Thursday, December 11, 2014

Plato’s Contest: Answering the Challenge of the Parmenides

Abstract: Plato’s contest for the early Academy was to answer Parmenides’ criticisms of the Theory of the Universal Forms through an interpretation of the dialectical exercises presented in the Parmenides (§I).  Plato’s Theory of the Universal Forms and the objections of the Parmenides may now be more precisely formulated in predicate logic using the notational convention developed by Edward Zalta (§II).  The two principal objections to Plato’s Theory of the Universal Forms are the Third Man Argument and the Greatest Difficulty Argument: the Third Man Argument can be answered by Constance Meinwald’s distinction of Self-Predication and Gail Fine’s distinction of Non-Identity (§III); and the Greatest Difficulty Argument implies the inconsistent set of Russell's Paradox, yet may be answered through the construction of a hierarchical set theoretical model that subsumes and restricts the semantic scope of each subordinate hypothesis (§IV).  The rejection of the external predication of the Third Man Argument and the two-world ontology of the Greatest Difficulty Argument suggests a monistic ontology of internal relations in the Concrete Universal form of all forms (§V). 

I. The Challenge of the Parmenides

The Parmenides recounts a dispute between the elderly Parmenides (age 65), the mature Zeno (age 40), and the young Socrates concerning the Theory of the Universal Forms, or Ideas.[1]  After reading a treatise on the absurdity plurality of beings, Zeno is questioned by Socrates as to whether the same argument might also repudiate the universal forms, (127e) and confirms that Socrates has correctly understood that the purpose of his argument is to defend Parmenides by responding to “those who assert plurality” by showing that the assumption “that there is a plurality leads to even more absurd consequences than the hypothesis of the one.” (128d)  Parmenides then joins the controversy with a battery of explosive criticisms to challenge the Theory of the Forms. (130a-134e)   He concludes that “these difficulties and many more besides are inevitably involved in the forms” (135a), and recommends a “severe training” of dialectical exercises by which the theory might yet be saved. (135d) 

No consensus has yet been reached on how to interpret these bewildering exercises.[2]  Thomas K. Seung describes them as “the most obscure and enigmatic pieces Plato ever wrote.”[3]  William F. Lynch, S.J. calls the Parmenides the “supreme puzzle of ancient philosophy.”[4]  Many ancient scholars interpreted the Parmenides as a discourse on theology which described "all things that get their reality from the One."[5]  Some modern scholars have - more modestly – interpreted the dialogue as either a “record of honest perplexity” or as merely a “gymnastic exercise, not a disclosure of supreme divinity.”[6]  Since the criticisms of the Parmenides present Plato’s most explicit examination of the Theory of the Forms, interpretations of this dialogue may establish the place of the universal forms in Plato's mature philosophy: if Parmenides’ criticisms may be answered then Plato could have affirmed, but if not then Plato should have rejected, the Theory of the Universal Forms.[7]  Scholarly disagreement on the interpretation of this dialogue thus pivots on the gigantomachy of Plato’s Academy between the idealist 'gods' who defended the universal forms and the materialist 'giants' who wished to “drag everything down to earth out of heaven.”[8] (246a)  If the Platonic dialogues may be read as a dramatic conflict, in which each unresolved aporia ends in tragedy, then the Parmenides concludes at the height of tragic agony: for not only do the criticisms of Parmenides deal a devastating blow to the central pillar of Plato’s ontology, but neither do the dialectical exercises clearly provide any satisfactory answer.  Plato's contest for the philosophers of the future was to discover a satisfactory interpretation of the dialectical exercises, to save the Theory of the Universal Forms, and to answer the challenge of the Parmenides.

In the celebrated dialogues the Phaedo, the Republic, and the Symposium, Plato expounds his famous Theory of the Universal Forms.  Heraclitean Flux had implied that at every moment any sensible object must possess some contrary opposite properties.[9] (402a)  Plato argues to the contrary (96a) that, if sensible objects must possess contradictory properties F and not-F then nothing can be explained; yet since explanations should be possible, there should be some supersensible universal forms with which to explain all properties in sensible objects.[10] (72c)  The Theory of the Universal Forms is thus the hypothesis that, if we are to ever explain a plurality of sensible objects that each share some common property we should, to avoid contradictions, postulate there to be one unchanging supersensible universal form, which is itself the prior ground of being and necessary condition for knowledge of each property in each particular sensible object.  To explain the transcendental conditions for the possibility of knowledge, Plato's Theory of the Universal Forms thus postulates an indefinite multitude of supersensible universal forms in a transcendent realm beyond the sensible realm of all appearances.[11] 

The resulting picture is a two-world ontological dualism in which the being of the supersensible universal forms are located in a transcendent world that is separated beyond the being of all sensible particular instances. (508e)  However, this ontological dualism conflicts with Plato's epistemological monism.  Since every property of a plurality of objects must have some single explanation, there must also be one explanation for these two-worlds of beings; yet since any explanation must postulate the being of one universal form over many particular beings, the consequence is a set of beings that is inconsistently both one and many.[12]  Moreover, since each universal form is itself a particular being when conceived of in relation to other universal forms, and every plurality of particular beings must be explained by some further universal form, this plurality of all universal forms must also be explained by one further universal form over all universal forms.  The many criticisms against the Theory of the Universal Forms in the second part of the Parmenides (130a-134e) each result from Plato’s two-world ontological dualism.[13]  Thus Aristotle thus reports that "it is not possible to acquire knowledge without the universal, but separating is the cause of the difficulty arising." (Metaphysics 1086a32) 

