Thursday, March 01, 2007

Theodorus' judgement and the art of measure

I mentioned earlier that we can see a tension between Socrates and Theodorus in the dialogues of the trilogy. Socrates and Theodorus, despite superficially friendly relations, seem to be fundamentally at odds, with Theodorus in expressing or implying doubts about Socrates' philosophical proficiency at several points (e.g. Theaetetus 169a6-b4). I also indicated that if we take this tension seriously we might read the dialogues in part as a critique of the limitations of certain mathematical modes of thinking. Here's a small example of what this could mean.

When Socrates expresses the fear that Theodorus might have brought a refuting god who has come to punish them to their gathering, rather than a mere "stranger," Theodorus ambiguously reassures him: this is not the way of the Stranger; he is more "measured" than those who take disputation too seriously. There is a more than a hint that Theodorus includes Socrates among the latter, i.e., somebody who takes disputation too seriously (Theaetetus 169a6-b4). As Seth Benardete (1984, p. II.70) puts it:

Theodorus, ... [w]ith his usual rudeness, tacitly agrees that Socrates is poor in speeches ... The Stranger is not another Socrates, whose “love of naked exercise in speeches” lets no one get away from him without first rendering an account of himself.

Now, when Theodorus says that the stranger is "more measured" than somebody like Socrates, he uses the word μετριώτερος, which evokes the notion of measure, τὸ μέτριον, discussed much later in the Statesman (beginning at 283c). There, the Stranger distinguishes between two arts of measure: one kind that measures things in relation merely to each other (as bigger or smaller than each other), and another kind that measures them in relation to a mean (as too much or too little in relation to it). The Stranger puts all the arts of measure that have to do with number, length, depth, and surface, i.e., the mathematical arts, among the arts of measure that do not measure "against the mean" and hence cannot find the proper measure (the neither too much nor too little) of things (284e4; for a fuller argument on this point, see my paper here). Mathematicians, in other words, are not qualified by virtue of their mathematical art to say whether someone is "too preoccupied" with disputation. But that is precisely what Theodorus is claiming by saying that the Stranger is "more measured" than somebody like Socrates; he is trying to measure against the mean.

Thus, to the extent that we can refer forwards to the discussion of measure in the Statesman when thinking about Theodorus' subtle put-down of Socrates, we can see that Socrates has the last laugh: Theodorus is not qualified, according to the implication of the Stranger's argument, to judge whether the Stranger is more or less measured than Socrates in the matter of disputation, except in the purely mathematical sense that the Stranger engages in less disputation than Socrates. Whether the Stranger engages in the right level of disputation is something that Theodorus cannot judge.

To be sure, all of this is somewhat speculative. Others see less of a tension between Socrates and Theodorus (e.g., Miller 1980, pp. 11-12), and most see no tension at all (most agree with Campbell 1867, note to 216a5, who long ago argued that Theodorus' reassurance merely shows that Socrates expressed an “ironical fear” of having the “Zenonian negative dialectic to bear on his own (i.e. Plato’s) mode of reasoning”). The point, however, is that if we take seriously both Theodorus' status as a mathematician and the apparent downgrading of a purely mathematical art of measure in the Statesman, then Theodorus' judgment about the Stranger and Socrates is put into question: he cannot tell us that the Stranger is a better philosopher than Socrates by engaging in a less disputatious form of philosophy.

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