A late Platonic dialogue on the one-many problem, in which a severe critique is launched against the middle-period version of Plato’s Theory of Forms.
The Parmenides is a narrated dialogue. The otherwise unknown Cephalus of Clazomenae – not to be confused with Cephalus of Syracuse of the– narrates to an anonymous audience an earlier conversation between forty-year-old Zeno of Elea, sixty-year-old Parmenides and young Socrates (127b-c), which is supposed to have taken place in the summer of 450 B.C. Altogether, seven men were present (129d), of whom a certain Aristotle, later a member of the Thirty Tyrants, is also mentioned by name (127d, 137b-c).
The Parmenides is later than the so-called middle-period dialogues (, , , ) and probably inaugurates the last period of Plato’s literary production, a period in which the Athenian philosopher critically evaluates his earlier .
The Parmenides is clearly divided into two distinct parts with a brief introduction before them (126a-127d).
In the first part (127d-137c), Socrates, after listening to Zeno reading from a book of his that defended Parmenides’ thesis according to which the whole of reality is an unbroken unity (128a-b), displays his own theory of Forms and subsequently falls victim to Parmenides’ pervasive and relentless critique. Unable to defend his intellectual offspring Socrates no longer knows where to turn his mind for support (135c). Parmenides, however, assures him that the postulation of Forms is in principle a sound method of inquiry whose content must always be rationally scrutinized by means of an elaborate dialectical exercise regarded by the ignorant many as useless prattle (135d-e). Parmenides then presents the theoretical framework of the dialectical exercise he has in mind (135e-136c).
The second, and longer, part of the dialogue (137e-166c) is an exemplary application of the dialectical method. Here, Parmenides’ interlocutor is Aristotle, the youngest member of the company, who only intervenes in order to confirm the soundness of Parmenides’ complex arguments. The dialogue ends with a summary of the radically contrary conclusions deduced from the two contradictory hypotheses thus far examined (166c).
The Parmenides is an exceptionally demanding dialogue. Any serious attempt at interpretation must be able to provide an answer to the question about the relation of the two parts and adequately explain the author’s intention in the longer, second part.
The first part seems to raise pertinent objections to the theory of Forms and can, therefore, be interpreted as a request for a better appraisal of the metaphysical status of the Forms (echoing perhaps also the internal critique of the theory within the Academy). But the second part, which comes as the culmination of the first, is full of logical fallacies and raises the question as to whether the author was aware of them or not, and, if he were, why he did not clear them out.
Some modern scholars have claimed that the second part is basically derisive in character and means to ridicule similar, purely logical, investigations conducted in the Megarian school and elsewhere. Others have discerned genuine metaphysical puzzles and/or solutions. In general, the dialogues continues to set interpreters at odds: the question as to whether the Parmenides contains some positive doctrine(s) or is a simply logical play meant for entertainment remains an open issue.
One of Zeno’s arguments against the existence of many things (127e) claims that if things are many, they have to be both similar to (since they are included in a common set), and dissimilar from (since they are distinct), one another – a thesis that is logically impossible to maintain. From this logical impasse Zeno concluded that things cannot be many.
In order to solve the burning issue of the one-many relation Socrates puts forward the distinction between the Similar in itself and the similar by participation. The Similar Itself, i.e. the Platonic Form of Similarity, cannot possess the opposite property of dissimilarity. But there is nothing to prevent sensible particulars from participating both in the Form of Similarity and that of Dissimilarity, both in the Form of One and the contradictory Form of Multitude, and be, as a result, both similar and dissimilar, one and many at once (128e-130a). Parmenides intervenes. After becoming convinced that Socrates means the Forms to be separate beings pertaining primarily to some universal concepts such as the just, the beautiful and the the good, probably to natural kinds (human species, water, fire etc.) but certainly not to things like hair, mud and dirt (130b-d), Parmenides wants to know how precisely the Forms are related to sensible things.
Socrates is at a loss. To begin with, he is unable to say whether each Form is present as a whole or with one of each parts in the sensible things that participate in it. Both alternatives turn out to be logically unsatisfactory (131a-e). In the first case, the Form will necessarily be separated from itself; in the second, a paradox will ensue: a small part of the Form of, say, the Large will make the sensible thing that possesses it larger than the Form itself which in the meantime will have lost one of its parts. The argument raises the question about the so-called “self-predication of Forms”. In middle-period dialogues Plato has, on the face of it, claimed that the Form of Beauty is the most beautiful thing and the Form of Goodness the best thing. Here this belief is seriously shaken.
In such a frame of mind Parmenides puts forward an argument (131a-b), later known in the history of philosophy as “the third-man argument” (Arist. Metaph. Z 13, 1039a2, K 1, 1059b8), according to which if the Form of F possesses the property f of which it is the cause, we will have to postulate the existence of a higher Form of F in order to explain the manner in which our initial Form of F and the sensible things that are f belong to the same class. The argument obviously leads to an infinite regress.