Plato never explicitly answers the challenge of the Parmenides.[14]  Paul Elmer More writes: “We have the whole doctrine of Ideas subjected to a process of destructive logic to which Plato makes no direct answer either here or elsewhere.”[15]  If the dialectical exercises of the third part of the Parmenides fail to answer the challenge of second part of the Parmenides, then the Parmenides must conclude in a tragic aporia that leaves the greatest objections to Plato’s Theory of the Universal Forms unanswered.  Socrates then asks: “What are you going to do about philosophy, then? Where will you turn while the answer to these questions remains unknown?” (135c)  The clearest indication of how Plato intends to answer this challenge is briefly hinted at in the transitional passage when Parmenides speculates: “Only a very gifted man can come to know that for each thing there is some kind, a being by itself; but only a prodigy more remarkable still will discover that and be able to teach someone else who has sifted through all these difficulties thoroughly and critically for himself.”[16] (135a-135b)  For the purpose of this instruction, Parmenides prescribes a "severe training" of dialectical exercises, to explore the semantic implications of supposing that "such and such a thing is" and "is not", so that the truth may not escape us.[17] (135d-136a)

Read the full essay here:

[1] Although Plato seems to prefer the term Idea (ἰδέα or εἶδος), this essay will assume the Aristotelian nomenclature of ‘universal forms’ to more clearly distinguish universal forms from particular instances.
[2] Kenneth M. Sayre reports that despite “almost two millennia of documented commentary, however, scholars today are still struggling to make sense of the dialogue. Cf. Parmenides' Lesson, 1996: XI
[3] Seung, Thomas K. Plato Re-Discovered: Human Value and Social Order, 1994: 185
[4] Lynch, William F. An Approach to the Metaphysics of Plato through the Parmenides, 1959: 3
[5] Proclus' Parmenides Commentary 638.18-19; For a summary of Neo-Platonist interpretations of the Parmenides see John Dillon’s introduction to Proclus' Commentary on Plato's Parmenides.
[6] Vlastos, The Third Man Argument in Plato’s Parmenides, The Philosophical Review Vo. 63, No. 3, 1954: 343; Cornford, Francis M. Plato and Parmenides, 1939: 131
[7] Plato scholars can be roughly divided according to their interpretation of the the status of the Theory of the Universal Forms after the Parmenides: Unitarians believe that Plato did not revise his theory, while Revisionists believe he did.  Aristotle’s contemporary testimony (Metaphysics Α987a29 & M1078b9) suggests that Plato neither answered these criticisms nor revised the Theory of the Universal Forms. The result is an apparent interpretive paradox: if Plato recognized the criticisms to be valid then he should have revised his theory, yet there is no explicit evidence for such a revision; while if Plato did not revise his theory then he should not have thought the criticisms to be valid, yet Plato gives no answer to the criticisms. Cf. John Pepple, Plato’s Answer to Speusippus: 18
[8] John N. Findlay plausibly associates this allusion to the gods and giants with idealist friends and materialist enemies of the Theory of Universal Forms. Cf. Plato and Platonism, 1978:12
[9] Aristotle reports Plato responded to Heraclitean Flux: “Plato accepted [Socrates’] approach but was lead by it to think that it must be concerned with things other than the sensible. For it is impossible to formulate a general definition of any sensible thing, since all is in flux.” Cf. The Metaphysics, 987a 29
[10] Gail Fine describes how since “sensibles suffer compresence [of contrary opposite properties], there must be nonsensible forms that escape compresence.” Cf. On Ideas: On Ideas: Aristotle's Criticism of Plato's Theory of Forms, 1995: 54-57
[11] Gail Fine observes that both Aristotle and his commentator Alexander of Aphrodisias regarded this argument for the possibility of knowledge as the primary motivation for the Theory of the Universal Forms. Cf. On Ideas: On Ideas: Aristotle's Criticism of Plato's Theory of Forms, 1995: 49
[12] Thomas K. Seung observes that set theory continues the ancient Pythagorean priority of being while formal logic continues the ancient Eleatic tradition of pure form. Cf. Plato Re-Discovered, 1994: 215
[13] Giovanni Reale concurs that all of the objections of the Parmenides “turn in their various and complex ways on the conception of the intelligible Ideas as separate from sensible things.” Toward a New Interpretation of Plato, 1996: 226.  For a similar opinion see also More, The Parmenides of Plato, 1916: 135
[14] Harold F. Cherniss claims that Plato suggested an answer to the Third Man Argument at Republic (597c) and the Timaeus (31a). Unfortunately, these texts do not explicitly answer the argument without additional assumptions.
[15] More, Paul Elmer, The Parmenides of Plato, The Philosophical Review, Vol. 25, No. 2, Mar., 1916: 128
[16] This allusion to a great dialectician of the future echoes Socrates' prognostication of a future "great man" who may resolve the aporiae of the Charmides (169a).
[17] Constance Meinwald observes that the third part of the Parmenides contains the longest single stretch of uninterrupted argument in the Platonic corpus (30 Stephanus pages) and concurs that it was meant to resolve the aporiae of the second part. Cf. Goodbye to the Third Man. In The Cambridge Companion to Plato: 366-7