In the Parmenides dialogue, Plato relates in a third-hand manner a discussion that is supposed to have taken place years earlier between an elder Parmenides (then 60-ish) and a "young" Socrates (then 20-ish). (Plato has the character of Antiphon recite the conversation as he heard it from Pythodorus, in whose house the conversation supposedly took place.)
According to the chronologists, the Parmenides dialog is one of Plato's later dialogues. If this is in fact true, it calls into question the purpose and intent of this dialogue. The third-hand approach can perhaps be interpreted as a means of separating the errors that "young"Socrates makes in dealing with the difficulties raised by the character of Parmenides, from the full blown development of the theory of Forms that Plato/Socrates had developed by this time in his career. For none of the six "difficulties"for the theory of Forms that are raised in this dialogue are at all difficult to overcome, given the full blown theory of Forms that Plato has described by this time in his (presumably) earlier writings -- even though they are portrayed as presenting serious difficulties for the "young"Socrates..
The six "difficulties" that Plato voices through the character of Parmenides are
(1) the extent of Forms;
(2) the whole-part dilemma;
(3) the "third man argument";
(4) Forms as Thoughts;
(5) Forms as Paradigms; and
(6) "The Greatest Difficulty".
I will deal with each in turn, and show how each supposed "difficulty" turns on a misunderstanding of Plato's description of Forms.
In this section of the dialogue, Parmenides adopts as a premise the "One-Over-Many" description of Forms that Plato provided in the Republic -- for any plurality of things which are F, there is a Form of F by virtue of partaking of which each member of the plurality is F.
As a result of some give and take with Parmenides, Plato has the young Socrates express uncertainty about whether there is truly a Form of humanity, fire, and water, and scepticism about the existence of Forms of mud, hair, and dirt.
But in the Phaedo (Phaedo, 65-66), Plato has already established that Forms are the "pure absolute essence"or "underlying quality" of all things, and that they are to be known by reason alone and not by the bodily senses. Additionally, in the Cratylus (Cratylus 436a, 438d), Plato is clear that names are not the essence, and that we must look to something else, not names, to show us the true things. And in the Republic (Republic, 523d), Plato suggests that Forms are necessary to explain apparently contradictory properties (like a finger being both large and small), but not necessary to explain what a thing is (like a finger being a finger). It is clear, therefore, that to Plato, the Forms are not epistemic existents in the manner in which we view "universals", but are instead ontological entities that express the underlying essences of things, rather than simply their sensible properties. More particularly, they are to be known by reason rather than by their sensible properties. It is, for example, difficult to comprehend how there could be a form for human or for mud that is different from the sensible existents of humans and mud. And water, fire, and hair are what they are in virtue of what they are, exhibiting no contradictory properties in need of explanation.
The rejoinder that the young Socrates ought to have provided, therefore, is the question whether the named property of F expresses a "pure absolute essence" or "underlying quality" of some property in need of explanation. If the answer is "Yes", then the plurality of F things exists because they partake of the form of F. If the answer is "No", then the plurality of F things exists because they partake of multiple forms, and one must seek the pure essences underlying their F-ness to learn about the Forms involved.
Hence, one can interpret Plato's "uncertainty"about the existence of Forms of humanity, fire, and water as an uncertainty about whether the sensible properties of these natural kinds (their F-nesses) express the true underlying essences of these kinds. Since sensible existents are mixtures of Forms, perhaps humanity, fire, and water, are in fact mixtures of Forms rather than partakers of the Forms of perfect humanity, perfect fire, and perfect water. After all, there are more things that are wet than water. Perhaps it is wetness that is the essence, rather than water. In the case of humanity, Plato has already expressed the view that humanity is a mixture of a soul with a body. So there need not be a form of humanity if there is a form of the Soul and a form of the Body. Or a form of hair or finger, if a hair or finger is but a small part of the Form of Body. Likewise, one can view mud as but a mixture of the forms of earth and wetness; dirt a particular manner of participating in the Form of Earth. And so forth.
The initial epistemic understanding of the One-Over-Many premise adopted by Parmenides is clearly wrong. And there is ample material in the other Platonic dialogues with which to refute it. Forms are, to Plato, ontological entities and not epistemic entities.
In this section of the dialogue, Parmenides adopts a "Pie Model"understanding of the partaking relationship between sensible existents and the relevant Forms. Parmenides argues that if each sensible existent that is F "partakes"of the form of F in total -- by partaking of the entire pie, then there will be multiple copies of the form of F, and Forms will be neither one nor unique as the young Socrates has described them. Alternatively, if each sensible existent that is F "partakes"of the form F in part -- by partaking of but a small part of the pie, then there will be multiple parts of the form F, and again Forms will not be one as Socrates has described.
