Does the Third Man Argument refute the theory of forms?

 

The simple answer is "No!" Explaining why not will take a bit of exposition.

First of all, the title question is a bit ambiguous in its reference to "the"theory of forms".   There are a number of different versions of Plato's "Theory of Forms".   There are: (a) Plato's own description of his notion of forms, as found in the Dialogues;   (b)   the theory of forms according to how modern philosophers interpret the writings by and about Plato, including commentaries on Plato by Aristotle and Simplicius;   (c)   the theory of forms that is Plato's notion subtly "interpolated" (modified) by modern philosophers in order to address certain criticisms, such as the "Third Man Argument".  

Given the context of a course on early Greek philosophy, I will assume that the title question is addressed to Plato's description of his own theory of forms, although this does entail the disadvantage that Plato himself nowhere in the Dialogues lays out a clear and unambiguous description of Forms.   In order to explain why the "Third Man Argument" does not refute Plato's description of Forms, therefore, I will first provide a brief précis of Plato's theory of forms, followed by a brief description of the Third Man Argument that appears in the Parmenides dialogue.   Only then will I document my contention that the "Third Man Argument" actually demonstrates a fundamental misunderstanding of Plato's Theory of Forms, and calls into question the purpose of the Parmenides dialogue.

(1)   Plato's Description of Forms

In the Phaedo, Plato draws a sharp contrast between the eternal unchanging and perfect Forms, and the changing nature of sensible particulars.   From (Phaedo, 79a), Forms are grasped only by the intellect (reason), and are invisible to the senses.   From (Phaedo, 65-66), we learn 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.   Hence, the Forms are the explanation of the F-ness of sensible things that are F.   From (Phaedo, 74-75) we learn that Forms are unqualifiedly and perfectly what partaking particulars are only imperfectly.   Things perceptible by the senses resemble the Forms, but fall short and are inferior to them.   From (Phaedo, 78c) we have that the Forms are always the same and unchanging, and hence are uncompounded simples.   Sensible particulars are, by comparison, complex or composite and always changing.   Sensible particulars are, in this respect, Heraclitan -- always in flux.   From (Phaedo, 79d), Forms are pure, everlasting, immortal, and changeless.   From (Phaedo, 80b), Forms are divine, intellectual, uniform, indissoluble and (again) ever unchanging.   Forms are, in this respect Parmenidean -- one, eternal, and unchanging.   From (Phaedo, 100c) comes a most important distinction - Forms are the source or cause of the being of any particular's quality.   And particulars have the qualities they have because they partake of the Forms that are those qualities.

From (Republic, Book X, 596a-596b), we learn that Forms represent "the various multiplicities to which we give the same name."From this passage it has often been assumed that Forms have a semantic basis -- equivalent to our modern notion of "universals".   But in (Cratylus, 436a), Plato cautions that the name is not the essence.   And as I said, from (Phaedo, 65-66), they are to be known by reason alone and not by the bodily senses.   So the Forms are the irreducible simple elements of our perceptive judgements, and not epistemic entities equivalent to "universals".

From (Timaeus, 27d-28a), we learn that Forms are uniformly existent, compared to particulars which are never really existent.   Forms are unchanging and hence are never "becoming".   Sensible particulars are always changing ("becoming") and hence are not really existent.   And from (Timaeus, 37e-38a), because they are ever changeless, Forms are non-temporal -- they are timeless, they simply are.   From (Timaeus, 51d-52d), Forms are "self-subsisting".   They are "ungenerated and indestructible, neither receiving into itself any other from any quarter nor itself passing anywhither into another, invisible and in all ways imperceptible by sense, it being the object which it is the province of Reason to contemplate".

From (Phaedrus, 247c) we learn that Forms are non-spatial, colourless, formless, intangible, truly existing essence, visible only to the mind, with which all true knowledge is concerned.   Plato maintains that the senses furnish no truth, and particularly no truth about particulars, because the senses are neither accurate nor clear.   From (Theaetetus, 182), because all sensible particulars are in flux, we cannot speak truly of them.   He argues that knowledge is of the Forms only, since sensible particulars do not have real existence.   "Knowledge of reality"is therefore knowledge of the Forms.   Knowledge comes from the mind "when it alone and by itself is engaged directly with realities."

