The Third Man Argument in Plato
A Presentation by Joe Newton
27 October 1998 for James F. Hill, Ph.D. in Plato Seminar
originally prepared 4 May 1992

1. Introduction
   
   
   1. This dialogue between the youthful Socrates and the Eleatic philosophers Parmenides and Zeno is retold by Cephalus who heard it from Antiphon, who heard it from Pythodorus, who was present.
      
      
   2. After listening to Zeno's treatises, Socrates applies his theory of forms in an attempt to show that Zeno's paradoxes are no paradoxes, but a confusion of absolute ideas with concrete things which participate in those ideas.
      
      
   3. Then Parmenides examines Socrates' doctrine of the independence of ideas from concrete things. Following out the consequences of this hypothesis, Parmenides shows that the problem of relating ideas to material things will require indefinitely higher ideas to relate the ideal and the material. This problem came to be known as the "Third Man Argument" within Plato's day. Socrates is unable to resolve the dilemma at this time.
      
      
   4. Socrates, Zeno, and the others implore Parmenides to demonstrate the Eleatic method of philosophy which takes an hypothesis and traces out the consequences of both its truth and falsity. Parmenides proceeds with a discussion of the hypothesis that "one is" and its opposite "one is not." Thus the principle of dichotomy or the method of division by contraries is demonstrated (Fowler, 196).
      
      
   5. According to scholars, the dialogue appears not to reach any definite conclusion about Socrates' theory of forms nor about the Eleatic doctrine of being. For such interpretation provides only to show the difficulties of Plato's philosophy. However, an overriding interest in the method of philosophy is demonstrated and it is probably for this that the dialogue should be valued. Furthermore, the difficulties may be only apparent to the uninitiated, the many. For those in Plato's Academy who were able to understand, perhaps the dialogue revealed the metaphilosophy of Plato stemming from the Eleatic school and before them the Pythagoreans.
      
      
2. Third Man Argument Presented in Parmenides
   
   
   1. Context of the Argument
      
      
      1. Zeno's Treatise
         
         
         1. All (one) is not a plurality (many).
            
            Where Fowler translates "existences:"
            
            "... if existences are many, they must be both like and unlike, which is impossible; for the unlike cannot be like, nor the like unlike ... Then if it is impossible for the unlike to be like and the like unlike, it is impossible for existences to be many ... existences are not many" (127E, Fowler).
            
            Where Cornford translates "things:"
            
            "'If things are many,' as you say, 'they must be both like and unlike. But that is impossible; unlike things cannot be like, nor like things unlike. ... if unlike things cannot be like or like things unlike, it is also impossible that things should be a plurality ... things are not a plurality'" (127E, Cornford).
            
            
         2. Zeno's treatise that "all is not many" is complementary to Parmenides' treatise that "all is one" (128B, Fowler).
            
            
         3. Zeno's argument takes the form of a reductio ad absurdum (127E,128D-E).
            
            
         4. From this argument stem all of the (in)famous paradoxes of Zeno which show that the many, unlikeness, and motion are unreal and illusory in contradistinction to the one, likeness, and rest. This is the conclusion of the Eleatic school of Greek philosophy on the subject of being: true being is one, not many; true being is at rest and not in motion.
            
            
      2. Young Socrates' Theory of Forms as Critique of Zeno's Treatises
         
         
         1. Socrates' criticism of Zeno's treatise amounts to criticizing Zeno for not making the distinction between abstract ideas and those things which partake in abstract ideas, a distinction which depends upon Socrates' theory of forms.
            
            
         2. In the Parmenides, where Fowler translates "abstract idea(s)" Cornford translates "form(s)."
            
            
         3. Socrates' initial statement of his theory of forms:
            
            "... there is an idea of likeness in the abstract, and another idea of unlikeness, the opposite of the first, and that you and I and all things which we call many partake of these two ... those which partake of likeness become like, and those which partake of unlikeness become unlike, and those which partake of both become both like and unlike, all in manner and degree of their participation" (129, Fowler).
            
            
         4. Socrates' criticism of Zeno's treatise:
            
            "For if anyone showed that the absolute like becomes unlike, or the unlike like, that would, in my opinion, be a wonder; but if he shows that things which partake of both become both like and unlike, that seems to me, Zeno, not at all strange, not even if he shows that all things are one by participation in unity and that the same are also many by participation in multitude; but if he shows that absolute unity is also many and the absolute many again are one, then I shall be amazed" (129B, Fowler).
            
