In the Treatise of Human Nature, David Hume mounts a spirited assault on the doctrine of the infinite divisibility of extension, and he defends in its place the contrary claim that extension is everywhere only finitely divisible. Despite this major departure from the more conventional conceptions of space embodied in traditional geometry, Hume does not endorse any radical reform of geometry. Instead Hume espouses a more conservative approach, claiming that geometry fails only “in this single point” – in its purported (...) proofs of infinite divisibility – while “all of its other arguments” remain intact. -/- In this paper, after laying out the prima facie case for Hume’s radical challenge to traditional geometry, I consider five strategies for blocking the arguments for infinite divisibility while conserving most of geometry. I show that each of these interpretive strategies suffers from serious substantive problems, and so none of them delivers an interpretation of Hume’s account that provides him with a way of blocking the geometric arguments for infinite divisibility while sustaining his geometric conservatism. (shrink)

According to the Ought-Implies-Can principle (OIC), an agent ought to perform a certain action only if the agent can perform that action. Proponents of OIC interpret this supposed implication in several ways. Some argue that the implication in question is a logical one, namely, entailment. Some think that the relation between ‘ought’ and ‘can’ is a relation of presupposition. Still others argue that ‘ought’ conversationally implicates ‘can’. Opponents of OIC offer a variety of counterexamples in an attempt to show that (...) there are cases in which an agent ought to perform a certain action even though she cannot perform that action. Such counterexamples often involve either culpable or nonculpable inability. In cases of culpable inability, the agent renders herself unable to fulfill an obligation. For example, a student is unable to submit a paper on the due date because she procrastinated until it became too late to write a paper by the assigned deadline. In cases of non-culpable inability, the agent somehow becomes unable to fulfill an obligation, through no fault of her own. For example, an agent becomes unable to pay back a loan to a bank because she was robbed on her way to the bank. This paper attempts to offer counterexamples to OIC of a sort different from the one discussed by opponents of OIC so far. If these counterexamples are correct, then they seem to suggest that there are cases in which an agent has an obligation to perform an action even though she may not be able to perform that action, and thus OIC is false. In other words, ‘ought’ does not imply ‘can’. (shrink)