Forms are the only real existents, and are what they are in virtue of themselves.   Forms are perfect and what particulars are but only imperfect participants of.   The Forms are the pure absolute essence of the property they initiate in the particulars.   Particulars are ever-changing dependents on their participation in the forms for the complex of qualities that they exhibit at any one time.   Forms are unchanging, simple (incomposite), and pure essence, while particulars are ever-changing complex mixtures of multiple forms.   The participation by particulars in the Forms explains their coming into being and destruction -- change.

Since the Forms are simples and one ("monoeides" -- Phaedo 78b), and do not participate in each other (Timaeus, 52d), that implies that the only property that can be predicated of a Form is itself.   Hence a Form does not partake of itself in the way that sensible particulars partake of forms.   Instead, every Form is its respective essence.   To predicate F-ness of the Form F is to identify the equivalence of the Form F and the essence of F-ness.   The Form F is F-ness.   To predicate F-ness of some particular X is to state that X partakes of the Form F.   The particular predication statement "X is F"means "X partakes of F".   While the self-predicating statement "F is F"means that "F identifies the essence F-ness".

(2)   The "Third Man Argument"

Which brings us to the Third Man Argument.   The so-called "Third Man Argument"is a line of reasoning that appears in the Parmenides dialogue.   It got its name from Aristotle's discussion of it, not from Plato himself.   Aristotle described the logic in terms of "man"and the "form of man", even though in Plato's Parmenides dialogue it is not about, nor does it involve, a discussion of "man".  

As we saw in the previous section, Plato's Theory of Forms can be said to be committed to:

Within the Parmenides dialogue, the character of the elder Parmenides exhibits an understanding of Plato's theory of forms that includes the thesis that, for any property F, the primary function of the form F is to explain the F-ness of those things that are F, and hence to make it possible to sense and know things as F.   The logic that Parmenides employs depends on the premise that Forms are what we would call "epistemic universals" -- for every set of things that we call F, there must be a Form of F.   At (Parmenides 132a) the elder Parmenides challenges the "young"Socrates"by supposing first that when there is a number of things that seem great (or "large"in some translations), 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, and for which there must be an explanation, 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.  

Gregory Vlastos'famous analysis of the Third Man Argument(1) claims that Parmenides' invocation of Plato's Theory of Forms in this argument invokes two inconsistent premises about Forms.   The "standard interpretation" of the Third Man Argument likewise maintains that these two premises are inconsistent.   (This is made obvious when one substitutes "F-ness" for X in the following NI premise.)  

The Self-Predication premise is obvious from (Phaedo 78b; Timaeus, 52d).   But the Non-Identity premise is an interpolation of the Forms as non self-partaking and unique, and the distinction that Plato draws between particulars that partake of forms, and the forms themselves.

  (3)   The Fundamental Misunderstanding

But the premises that Parmenides adopts in order to make his reasoning work are simply wrong -- they are inconsistent with the descriptions that Plato has provided of Forms in his other dialogues.   According to the descriptions I have cited above, Plato's theory of forms proposes that for any irreducible simple element F exhibited by particulars, the primary function of the form F is to explain (give being or existence to) the F-ness of those particulars that partake of F.   Specifically excluded from Plato's description is any attempt to explain the F-ness of F.   Plato does not open the possibility of an infinite regress of forms of F-ness, each of which explaining the F-ness of the forms of F-ness below it in the hierarchy.   The form of F can explain the F-ness of the original plurality of F particular things.   But it cannot explain the F-ness of F.   That requires no explanation because he maintains that F-ness is equivalent / identical to F.   Hence, the move in the Third Man Argument 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.

In addition, the apparent inconsistency of SP and NI rests on the ambiguous sense of "is"in the two premises identified by Vlastos.   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."
But from numerous passages (some of which are cited above), we know that Plato specifically distinguishes sensible particulars from the Forms, and from F-ness.   So it is an invalid move to suggest substituting F-ness or the Form of F for X in the NI premise.   The two premises are incommensurable, and hence cannot be inconsistent.

Similarly, the sense of predication employed in the self-predication premise must needs be understood in two separate ways, depending on whether one is talking about particulars or about forms.   Any form can be predicated of itself only because the quality that is predicated and the form itself are identical.   As in -
                      "(SP):   F-ness is equivalent / identical to F."
Hence one commits the fallacy of equivocation if one 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.   So, contra Vlastos and the "standard interpretation", the Third Man Argument does not refute the theory of forms.   What the Third Man Argument does do is demonstrate that neither of the characters Parmenides nor the "young Socrates"properly understood the theory of forms.

