Although Plato did not refer to the Third Man Argument as such in his dialogues it was a name given to the theory years later by Aristotle, who briefly discussed the idea in his Metaphysics and Sophistical Refutations. This particular argument of the Parmenides, according to Vlastos, seeks to exposes two “inconsistent premises” within the Forms which together lead to the theory’s alleged infinite regress.
The character of Parmenides endeavours to establish this in two different ways, though each aims to present the same absurdity.
The first of these works on the understanding that for all things that display F-ness—say, A, B and C—there must be a Form F by virtue of which we comprehend A, B and C as F. This is a standard interpretation of Plato, and one he himself appears to sanction. The issue arises when one considers the nature of F. Parmenides uses the example of ‘Greatness’ (‘Largeness’ in other translations) to illustrate this problem: For all things that are large (A, B and C) there must be a Form of Largeness by virtue of which we see A, B and C as such. The Form of Largeness is immutably perfect, and therefore the perfect archetype of largeness; but if F is itself large, and thereby an example of F-ness, it must, by the above understanding, require its own explanation, namely a partaking in another Form by virtue of which it is large. This Form can be called F2. This continues ad infinitum—into F3 and F4—with each set of F things consuming F and requiring a further F to serve as cause of their F-ness.
The second version of the Third Man Argument works in a similar way and reveals the same glitch in the uniqueness and intelligibility of the Forms. This argument was well expounded by Pelletier and Zalta in their example of ‘Loveliness’: If all things lovely become such and acquire their loveliness by virtue of partaking in the respective Form of Loveliness, then they must themselves be ‘like’ that Form. Following from the “symmetry of likeness” it can be said that the Form must, then, be ‘like’ the objects which partake in it. If this is true, the Form of Loveliness and the lovely objects must resemble one another by virtue of a further Form, of which they both partake. This, again, continues ad infinitum, creating Forms interminably to explain the likeness of the Form to its instantiations.
In the simpler terms used in the previous explanation, this argument can be understood as the following: If A, B and C each possess F-ness by partaking in F, they must (in their F-ness) resemble F. From the “symmetry of likeness” it follows that F must resemble A, B and C. This incurs the requirement of a further Form (F2) by virtue of which F resembles its instantiations—ad infinitum.
Though they have different approaches, each of these arguments depend on the same premises and threaten the Forms in the same way. The above account of the Third Man Argument relies on two distinct features of the Forms: First, Non-Identity, which demands that if something has a certain property it cannot be the same as the Form by virtue of which we understand that property (If X has F-ness, then A cannot be the same as F). Second is Self-Predication, which states that any Form partakes of itself (F has F-ness). These qualities of the Forms are drawn from a number of Plato’s dialogues in which they are discussed, and are essential to the Third Man Argument’s refutation. They do, however, remain questionable, as the following section will expound.
Literature on the Third Man Argument is expansive and “voluminous,” but in all its versions the reproach threatens the uniqueness of the Forms and, in its subsequent infinite regress, their claim to being knowable and the only true basis for knowledge. The importance of the Forms’ uniqueness is described first in the Phaedo, and can be fathomed as a simple requirement of the Form to be the only one of its sort. This condition is linked with the Forms’ immutability: Plato states that those objects and properties that are “composite”—in other words, not unique—are “naturally liable to be decomposed.” Immutability is a requirement of the Forms because they would be otherwise susceptible to the change and decay of time, and would thereby become imperfect; so Plato concludes that “it is most probable that things which are always the same and unchanging are the uncompounded things.” If the Forms were not unique, as the Third Man Argument proposes, then they are neither immutable nor perfect—and it is by these very qualities, among others, that Plato defines the Forms. How, after all, could F be the perfect example of F-ness if there are multiple Fs?
