On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of (...) indeterminacy nor a type of ignorance. Rather, it is sui generis. (shrink)

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of (...) indeterminacy nor a type of ignorance. Rather, it is sui generis. (shrink)

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that (...) nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken. (shrink)

According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice (...) of future-tense propositions, with truth values in the interval [0, 1], and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history. (shrink)

We explore in an experimental spirit the prospects for extending classical propositional logic with a new operator P intended to be interpreted when prefixed to a formula as saying that formula in question is at least partly true. The paradigm case of something which is, in the sense envisaged, false though still "partly" true is a conjunction one of whose conjuncts is false while the other is true. Ideally, we should like such a logic to extend classical logic - or (...) any fragment thereof under consideration - conservatively, to be closed under uniform substitution (of arbitrary formulas for sentence letters or propositional variables), and to allow the substitutivity of provably equivalent formulas salva provabilitate. To varying degrees, we experience some difficulties only with this last ('congruentiality') desideratum in the two four-valued logics we end up giving our most extended consideration to. (shrink)