(4)   The Purpose of the Parmenides Dialogue

Which naturally raises the question of why this argument (along with the other "critiques of Forms"contained in the Parmenides) appears in one of Plato's later dialogues.   It is curious that Plato does not have the Young Socrates correct Parmenides'interpretation of his theory.   The chronology of the Platonic dialogues generally places the Parmenides dialogue among the later efforts.   As I have indicated in the description above, by this point in his writings, all the necessary material exists to correct the flawed version that generates the Third Man Argument.   Yet the Parmenides dialogue can be characterized as a catalogue of misunderstandings of his earlier descriptions of Forms.   The "young Socrates"repeatedly misses the opportunity to correct the reasoning of the elder Parmenides.   One can only suggest, therefore, that the Parmenides dialogue is an "exercise for the student" -- a presentation of then common misconceptions of his theory with which to exercise the abilities of his students.

Whatever his purpose, Plato has certainly led generations of philosophers to wonder at his purpose, for both the dialogue as a whole and the Third Man Argument in particular.

 

Notes & References

(1)               Vlastos, Gregory.   The Third Man Argument in the Parmenides, The Philosophical Review, Vol. 63, No. 3. (Jul., 1954), pp. 319-349.

Fine, Gail. Plato on Naming. The Philosophical Quarterly, Vol. 27, No. 109. (Oct., 1977), pp. 289-301.

Fine, Gail. The One Over Many.   The Philosophical Review, Vol. 89, No. 2. (Apr., 1980), pp. 197-240.

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/>.

Silverman, Allan, "Plato's Middle Period Metaphysics and Epistemology", The Stanford Encyclopedia of Philosophy (Summer 2003 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2003/entries/plato-metaphysics/>.

Vlastos, Gregory.   Plato's "Third Man" Argument (PARM. 132A1-B2): Text and Logic,   The Philosophical Quarterly, Vol. 19, No. 77. (Oct. 1969), pp. 289-301.

Wikipedia contributors. Third Man Argument. Wikipedia, The Free Encyclopedia. Available at: http://en.wikipedia.org/w/index.php?title=Third_Man_Argument. Accessed August 26, 2007.

Appendix   -   Relevant Dialog Excerpts

Note:   All of these excerpts are taken between July 20th and August 30 th, 2007 from
           http://www.perseus.tufts.edu/cache/perscoll_Greco-Roman.html

(Phaedo, 65-66)   "Now how about such things as this, Simmias? Do we think there is such a thing as absolute justice, or not?"[Simmias] "We certainly think there is."[Socrates] "And absolute beauty and goodness."[Simmias] "Of course."[Socrates] "Well, did you ever see anything of that kind with your eyes?"[Simmias] "Certainly not!"[Socrates] "Or did you ever reach them with any of the bodily senses? I am speaking of all such things, as size, health, strength, and in short the essence or underlying quality of everything. Is their true nature contemplated by means of the body? Is it not rather the case that he who prepares himself most carefully to understand the true essence of each thing that he examines would come nearest to the knowledge of it?"[Simmias] "Certainly."[Socrates] "Would not that man do this most perfectly who approaches each thing, so far as possible, with the reason alone, not introducing sight into his reasoning nor dragging in any of the other senses along with his thinking, but who employs pure, absolute reason in his attempt to search out the pure, absolute essence of things, and who removes himself, so far as possible, from eyes and ears, and, in a word, from his whole body, because he feels that its companionship disturbs the soul and hinders it from attaining truth and wisdom? Is not this the man, Simmias, if anyone, to attain to the knowledge of reality?"

(Phaedo, 74-75)   "Do we agree, then, that when anyone on seeing a thing thinks, "This thing that I see aims at being like some other thing that exists, but falls short and is unable to be like that thing, but is inferior to it, he who thinks thus must of necessity have previous knowledge of the thing which he says the other resembles but falls short of?"…   "Then we must have had knowledge of equality before the time when we first saw equal things and thought, 'All these things are aiming to be like equality but fall short.'"

(Phaedo, 78b-c)   "Now is not that which is compounded and composite naturally liable to be decomposed, in the same way in which it was compounded? And if anything is uncompounded is not that, if anything, naturally unlikely to be decomposed?   …   Then it is most probable that things which are always the same and unchanging are the uncompounded things and the things that are changing and never the same are the composite things?"

