Monday, November 05, 2007

Vaguely Logical

Kit Fine was, rather appropriately, rather vague about his extraordinary logic of vagueness (not its name, probably) last night (in St Andrews), which got me wondering what we could possibly want a logic of vagueness for... Our predicates are naturally usually as definite as our ordinary uses of them require them to be, and even in situations in which they're insufficiently definite, the usual logic (of definite predicates) will inform of us that fact, by throwing up a simple contradiction, the resolution of which is also quite ordinary: We need only precisify some predicate(s) somewhat, and we can continue as before. That's all very rough and ready, but at least it works well enough. When devising our more logical theories of things, our theoretical languages must at present contain only definite predicates, but is that a bad thing? (Do we want vague terms in our scientific theories?) The selection of the more precise predicate(s) is a free act of human creativity, but there is no more logical science than mathematics, and our choices of its axioms are similarly free.

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