Blogosophy

Sorites, ShmoritesI was discussing Sorites

Sorites, Shmorites

I was discussing Sorites paradoxes with my friend RI, the computer scientist, and he impatiently dismissed the reasoning as fallacious. According to RI, you can easily demonstrate sequences of sets such that each set and its immediate neighbors are computationally indistinguishable (no efficient algorithm can tell them apart), but where the endpoints of the sequence are computationally distinguishable. He regards it as obvious that vague predicates like "is a heap" are such sets: although the number of grains in the heap is of course efficiently computable, the distinction between heaps with n and n+1 grains in terms of "is a heap" is not. I'm not sure it's quite that easy. For one thing, it assumes that the identification of heaps is probabilistic; I think that's true empirically (for any group of grains there is some probability that a competent speaker will assent that it's a heap), but as a theory of meaning I suspect it's controversial. I certainly think, though, that as an example it completely undermines the intuition that justifies the sorites induction: namely that because the difference seems too small to matter, the sum of successive differences should still be too small to matter. Given the existence of a counter-example to the general principle, the burden of proof should rest with those trying to justify the intuition.

On the other hand, I never thought that intuition particularly sound; it would seem to rely on the imperceptibility of the individual difference. If we were confident in our ability to discern a single grain's difference in the size of two heaps would it still seem true that "if n grains is a heap, n-1 grains is a heap?" Suppose we made perceptibility explicit: If group of grains X is a heap, then a visibly smaller group of grains Y is still a heap. Does that even seem plausible, much less obviously true? Yet if we could always perceive one grain's difference, they would be equivalent.

One might object that of course sorites predicates rely on imperceptibility, that's what makes them vague, and if one grain was a perceptible difference you could always rescue the original intuition by proposing a smaller, imperceptible change, e.g. removing a fraction of a grain. I don't think that works, because you can calculate empirically how many imperceptible changes of a given size amount to a perceptible change. Posted by joshua at June 11, 2003 07:11 AM