            
         5. Socrates defines the forms as "among the objects we apprehend in reflection" (130, Cornford) or the abstract ideas as "intellectual conceptions" (130, Fowler).
            
            
   2. Parmenides Examines Socrates' Theory of Forms
      
      
      1. Socrates' theory of forms entails the distinction and separation of forms (abstract ideas) from things which partake of forms (130B).
         
         
      2. Socrates' theory of forms asserts certain forms (130B):
         
         likeness, unlikeness
         one, many (unity, plurality)
         justice, injustice
         beauty
         good.
         
         
      3. Socrates' theory of forms is unsure whether or not to assert forms such as (130C-D):
         
         man
         hair
         mud
         dirt
         
         
      4. However, if "what is true of one thing is true of all" (130D, Fowler) then to deny forms of man, hair, mud, dirt, or any thing is to deny any forms whatsoever.
         
         
      5. To deny any forms whatsoever would make further dialogue impossible and cause thought to fall "into some abyss of nonsense and perishing" (130D, Fowler).
         
         
   3. Problems of Participation
      
      
      1. Participants are named after the forms of which they partake.
         
         "... there are ideas, and that these other things which partake of them are named from them, as, for instance, that that partake of likeness become like, those that partake of greatness great, those that partake of beauty and justice just and beautiful" (131, Fowler).
         
         
      2. How many ways could a thing (object) partake of its form?
         
         
         1. An object partakes of the whole its idea.
            
            "... like day, which is one and the same, is in many places at once, and yet is not separated from itself; so each idea, though one and same, might be in all its particpants at once" (131B, Fowler).
            
            
         2. An object partakes of only a part of its idea.
            
            "... spread a sail over many persons ... the whole sail " would not "be over each person," but "a part over each." Thus, "the ideas themselves ... are divisible into parts, and the objects which partake of them would partake of a part, and each of them there would be not the whole, but only a part of each idea" (131C, Fowler).
            
            
         3. Is there some other way than for an object to partake of its idea either in whole or in part?
            
            Parmenides asks, "... could there be some other third kind of participation?"
            
            Socrates answers, "How could there be?" (131, Fowler)
            
            Parmenides asks, "How, then ... will other things partake of those ideas ... if they cannot partake of them either as parts or as wholes?"
            
            Socrates answers, "By Zeus... I think that is a very hard question to determine" (131E, Fowler).
            
            
      3. Socrates is unwilling "to assert that the one idea is really divided and will still be one" (131C, Fowler).
         
         
   4. Third Man Arguments
      
      
      1. "Each idea is one" (132, Fowler):
         
         "... 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" (132, Fowler).
         
         
      2. An idea of the idea emerges:
         
         "... 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?" (132, Fowler)
         
         
      3. Ideas of ideas propogate indefinitely (infinitely):
         
         "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" (132B, Fowler).
         
         
      4. First Objection: Socrates objects that ideas are only in the mind.
         
         
         1. "But ... each of these ideas may be only a thought, which can exist only in our minds; then each might be one, without being exposed to the consequences you have just mentioned" (132B, Fowler).
            
            
         2. Parmenides responds that this position compels Socrates to a kind of mentalist idealism where reality is only in the mind.
            
            
            1. Each thought is one, of something and not nothing, of something that is and not something that is not.
               
               "A thought of some single element which thought thinks of as appertaining to all and as being one idea" (132C, Fowler).
               
               
            2. The object of a thought would itself be a thought.
               
               "Then will not this single element, which is thought of as one and always the same in all, be an idea?" (132C, Fowler).
               
               
            3. Thus, if forms are only in the mind, then all reality is only mental.
               
               "... does not the necessity which compels you to say that all other things partake of ideas, oblige you also to believe either that everything is made of thoughts, and all things think, or that, being thoughts, they are without thought" (132D, Fowler).
               
               
      5. Second Objection: Socrates objects that ideas exist in nature as patterns and participation is by imitation (132D-133).
         
         
         1. "... these ideas exist in nature as patterns, and the other things resemble them and are imitations of them; their participation in ideas is assimilation to them, that and nothing else" (132D, Fowler).
            