Socrates’ attempts to present the Forms (i) as thoughts (132b) or (ii) as paradigms of nature which other things tend to imitate through a process of assimilation (132d) turn out to be equally unsatisfactory. Parmenides objects that thoughts are always thoughts of things external to the thinking mind (132b-c) and mobilizes, once again, the third-man argument (132d-133a). The upshot of Parmenides’ elenchus is that the Forms should be regarded as either non-existent or so fundamentally separated from the things meant to be explained thereby as to be essentially unknown to us (133b-135b). However, Parmenides emphatically claims that without the postulation of Forms our minds will have no stable objects to think of, and the dialectical power of thinking will eventually crumble down (135b-c).
Later, at the precise juncture where the two parts of the dialogue meet (136a-137c), Parmenides takes as an example Zeno’s initial hypothesis (“if there are many”) and asks Socrates to see what logical consequences follow both from it and from its denial (“if there are not many”). He then undertakes to show what he precisely means through a long exercise in dialectic. He makes it clear that the dialectical exercise will deal exclusively with Forms (135d-e).
In the dialectical exercise which constitutes the second part of the dialogue, explicitly characterized as a huge “ocean of discourses” (πέλαγος λόγων) as well as “laborious play” (πραγματειώδης παιδιά) (137a-b), the hypothesis to be examined, both in the affirmative and in the negative with respect to its consequences both to its subject and to other things, is the hypothesis of the One. In accordance with the theoretical formulation of the method in the first part of the dialogue we should expect eight logical deductions in total as follows:
A. “If the One is” (affirmative hypothesis)
1. what follows for the One in relation to itself,
2. what follows for the One in relation to other things,
3. what follows to other things in relation to themselves,
4. what follows to other things in relation to the One.
B. “If the One is not” (negative hypothesis)
5. what follows for the One in relation to itself,
6. what follows for the One in relation to other things,
7. what follows to other things in relation to themselves,
8. what follows to other things in relation to the One.
However, the actual dialectical exercise comprises nine rather than eight deductions. The unexpected third deduction (155e-157b) is the sole to be explicitly numbered (ἔτι δὲ τὸ τρίτον λέγωμεν) and the sole to combine the contradictory results of the earlier two deductions by means of the novel notion of the sudden moment (τὸ ἐξαίφνης). Moreover, the deductions do not distinguish the consequences of the initial hypothesis according to the limitation meant by the “in relation to...” qualification. They, rather, draw consequences for the One (or other things) both in relation to itself (or themselves) and in relation to other things (or the One) at once.
In actual fact, Parmenides examines twice each hypothesis as to its subject or other things so that the deductions, apart from the third one, can be classified in couples: 1+2 (what follows for the One from the hypothesis that the One is), 3 (what follows for the One from the hypothesis that the One is if we combine the results of deductions 1 and 2), 4+5 (what follows for the others from the hypothesis that the One is), 6+7 (what follows for the One from the hypothesis that the One is not), 8+9 (what follows for the others from the hypothesis that the One is not). This classification clearly shows the very peculiar role of the third deduction in the overall exercise and highlights the open (i.e. non-definitive) character of Parmenides’ results as he draws contradictory conclusions from the same hypothesis about the same subject.
The Parmenides brings to focus the kind of logical and conceptual exercises in which the aspiring Platonic philosopher is to be trained before he manages to conceive the essential meaning of the Theory of Forms. The two basic concepts in the exercise are the One and Being. Because of their unexceptional universality those two notions are necessarily presupposed in any kind of thinking. Nevertheless, they tend to appear exceptionally problematic once one tries to conceive them in all their logical consequences.
The historical significance of the Parmenides has been great. In late antiquity, the dialogue was interpreted in theological terms. In order to solve the problem caused by the presence of so many contradictions in the second part of the dialogue, the Neoplatonists assumed that each one of the nine deductions refers to a different divine hypostasis or its products. Already Plotinus thought that the first three deductions refer to the One, the Intellect, and the Soul, respectively. In the post-Plotinian period the significance of the Parmenides was maximized. The common assumption was that the second part of the dialogue contained the sum of Plato’s theological doctrines. Together with the Timaeus the Parmenides was considered the very culmination of Platonic metaphysics. Of the many commentaries written to explicate the dialogue from the third to the sixth centuries C.E. only those ofand survive – the former in part and the latter in full.
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- Meinwald, C.C. Plato's Parmenides. New York & Oxford, 1991.
- Miller, M.H. Plato's Parmenides: The Conversion of the Soul. Princeton, 1986.
- Rangos, S. "Plato on the Nature of the Sudden, and the Asymmetry of the Second Part of the Parmenides (υπό δημοσίευση)." Dialogue (2014)
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- Turner, J.D. , Corrigan, K. eds. Plato’s Parmenides and Its Heritage. Atlanta, 2010.
- Wood, K. Troubling Play: Meaning and Entity in Plato's Parmenides. New York, 2005.