Often we have coarsely grained knowledge: for example, we know about how many people are present. In possessing such knowledge, we also have finer grained knowledge of what is not: there certainly is nothing like that number of people here. The combination of such knowledge types, through sorites, generates contradiction and bafflement. This paper seeks to resolve the bafflement: it rejects a Timothy Williamson proposal, introduces muddle numbers and inference gaps, and shows how the different grains of knowledge do not (...) always meet. In so doing, the paper identifies a distinctive first‐person inferring. (shrink)

Applying a broadly Wittgensteinian view of knowledge and its relation to the conditions in which the word “know” is ordinarily used, the paper defends the claim that there can be knowledge (and thus also truth) in moral matters and rejects the idea that a cross‐culturally homogeneous moral language is a necessary condition for this. However, the fact that moral knowledge is available sometimes does not imply that it is available always. Taking issue in particular with Ronald Dworkin, the paper also (...) argues that where moral questions are a matter of judgement, there may well be no right answer to them and, further, that this is a feature by no means unique to moral discourse. (shrink)

Ways and words about infinity have frequently hidden a continuing paradox inspired by Zeno. The basic puzzle is the tortoise's – Mr T's – Extension Challenge, the challenge being how any extension, be it in time or space or both, moving or still, can yet be of an endless number of extensions. We identify a similarity with Mr T's Deduction Challenge, reported by Lewis Carroll, to the claim that a conclusion can be validly reached in finite steps. Rejecting common solutions (...) to both challenges, we use a Wittgensteinian approach for dissolution, noting also that other paradoxes, such as the Surprise Examination and Yablo's, trap us inconsistently into similar endlessnesses. In so doing, we encounter a hopping flea, generate a proportionality paradox and consider the knight's move in chess. (shrink)

Applying a broadly Wittgensteinian view of knowledge and its relation to the conditions in which the word “know” is ordinarily used, the paper defends the claim that there can be knowledge in moral matters and rejects the idea that a cross‐culturally homogeneous moral language is a necessary condition for this. However, the fact that moral knowledge is available sometimes does not imply that it is available always. Taking issue in particular with Ronald Dworkin, the paper also argues that where moral (...) questions are a matter of judgement, there may well be no right answer to them and, further, that this is a feature by no means unique to moral discourse. (shrink)

The postulation by the “epistemic” theory of vagueness of a cut-off point between heaps and non-heaps has made it seem incredible. Surely, the critics argue, a vague predicate doesn’t divide the universe into a set and its complement. I argue in response that an objection of a similar kind can be leveled against most theories of vagueness. The only two which avoid it are untenable. The objection is less compelling than it initially seems. However, even when this obstacle is removed, (...) the epistemic theory is not yet vindicated. (shrink)