            
         2. Parmenides responds:
            
            
            1. An idea is like the particular thing which resembles the idea (132E).
               
               
            2. This idea would participate together with its like in yet another idea (132E).
               
               
            3. This further idea would in turn particpate together with the thing and its original idea in yet another idea, and so on (133).
               
               
      6. According to Parmenides, the emergence of the third man problem is the result of maintaining "that ideas are separate, independent entities" (133, Fowler).
         
         
3. Solutions to the Third Man Argument
   
   
   1. Gregory Vlastos' Analysis and Critique of the Third Man Argument: Location of Implied Theses
      
      
      1. Logical restatement of the Third Man Argument (Vlastos, 1973):
         
         
         1. [1] If any set of things share a given character then there exists a unique Form corresponding to that character; and each of these things has that character by participating in that Form.
            
            
         2. [1A] a, b, c are F.
            
            { given a set things a, b, and c and from [1] }
            
            
         3. [1B] There exists a unique Form (which we may call F-ness) corresponding to the character, F, and a, b, c are F by participating in F-ness.
            
            { from [1] and [1A] }
            
            
         4. [2] If a, b, c, and F-ness are F, then there exists a unique Form, (which we may call F-nessII), corresponding to F, but not identical with F-ness; and a, b, c, and F-ness are F by participating in F-nessII.
            
            { This hypothesis does not follow from any of the premises above, but requires and thus implies the following premise [SP].}
            
            
         5. [SP] The Form corresponding to a given character itself has that character.
            
            { implied by [2] }
            
            
         6. [2A] a, b, c, and F-ness are F.
            
            { from [SP] and [1A] and [1B] }
            
            
         7. [NI] If anything has a given character by participating in a Form, it is not identical with that Form.
            
            { implied by [2] }
            
            
         8. [2B] There exists a unique Form (which we may call F-nessII), corresponding to F, but not identical with F-ness; and a, b, c, and F-ness are F by participating in F-nessII.
            
            { from [1], [2A], and [NI] }
            
            
      2. According to Gregory Vlastos, the problem of the third man arises from the inconsistency of two implied premises of self-predication and non-identity. Thus the Third Man Argument fails to demolish Plato's Theory of Forms.
         
         
      3. Vlastos identifies a problem between self-predication and those forms Plato recognized as forms of change, becoming, and perishing. If these forms were self-predicating they could do so only at the cost of their very being. This same problem occurs with any forms whose corresponding characters contradict the Platonic concept of being (Vlastos, 1965).
         
         
4. Greater implications of Socrates' theory of forms (133B-):
   
   
   1. Parmenides proceeds to examine the "assumption that each idea is one and is something distinct from concrete things" (133B, Fowler).
      
      
   2. First, absolute ideas are established as not being inside of us.
      
      First, "an absolute idea of each thing" would not exist "in us ... for if it did ... it would no longer be absolute" (133C, Fowler).
      
      
   3. Second, absolute ideas are separated from particulars.
      
      "Then those absolute ideas which are relative to one another have their own nature in relation to themselves ... and these concrete things, which have the same names with the ideas, are likewise relative only to themselves, not to the like-named ideas" (133D, Fowler).
      
      
      1. Parmenides cites the example of particulars of master and slave as separate from the abstract ideas of mastery and slavery.
         
         
      2. So "abstract or absolute" knowledge "would be knowledge of abstract or absolute truth" (134, Fowler).
         
         
      3. "And likewise each kind of absolute knowledge would be knowledge of each kind of being" (134, Fowler).
         
         
      4. "And would not the knowledge that exists among us be the knowledge of the truth that exists among us, and each kind of our knowledge be the knowledge of each kind of truth that exists among us?" (134B, Fowler).
         
         
   4. Thus, because the ideas are not within us, "and the various classes of ideas are known by the absolute idea of knowledge ... which we do not possess ... we do not partake of absolute knowledge" (134B, Fowler). Thus we cannot know absolute truth, good, or beauty.
      
      
   5. Still further, if it is God who partakes of absolute knowledge, then God can have no knowledge of humans nor humans of God! (134C-E).
      
      
5. Parmenides' demonstration of the Eleatic method of philosophy:
   
   
   1. That "everything has a class and absolute essence" is affirmed by Parmenides, but it could not be found through Socrates' prior line of reasoning but only through an exceptionally thorough understanding (135).
      
      
   2. Furthermore, to deny forms or essences is to destroy any further dialogue (135C).
      
      
   3. After Parmenides' demolition of Socrates' theory of forms as separate, independent entities, Socrates fails to answer how he is to proceed with philosophy? Parmenides advises Socrates that he begins philosophy by seeking the forms too soon, before he has exercised and trained in the true method of philosophy.
      
      
      1. Method takes the form of Zeno's treatises (135E).
         
         
      2. Method takes the form of reductio ad absurdum,
         tracing the consequences of the negation as well as the affirmation of given hypotheses (136).
         
         
      3. Method also makes a distinction that Socrates already made:
         that distinction between visible appearance and intellible reality (135E).
         
         
   4. Socrates, Zeno, and the rest (137) implore the aged Parmenides to demonstrate the complete framing of an hypothesis (136D). Parmenides agrees, though "full of terror when " he remembers "through what fearful ocean of words I must swim" (137B). Such demonstration is not for the multitude, but for the few who understand the necessity of "this devious passage" (136E, Fowler) of "ranging in this way over the whole field" (136E, Cornford).
      
      
   5. Aristoteles (who later become one of the "Thirty Tyrants" of Athens) is selected as interlocutor because of his youth, and Parmenides proceeds with framing the hypothesis that "if the one exists, the one cannot be many" (137C, Fowler).
      
      
      1. Conclusions drawn from this discussion:
         
         The one is not many (137C).
         
         The one is neither a whole nor does it have parts (137D).
         
         The one is unlimited, without beginning, middle, or end, and without form (137E).
         
         The one is not anywhere, it is not in anything, neither itself nor anything else (138B).
         
         The one "is neither in motion nor at rest" (139B, Fowler).
         
         "...the one cannot be like or unlike either another or itself" (140B, Cornford).
         
         "...the one cannot be younger or older than, or of the same age as itself or another" (140E, Cornford).
         
         "...the one has nothing to do with time and does not occupy any stretch of time" (141D, Cornford).
         
         "...the one neither is one nor is at all ... the one in no sense is" (142, Cornford). But this cannot be so:
         
         "If a one is, it cannot be, and yet not have being" (142B, Cornford).
         
         "Since 'is' is asserted to belong to this one which is, and 'one' is asserted to belong to this being which is one, and since 'being' and 'one' are not the same thing, but both belong to the same thing, namely that 'one which is' that we are supposing, it follows that it is 'one being' as a whole, and 'one' and 'being' will be its parts. So we must speak of each of these parts, not merely as a part, but as part of whole" (142D, Cornford).
         
         
      2. From this point, the discussion seems to turn over all of the conclusions reached before, reaching new conclusions such as that the one is whole and also has parts (142D), that one is plurality (144E), and that one partakes of the forms (145B).
         
         
      3. The dialogue ends:
         
         "It seems that, whether there is or is not a one, both that one and the others alike are and are not, and appear and do not appear to be, all manner of things in all manner of ways, with respect to themselves and to one another.
         
         "Most true" (166B, Cornford).
         

Bibliography

Cornford, F. M., trans. (1939) Parmenides in The Collected Dialogues of Plato, Including the Letters. E. Hamilton and H. Cairns eds. Bollingen Series LXXI. Princeton, NJ: Princeton U. Pr., 1989 [1961].

Fowler, H. N., trans. Parmenides. in Plato in Twelve Volumes: Cratylus, Parmenides, Greater Hippias, Lesser Hippias. Cambridge, MA: Harvard U. Pr., 1977 [1926].

Jiyuan, Yu. "On Plato's Theory of the Metheksis of Ideas." Philosophical Inquiry. 13: 1-2 (1991), 27-37.

Sharvy, Richard. "Plato's Causal Logic and the Third Man Argument." No–s. 20: 4 (Dec. 1986), 507-530.

Vlastos, Gregory. "The Third Man Argument in the Parmenides." Bobbs-Merrill reprint. London: Routledge & Kegan Paul, 1965.

Vlastos, Gregory. "Plato's 'Third Man' Argument (Parmenides 132A1-B2): Text and Logic." Platonic Studies. Princeton, NJ: Princeton U. Pr., 1973.