Saturday, August 23, 2008

David Hume and the Existential Quantifier

As I've said before, one advantage of doing History of Philosophy is that it yields real evidence. For instance, instead of pretending that you know offhand what 'The Mind-Body Problem' is, you look at what people have said through the years and decades and centuries about mind and body and the problems association with the union of the two; and you start exploring the ways in which an Aristotelian approach (for instance) is different from a Cartesian one; and you start realizing that this version of the problem requires that assumption and that one requires this assumption; and then when you actually talk about 'The Mind-Body Problem' you actually know what you are talking about. (This is what I've blogged about before under the name, 'The Problem of the Philosophical Problem', which sounds a bit like a Sherlock Holmes mystery.) But another advantage is that it also frees you up for more purely imaginative things, like asking dead philosophers questions they could not possibly have been asked when alive and figuring out, within a degree of plausibility, what answers they could have given.

Suppose, for instance, we asked David Hume about existential quantifiers and their relation to particular quantifiers. Does "There is at least one x" imply that at least one x exists? And it's interesting that there really is only one answer that could be given by him. On Hume's account, existence only has to do with matters of fact, not relations of ideas. We can quantify over relations of ideas using a particular quantifier, e.g., "There is at least one type of triangle that does not have right angles." On a Humean view this can have nothing to do with existence; it merely shows how two ideas, triangles and right angles, are related to each other, i.e., they do not exclude each other, but the former does not require the latter. Existence is not even remotely in view. So David Hume would have to say that some cases of particular quantification are not existential.

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