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Third Man Argument and Antinomies in Plato's Parmenides
Third Man Argument and Antinomies in Plato’s Parmenides
Akihiro Matsuura


In the second part of the Parmenides, Plato replies to the criticism of his Theory of Idea described in its first part. In the form of the Antinomies written in the second part from the viewpoint of his later dialectic, i.e., Division and Collection, Plato suggests his solution to the so-called Third Man Argument, one criticism of his Theory of Idea.

First, the Antinomies, in my interpretation, are configured to the aspects of Division and Collection. The former is the separative way of classification, which implies the relation of one thing to another among many to be classified. In contrast, the latter is the collective one, which does not have the same relative way of thinking but instead abstracts common features from all the elements. The abstraction does not concern the relation to those elements, at least, in the same sense as the one implied in the Division. Now, Plato expresses these two aspects, that is, the relative and the non-relative, in the form of the Antinomies in the second part of the dialogue. For instance, in the so-called first hypothesis, the One has relation neither to itself (pros heauto) nor to others (pros ta alla). We cannot apply any words to it because this application is a type of relation. It means we cannot speak anything at all about it. As a result, they say the first hypothesis is the origin of the negative theology. In contrast, at the end of the so-called second hypothesis, Plato concludes that we can speak anything of it including contradiction because the One has relation both to itself and to others. Thus, as mentioned above, the Antinomy reflects the two aspects concerned.

Then, what is the Third Man Argument? I think it is a criticism of the Theory of Idea that is formed from the confusion of the two aspects mentioned above. To be more precisely, the criticism is as follows. According to the Theory of Idea, we find the Idea of, e. g., Large from surveying many large things. But if so, then, as one who opposes this theory says, we must find one more Idea of Large from surveying many large things and the Idea of Large mentioned above. Then, the third Idea of Large appears in the same way, and the fourth, the fifth, and so on. Therefore, the Theory of Idea, according to this criticism, has an infinite number of Ideas while Plato insists that there is only one Idea. But, I think the opponent clearly muddles the abstract entity with the concrete entity. He confuses the aspect of Collection with that of Division. Division implies the relationship between one element and the other elements, in other words, the comparison of those elements with each other to a benchmark or type. In contrast, Collection is not the comparison of the elements but the discovery of the benchmark immanent in all of the elements. In this sense, Collection is a non-relative way of thinking. The Third Man Argument puts the benchmark into the many elements, which means it mixes up the non-relative way of thinking with the relative one.

Accordingly, we can conclude that Plato presents the Antinomies as his solution to the Third Man Argument because the infinite regress does not occur if we do not confuse the aspect of Division and that of Collection, that is, the aspect of relation and that of non-relation.
by matsuura2005 | 2016-03-18 21:28 | 研究ノート
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