But in other dialogues (particularly the Phaedo), Plato makes it clear that sensible existents get their existence from their participation in the Forms, and that Forms do not exist in the same realm as those sensible existents. Further, Plato is clear that the realm of Forms is more "real"than the realm of sensible existents. In Plato's understanding, therefore, a Form is something that can invest its essence in a sensible particular without loosing any part of itself, or dividing itself. So neither version of Parmenides'"pie model"is an appropriate way of understanding the "partaking"relation.
To overcome this "difficulty"it is merely sufficient to provide a better model of "partaking"than the "pie model"used by Parmenides. The young Socrates should have suggested that a Form is more appropriately modelled by a song, with the partaking relation being modelled by the entertainment that a song provides. A song "entertains"sensible particulars (people) explaining their F-ness (their pleasure). The Form of F is partaken of by the sensible particulars and that explains their property of F-ness. Any number of people can be entertained by a song without replicating, dividing, or decreasing the unity (one-ness) or uniqueness of the song, in the same way that any number of sensible existents can partake of a Form. And any number of people can be entertained by any number of songs, in the same way that any number of sensible existents can partake of any number of Forms.
In this section of the dialogue, Parmenides introduces what has come to be known as the Third Man Argument. It actually gets its name from Aristotle's discussion of it. Aristotle described the logic in terms of "man"and the "form of man", even though in the Parmenides dialogue it is not about, nor does it involve, a discussion of "man".
Parmenides'reasoning in this argument depends on his misunderstanding of two premises that he argues are inconsistent:-
The elder Parmenides challenges the young Socrates by supposing first that when there is a number of things that seem great, there is a single Form that is the form of absolute greatness. Then, on the assumption that this form also must be amongst those things that are great, there must be an additional form that encompasses and explains the greatness of this larger set. And so forth to infinity. Parmenides implies that this constitutes a reductio ad absurdum proof that the notion of Forms is wrong.
But the understanding of these two premises that Parmenides must adopt in order to make his reasoning work is simply wrong -- his particular understanding of these two premises is inconsistent with the descriptions that Plato has provided of Forms in his other dialogues.
From the Phaedo and other dialogues, we can see that Plato's theory of forms proposes that for any irreducible pure absolute essence F exhibited by sensible particulars, the primary function of the form F is to explain the F-ness of those particulars that partake of F. Sensible particular that are F, are F because they partake of the Form of F. Specifically excluded from Plato's description is any attempt to explain the F-ness of the Form of F itself. The form of F can explain the F-ness of the original plurality of F sensible particulars. But it cannot explain the F-ness of F. That requires no explanation because Plato maintains that F-ness is equivalent / identical to F. Hence, the move by Parmenides to demand a "higher level"Form in order to explain the F-ness of the larger set of things that includes the Form of F is specifically invalid.
The apparent inconsistency that Parmenides draws upon rests on the ambiguous
sense of "is"he employs. For NI can be understood as an accurate
consequence of Plato's description of Forms only if one understands the
"is"involved to mean "partake". As in -
"(NI): If X (a sensible particular) partakes of F, then X is not the same thing as F-ness."From numerous passages, we know that Plato specifically distinguishes sensible particulars from the Forms, and from F-ness. Similarly, any form can be predicated of itself only because the quality that is predicated and the form itself are identical. SP can be understood as an accurate description of Forms only if one understands the "is"involved to mean "equivalence / identity". As in -
"(SP): F-ness is equivalent / identical to F."
Hence Parmenides commits the fallacy of equivocation when he attempts to substitute a Form for X in the Non-Identity premise, or to employ the sense of self-predication that applies for forms when discussing particulars. The two premises are properly understood as incommensurable, and hence cannot be inconsistent. So, the Third Man Argument does not actually present any difficulty for the theory of forms.
In response to the challenges by Parmenides, the young Socrates attempts to recover his position by suggesting that Forms might be understood as thoughts. It is curious why Plato would have his character of "young Socrates"make this suggestion at this point. It is obvious from his description of Forms in other, earlier, dialogues, that Forms are in no way similar to thoughts as thoughts are commonly considered. (Although they might be considered as a kind of concept -- a particular sub-species of thought.)
Be that as it may, the character of Parmenides immediately jumps upon this suggestion. But his first argument is based on the faulty premise that if all Forms are thoughts, then necessarily all thoughts are Forms. In particular, he suggests that any thought necessarily includes a One-Over-Many notion, and is hence a Form. But this is clearly not a necessary or even a likely consequence of Socrates'suggestion that Forms are thoughts. For nowhere does Socrates suggest that the One-Over-Many premise is itself a sufficient condition to identify a Form.