Where the question of the Forms’ value is concerned, the Third Man Argument provides us with strong reason to abandon them altogether. Plato claims in the Cratylus that the Forms alone may ground our knowledge, that everything else—that is, their transient instantiations—are wholly unreliable and in a constant state of “becoming.” As far as Plato was concerned, everything but the Forms was in a perpetual state of flux—unknowable, untouchable—where the Forms themselves remained intact, able to provide a basis for our beliefs about the world and all that within it. But how are they able to serve as such a basis in view of the infinite regress presented by the Third Man? How, by our understanding of the Forms, are we able to acquire knowledge of the ultimate if that understanding leads us straight into an infinite regress?
It is clear that Plato formulated the Theory of the Forms not only to provide a solution to the problem of universals, but to also rescue the plight of knowledge from our seeming inability to truly ‘know’ anything. The Forms played an integral part in Plato’s epistemological, metaphysical and political philosophy, and without them many of his ideas would appear unfounded. The Third Man Argument challenges this theory, and therein a vital cornerstone of Plato’s thinking.
(All excerpts from Plato’s dialogues taken between December 19th and 22nd 2013 from: www.perseus.tufts.edu/cache/perscoll_Greco-Roman.html)
· Beck, M.C. (1999). Plato’s Self-corrective Development of the Concepts of Soul, Forms and Immortality in Three Arguments of the “Phaedo. Oxford: Clarendon Press.
· Cohen, S.. (2011). Readings in ancient Greek philosophy from Thales to Aristotle. In: Cohen, S. and Curd, P. Ancient Greek Philosophy . 4th ed. London: Hackett Publishing.
· Hales, S.D.. (1990). The Recurring Problem of the Third Man. Auslegung.
· Kraut, Richard, “Plato”, The Stanford Encyclopedia of Philosophy (Summer 2012 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2012/entries/plato/>
· Kung, J.. (1985). Aristotle on Thises, Suches and the Third Man Argument. Available: <www.stanford.edu/~mvr2j/sfsu12/reading/phil770_kung.pdf>. Last accessed 19/12/13.
· Lacewing, M.. (2007). Plato’s Theory of the Forms. Available: <cw.routledge.com/textbooks/alevelphilosophy/data/A2/Plato/PlatoTheoryForms.pdf>. Last accessed 19/12/13.
· Macintosh, D. . (2012). Plato: A Theory of Forms. Available: <philosophynow.org/issues/90/Plato_A_Theory_of_Forms>. Last accessed 19/12/13.
· Pelletier, F.J. and Zalta, E.N.. (2003). How to Say Goodbye to the Third Man. Available: <mally.stanford.edu/plato.pdf>. Last accessed 20/12/13.
· Rickless, S.. (2012). Plato’s Parmenides. Available: <plato.stanford.edu/entries/plato-parmenides/>. Last accessed 19/12/13.
· Russell, B. (1972). The History of Western Philosophy. New York: Touchstone.
· Saburns, D.. (2009). Does the Third Man Argument refute the theory of forms?. Available: <http://www3.sympatico.ca/saburns/pg0715e13.htm. Last accessed 19/12/13>.
· Sanday, E.C.. (2009). Eleatic Metaphysics in Plato’s Parmenides: Zeno’s Puzzle of Plurality. The Journal of Speculative Philosophy. 23 (3).
· Santayana, G. (2010). Egotism in German Philosophy. Charleston: Nabu Press.
· Sharma, R.. (2005). What is Aristotle’s “Third Man” Argument Against the Forms?. In: Sedley, D. Oxford Studies in Ancient Greek Philosophy. Oxford: Oxford University Press.
· Vlach, M. . (2012). Plato’s Theory of the Forms. Available: <www.theologicalstudies.org/resource-library/philosophy-dictionary/158-platos-theory-of-forms>. Last accessed 19/12/13.
· Watt, S.. (1997). Introduction: The Theory of Forms (Books 5-7). In: Plato: Republic. London: Wordsworth Editions.
 Sharma (2005) pp. 123
 Saburns (2009)
 Sharma (2005) pp. 132
 Pelletier (2003) pp. 12
 Hale (1990) pp. 67
 Phaedo, 78b-c
 Cratylus, 440a