I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...) argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

Here I propose a coherent way of preserving the identity of material objects with the matter that constitutes them. The presentation is formal, and intended for RSL. An informal presentation is in preliminary draft! -/- Relative-sameness relations—such as being the same person as—are like David Lewis's "counterpart" relations in the following respects: (i) they may hold between objects that aren't identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different (...) contexts. They differ from counterpart relations, however, in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis's Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). (shrink)

The paper explicates a new way to model the context-sensitivity of 'knows', namely a way that suggests a close connection between the content of 'knows' in a context C and what is pragmatically presupposed in C. After explicating my new approach in the first half of the paper and arguing that it is explanatorily superior to standard accounts of epistemic contextualism, the paper points, in its second half, to some interesting new features of the emerging account, such as its compatibility (...) with the intuitions of Moorean dogmatists. Finally, the paper shows that the account defended is not subject to the most prominent and familiar philosophical objections to epistemic contextualism discussed in the recent literature. (shrink)