In his second argument, Parmenides draws again upon his "pie model"understanding of the partaking relation to argue that if Forms are thoughts, then everything is composed of thoughts, and further that all things think -- which is absurd. Of course, as I discussed above, the pie model is an inappropriate understanding of the partaking relation. So Parmenides'conclusion that all things are composed of thoughts is nonsense. His further absurdity, that all things must think, is based on the absurd premise that anything composed of thoughts must therefore think.
Clearly, although the suggestion by the young Socrates that Forms are thoughts is a poor choice given the then common understanding of what thoughts are, the difficulties raised by Parmenides in response pose no challenge to the Theory of Forms.
In this section of the dialogue, Parmenides grasps the suggestion by Socrates that Forms are patterns set in nature, and the partaking relation is a kind of "like-ness". Parmenides argues that because the relationship of "like"is symmetrical, then the form of Greatness is like the plurality of things that are great, and the Form of Small is like the plurality of things that are small. And hence the two Forms are alike, and must partake of a form of Like-ness. And so forth to infinity.
But the reasoning fails on two grounds. Firstly, the partaking relation is more than likeness. Forms (even if viewed as set patterns in nature) play a causative role. Sensible existents have their F-ness because of their partaking of the form of F. So the relationship of partaking, while being similar to the relationship of "like", is not in fact symmetrical. Hence Parmenides cannot reason that the Form is "like"the plurality of sensible particulars that are F, and his reasoning fails. Secondly, Plato has been quite clear in the Phaedo, that Forms do not partake of Forms. Forms are not sensible existents whose F-ness needs to be explained by a form of F. Hence Parmenides cannot reason that there needs to be a higher level Form to explain the "partaking"relationship shared by all Forms, and again his reasoning fails.
In this final challenge to the theory of forms presented by the young Socrates, Parmenides argues that people can have no knowledge of Forms, and the Gods can have no knowledge of human affairs. Clearly an absurd conclusion, hence the theory of forms is wrong.
However, Parmenides'reasoning is based on the erroneous premise that knowledge is what it is in relation to what it is knowledge of. In other words, Parmenides is defining knowledge as having merely relative rather than absolute being. The young Socrates should have responded that the absurd conclusions reached by Parmenides demonstrate not that the Theory of Forms is flawed, but that the applied definition of knowledge is flawed. In the Theaetetus dialogue, Plato goes to great lengths to demonstrate that knowledge is what it is in virtue of itself. In the terms of Parmenides'argument in this section, knowledge has absolute rather than relative being. Hence Parmenides'argument is flawed.
But the young Socrates might have argued further that even if Parmenides'definition of knowledge is accepted, his conclusions are still false. In a number of dialogues, Plato describes a human as the mixture of a sensible existent (a body) and an element from the realm of Forms and Gods (the soul). Hence, a human being bridges the supposed gap between sensible existents and the realm of Forms. Hence human beings can have knowledge of the Forms through the acquaintance of the soul with the Forms. And the Gods can have knowledge of human affairs through their acquaintance with the activities of the souls inhabiting human bodies. So again, Parmenides'challenge is no difficulty at all
The nature of the "difficulties" presented in the Parmenides dialogue raises serious questions as to the purpose that Plato had in mind for the dialogue. As a later work, it is puzzling why Plato would present a picture of his "hero" Socrates in such an unflattering light. And why is the dialogue delivered at third-hand?
Perhaps the entire thing is an "exercise for the student". By presenting a third-hand rendition of what perhaps might be a collection of then common misunderstandings about the Theory of Forms, he is setting the stage for students familiar with his other dialogues, so that they may correct the alleged errors of his "young Socrates" without detracting from the reverence in which he wishes to hold a wiser Socrates. Since the latter part of the Parmenides dialogue is a series of training exercises offered by the character of Parmenides as ways to think about the Theory of Forms, the suggestion that this is a student exercise work gains weight.
In any event, all of the difficulties raised for the Theory of Forms in Plato's Parmenides dialogue can be easily overcome by drawing upon Plato's description of Forms in such other dialogues as the Phaedo, the Timeaus, the Theaetetus, the Republic, the Cratylus, and others to a lesser extent.
Rickless, Samuel, "Plato's Parmenides", The Stanford Encyclopedia of Philosophy (Fall 2007 Edition), Edward N. Zalta (ed.), forthcoming URL=<http://plato.stanford.edu/archives/fall2007/entries/plato-parmenides/>.