Wednesday, November 14, 2007

Aristotle and indexicals

In the Topics, Aristotle describes accidents as "now belonging, now not belonging." This is an interesting thing to note since, at least how the translation renders it, it looks like it is part of one sentence. Clearly if you are saying this, it would be spread out over time and would be evaluated in slightly different contexts. The time parameter would have shifted. Considered as written and as a type, rather than a token, it seems reasonable to deny that there is a principled reason to shift the context. The whole thing would be evaluated relative to one context. In that case though what Aristotle says is false and can't be true. It would require something to be both P and not P.

I mention this because one of the features of Kaplan's setup for indexicals is that he evaluates types in context. This is because types, not being spread out in time, can be evaluated relative to one context. This lets us get at the logic of the terms rather than getting bogged down in details about tokenings. Aristotle's example seems to be one place where this supposed virtue breaks down. In order to understand it and properly evaluate it we must consider both the type and the tokenings as temporally spread out.

No comments: