Russell Pannier

Mindful logic: how to resolve some paradoxes of identity.

It seems a tame and unexciting contention that logic ought not be mindless. After all, one cannot construct a logical theory or apply logic without thinking. But we mean more than this. Contrary to the common assumption that logical theory can be successfully constructed without so much as mentioning thoughts or anything like them, and in fact is better off utterly detached from considerations of the mental, it seems to us that some logical problems are insoluble if one insists on approaching them with such self-imposed restrictions. Our purpose here, however, is not to argue this conviction at length, but to illustrate the value of permitting oneself to mention the mind and its acts when working on logical theory. We shall discuss a problem concerning the principle of the indiscernibility of identicals. After stating the problem, we shall propose a way of understanding the principle which preserves both self-evidence and utility. In particular, we shall argue that this understanding dissolves certain apparent counterexamples to the principle. These counterexamples arise from application of the principle of indiscernibility to epistemic, modal, and definitional contexts.