(Phaedo, 79a)   "And you can see these and touch them and perceive them by the other senses, whereas the things which are always the same can be grasped only by the reason, and are invisible and not to be seen?"

(Phaedo, 79d)   "But when the soul inquires alone by itself, it departs into the realm of the pure, the everlasting, the immortal and the changeless, and being akin to these it dwells always with them whenever it is by itself and is not hindered, and it has rest from its wanderings and remains always the same and unchanging with the changeless, since it is in communion therewith. And this state of the soul is called wisdom. Is it not so?"

(Phaedo, 80b)   "…   the soul is most like the divine and immortal and intellectual and uniform and indissoluble and ever unchanging, and the body, on the contrary, most like the human and mortal and multiform and unintellectual and dissoluble and ever changing."

(Phaedo, 100c)   "I think that if anything is beautiful besides absolute beauty it is beautiful for no other reason than because it partakes of absolute beauty; and this applies to everything."

(Timaeus, 27d-28a)   "What is that which is Existent always and has no Becoming? And what is that which is Becoming always and never is Existent? Now the one of these is apprehensible by thought with the aid of reasoning, since it is ever uniformly existent; whereas the other is an object of opinion with the aid of unreasoning sensation, since it becomes and perishes and is never really existent."

(Timaeus, 37e-38a)     "And these are all portions of Time; even as "Was"and "Shall be"are generated forms of Time, although we apply them wrongly, without noticing, to Eternal Being. For we say that it "is"or "was"or "will be,"whereas, in truth of speech, "is"alone is the appropriate term; "was"and "will be,"on the other hand, are terms properly applicable to the Becoming which proceeds in Time, since both of these are motions; but it belongs not to that which is ever changeless in its uniformity to become either older or younger through time, nor ever to have become so, nor to be so now, nor to be about to be so hereafter, nor in general to be subject to any of the conditions which Becoming has attached to the things which move in the world of Sense, these being generated forms of Time, which imitates Eternity and circles round according to number."

(Timaeus, 51d-52d)   "If Reason and True Opinion are two distinct Kinds, most certainly these self-subsisting Forms do exist, imperceptible by our senses, and objects of Reason only; whereas if, as appears to some, True Opinion differs in naught from Reason, then, on the contrary, all the things which we perceive by our bodily senses must be judged to be most stable. Now these two Kinds must be declared to be two, because they have come into existence separately and are unlike in condition. For the one of them arises in us by teaching, the other by persuasion; and the one is always in company with true reasoning, whereas the other is irrational; and the one is immovable by persuasion, whereas the other is alterable by persuasion; and of the one we must assert that every man partakes, but of Reason only the gods and but a small class of men. This being so, we must agree that One Kind is the self-identical Form, ungenerated and indestructible, neither receiving into itself any other from any quarter nor itself passing anywhither into another, invisible and in all ways imperceptible by sense, it being the object which it is the province of Reason to contemplate; and a second Kind is that which is named after the former and similar thereto, an object perceptible by sense, generated, ever carried about, becoming in a place and out of it again perishing, apprehensible by Opinion with the aid of Sensation; and a third Kind is ever-existing Place, which admits not of destruction, and provides room for all things that have birth, itself being apprehensible by a kind of bastard reasoning by the aid of non-sensation, barely an object of belief; for when we regard this we dimly dream and affirm that it is somehow necessary that all that exists should exist in some spot and occupying some place, and that that which is neither on earth nor anywhere in the Heaven is nothing. So because of all these and other kindred notions, we are unable also on waking up to distinguish clearly the unsleeping and truly subsisting substance, owing to our dreamy condition, or to state the truth -- how that it belongs to a copy -- seeing that it has not for its own even that substance for which it came into being, but fleets ever as a phantom of something else -- to come into existence in some other thing, clinging to existence as best it may, on pain of being nothing at all; whereas to the aid of the really existent there comes the accurately true argument, that so long as one thing is one thing, and another something different, neither of the two will ever come to exist in the other so that the same thing becomes simultaneously both one and two."

(Phaedrus, 247c)   "For those that are called immortal, when they reach the top, [247c] pass outside and take their place on the outer surface of the heaven, and when they have taken their stand, the revolution carries them round and they behold the things outside of the heaven. But the region above the heaven was never worthily sung by any earthly poet, nor will it ever be. It is, however, as I shall tell; for I must dare to speak the truth, especially as truth is my theme. For the colorless, formless, and intangible truly existing essence, with which all true knowledge is concerned, holds this region and is visible only to the mind, the pilot of the soul."

