Though the reasoning of the Third Man Argument is certainly sound, whether or not it can provide an adequate criticism of the Theory of the Forms is another matter. The theory introduces problems for the Forms in its conjuring of a ‘Third Man,’ who himself entails a Fourth and a Fifth, ad infinitum. The introduction of a ‘higher’ Form of which the original partakes brings about an infinite regress, and demeans the very substance of Plato’s theory. But is the Third Man necessary, and are his antecedents valid?
As mentioned before, the Third Man Argument as posed by the Parmenides relies on two distinct qualities of the Forms: Non-Identity and Self-Predication. If either were to be disproven, as this section aims, then the logic of the Third Man would be disrupted and it would no longer proffer a legitimate repudiation. It is my belief, and that of others, that these premises are based on a misunderstanding of Plato’s Forms, namely of the distinctions he made between them and their particulars.
It can be understood that the “primary function” of F is to “explain [or give being] to the F-ness of those particulars that partake of F.” It is not said by Plato that F was able to explain or give being to its own F-ness because F is in fact “equivalent/identical” to F-ness—F is self-defined, and an ultimate property of itself. This can be seen to cohere with others of the Forms’ qualities, viz. its absolute perfection: the Forms are self-defining in the way of a proven mathematical theorem, immutable, aspacial and atemporal.
This meddles with the premises of the Third Man Argument in that they neglect this central understanding of the Forms and instead treat them as if they were particulars. The Non-Identity premise, for instance, states that if X has F-ness, then X cannot be the same as F. This is to say that if something possess a certain property it requires a respective Form to explain or give being to that property. This is certainly true of particulars, which necessitate the Forms to explain their qualities, but not so of the Forms: as aforementioned, the Forms give being to themselves; F is identical to F-ness, and does not require the vindication of a further Form to realise its own properties. So if X (a particular) has F-ness, then it indeed cannot be the same as F; but if F has F-ness, it most certainly can be the same as F, for they are necessarily one-in-the-same.
The premise of Self-Predication is subject to the same error. If something were to partake of itself in the style of a particular partaking of a Form, it would surely require a further Form to bring light to that property of which is being partaken. But the Form is not partaking of itself in the way of a particular, for it is self-defining and the property being predicated is therefore equivalent to the Form itself. An additional Form is not obliged, for the original brings about explanation on its own. This can be seen as the following: F, which is both F and F-ness, partakes of F and gives being to its own F-ness by virtue of F. Again, the solution emerges with the realisation that F and F-ness are one-in-the-same.
The Non-Identity and Self-Predication premises of the Third Man Argument are defenceless once this understanding of the Forms has been fully implemented. With the Form itself accounting for its own properties in a way which does not require succour, the Third Man becomes superfluous and indeed logically unfeasible. Of what would F1 be the Form if F-ness had been fully accounted for by F? It can be seen here that the criticisms of the Third Man Argument are built upon a parochial interpretation of Plato’s Forms, without which its premises are unable to support its argument.
Though the remaining arguments of the Parmenides may well deliver a more satisfactory refutation of the Theory of the Forms, it is clear that the Third Man Argument relies too heavily on assumptions generated by a swift and unsophisticated interpretation of Plato’s thinking. Though to commit to the Third Man Argument’s premises is to perhaps acknowledge allusions made by Plato in some of his dialogues, it is also to overlook a great many more elsewhere.
The Third Man Argument undertakes the task of dislodging Plato’s Theory of the Forms in proving it to lead to an infinite regress out of which it is unable to break. Its subscribers since Plato have used its inclusion in the Parmenides to suggest that Plato himself no longer believed in the Forms, and was eager to refute their existence. But how could this be the case considering the characters of the Parmenides display a vitally limited understanding of the Forms? Why would Plato devise a complex theory of the Forms in his Republic and Phaedo just to deny it on a provincial basis in the Parmenides? Perhaps he struck an epiphany and no longer believed in the Forms, but this would not explain why Plato would confront them from the perspective of one who did not fully comprehend their nature. I would be as bold as to surmise that Plato wrote the Parmenides to test his students, to present them with the ill-informed criticisms of his work that frequented Athens at the time. Perhaps the Parmenides was a trial, conceived to emphasise areas of the Forms Plato believed were being overlooked.
(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.
 Kung (1985) pp. 225
 Saburns (2009)
 Beck (1999) pp. 148