Intuitionists think that there are cases in which, say, some identity statement between real numbers is neither true nor false, even though we know that it cannot possibly be false. That is: We know that it cannot not be that a = b, say, but we cannot conclude that a = b. We can't, in general, move from not-not-p to p in intuitionistic logic. , I suggest that the believer in vague objects should say something similar. It can never be true that it is vague whether A is B. But that does not imply that there is always a fact of the matter whether A is B.

Generally speaking, I tend to think that whether a philosopher's views are true is a poor test of their quality. What matter are the arguments they give, and the insights those arguments inspire.

Many people who call themselves deflationists are deflationists about propositional truth but not about sentential truth. I only ever mention that view to distinguish it from disquotationalism. I don't really have any objection to it, other than that I don't believe in propositions, so I don't think there's any such thing as a proposition's being true. Truth, on my view, is primarily a property of representations, such as sentences and certain kinds of mental states.

To borrow from Mark Twain, I tend to think that reports of the death of supervaluationist approaches have been greatly exaggerated. The arguments that have been given against supervaluationism usually aim to show that it is just incoherent. But it's not. It may be false, as a general theory of vagueness, but it's a coherent and, I think, even correct way to think about some vagueness.

Intuitionists think that there are cases in which, say, some identity statement between real numbers is neither true nor false, even though we know that it cannot possibly be false. That is: We know that it cannot not be that a = b, say, but we cannot conclude that a = b. We can't, in general, move from not-not-p to p in intuitionistic logic. , I suggest that the believer in vague objects should say something similar. It can never be true that it is vague whether A is B. But that does not imply that there is always a fact of the matter whether A is B.

One of the central developments of 19th century mathematics involved a dramatic increase in the standards of mathematical rigor. This was for a variety of reasons, but the short version is that there was a need to be stricter about the standards of proof, because certain familiar modes of reasoning had started to lead people astray, or at least threatened to do so.

One thing I really like about philosophy is that it's possible actually to do work in a wide range of different areas. I am particularly happy that I've even been able to do work in logic that has allowed me to use and develop my mathematical abilities, as well as to work on quite distant topics in philosophy of language and mind.