(Republic, Book X, 596a-596b)   "We are in the habit, I take it, of positing a single idea or form in the case of the various multiplicities to which we give the same name."…   "there are many couches and tables."…   "But these utensils imply, I suppose, only two ideas or forms, one of a couch and one of a table."…   "And are we not also in the habit of saying that the craftsman who produces either of them fixes his eyes on the idea or form, and so makes in the one case the couches and in the other the tables that we use, and similarly of other things?"

(Theaetetus, 182a-182d)   [Socrates] "Did we not find that they say that heat or whiteness or anything you please arises in some such way as this, namely that each of these moves simultaneously with perception between the active and the passive element, and the passive becomes percipient, but not perception, and the active becomes, not a quality, but endowed with a quality? Now perhaps quality seems an extraordinary word, and you do not understand it when used with general application, so let me give particular examples. For the active element becomes neither heat nor whiteness, but hot or white, and other things in the same way; you probably remember that this was what we said earlier in our discourse, that nothing is in itself unvaryingly one, neither the active nor the passive, but from the union of the two with one another the perceptions and the perceived give birth and the latter become things endowed with some quality while the former become percipient."…   "But since not even this remains fixed -- that the thing in flux flows white, but changes, so that there is a flux of the very whiteness, and a change of color, that it may not in that way be convicted of remaining fixed, is it possible to give any name to a color, and yet to speak accurately?"[Theodorus] "How can it be possible, Socrates, or to give a name to anything else of this sort, if while we are speaking it always evades us, being, as it is, in flux?"

(Theaetetus, 187a)   "But surely we did not begin our conversation in order to find out what knowledge is not, but what it is. However, we have progressed so far, at least, as not to seek for knowledge in perception at all, but in some function of the soul, whatever name is given to it when it alone and by itself is engaged directly with realities."

(Theaetetus, 206b)   "Then if we are to argue from the elements and combinations in which we ourselves have experience to other things in general, we shall say that the elements as a class admit of a much clearer knowledge than the compounds and of a knowledge that is much more important for the complete attainment of each branch of learning, and if anyone says that the compound is by its nature knowable and the element unknowable, we shall consider that he is, intentionally or unintentionally, joking."

(Parmenides, 132a)   [Parmenides] "I fancy your reason for believing that each idea is one is something like this; when there is a number of things which seem to you to be great, you may think, as you look at them all, that there is one and the same idea in them, and hence you think the great is one."[Young Socrates] "That is true."[Parmenides] "But if with your mind's eye you regard the absolute great and these many great things in the same way, will not another great appear beyond, by which all these must appear to be great?"[Young Socrates] "So it seems."[Parmenides] "That is, another idea of greatness will appear, in addition to absolute greatness and the objects which partake of it; and another again in addition to these, by reason of which they are all great; and each of your ideas will no longer be one, but their number will be infinite."

(Cratylus, 436a)   "Do you not see that he who in his inquiry after things follows names and examines into the meaning of each one runs great risks of being deceived?"

(Cratylus, 438d)   "Then since the names are in conflict, and some of them claim that they are like the truth, and others that they are, how can we decide, and upon what shall we base our decision? Certainly not upon other names differing from these, for there are none. No, it is plain that we must look for something else, not names, which shall show us which of these two kinds are the true names, which of them, that is to say, show the truth of things."

 (Cratylus, 439e)   "How, then, can that which is never in the same state be anything? For if it is ever in the same state, then obviously at that time it is not changing; and if it is always in the same state and is always the same, how can it ever change or move without relinquishing its own form?"

 (Cratylus, 440a)   "For at the moment when he who seeks to know it approaches, it becomes something else and different, so that its nature and state can no longer be known; and surely there is no knowledge which knows that which is in no state."…   "But we cannot even say that there is any knowledge, if all things are changing and nothing remains fixed; for if knowledge itself does not change and cease to be knowledge, then knowledge would remain, and there would be knowledge; but if the very essence of knowledge changes, at the moment of the change to another essence of knowledge there would be no knowledge, and if it is always changing, there will always be no knowledge, and by this reasoning there will be neither anyone to know nor anything to be known. But if there is always that which knows and that which is known -- if the beautiful, the good, and all the other verities exist -- I do not see how there is any likeness between these conditions of which I am now speaking and flux or motion."

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