish to express, yet again, profound gratitude
and admiration, for the joy of our life together and for her courage in the most dire
of circumstances. In the midst of all this, there has been a singular bright spot—our
Kerry Blue Terrier, Charlie, rescued by Janet from the plains of central Texas—an
ever-affectionate mischief-maker who prefers the intrigues of our kitchen to the
confines of my study. He has been a godsend.
Contents
Introduction 1
Part I. Th e Governing Deduction and Parmenides’
Master Argument
1. Parmenides’ Canonical Paths of Inquiry 9
2. Path II and the Governing Deduction 21
3. Path I and the Corollary to the Governing Deduction 29
4. Modal Extension and the Third Path 34
5. A Covert Fallacy in the Governing Deduction? 43
6. Self-Defeat and the Second-Order Defense of the Governing Deduction 48
7. The Ionian Interpretation of Fr. 6 53
8. Does Parmenides Argue for the Existence of Something? 71
9. A Remark on Quantification and the Subject of ἔστιν 79
Part II. The Deductive Consequences of the Governing
Deduction
10. Consequence (A): That what is is uncreated and imperishable (Fr. 8, 5–21) 85
11. Against an Emendation and a Proposal about the Subject of (A1) 100
12. Consequence (B): That what is is indivisible and continuous (Fr. 8, 22–5) 105
13. Monism and Deductive Consequence (B) 109
14. Consequence (C): That what is is motionless (Fr. 8, 26–31) 118
15. Consequence (D): That what is is complete (Fr. 8, 32–49) 134
16. A Causal Theory of Thought and Fact Monism: D2 (Fr. 8, 34–41) 143
17. Fact Monism and Gödel’s Slingshot 160
18. Parmenides’ Anomalous Sphere: D3 (Fr. 8, 42–9) 171
19. The Eleatic Inference Ticket 179
20. The Perils of Prescription: The Deductive Consequences at Risk 184
