Ned Hall

Arguably, Hume's greatest single contribution to contemporary philosophy of science has been the problem of induction (1739). Before attempting its statement, we need to spend a few words identifying the subject matter of this corner of epistemology. At a first pass, induction concerns ampliative inferences drawn on the basis of evidence (presumably, evidence acquired more or less directly from experience)—that is, inferences whose conclusions are not (validly) entailed by the premises. Philosophers have historically drawn further distinctions, often appropriating the term “induction” to mark them; since we will not be concerned with the philosophical issues for which these distinctions are relevant, we will use the word “inductive” in a catch-all sense synonymous with “ampliative”. But we will follow the usual practice of choosing, as our paradigm example of inductive inferences, inferences about the future based on evidence drawn from the past and present. A further refinement is more important. Opinion typically comes in degrees, and this fact makes a great deal of difference to how we understand inductive inferences. For while it is often harmless to talk about the conclusions that can be rationally believed on the basis of some..

Lewis's work on causation was governed by a familiar methodological approach: the aim was to come up with an account of causation that would recover, in as elegant a fashion as possible, all of our firm “pre‐theoretic” intuitions about hypothetical cases. That methodology faces an obvious challenge, in that it is not clear why anyone not interested in the semantics of the English word “cause” should care about its results. Better to take a different approach, one which treats our intuitions about cases merely as guides in the construction of a causal concept or concepts that will serve some useful theoretical purpose. I sketch one central such purpose, suggesting, first, that an account of causation that, like Lewis's, gives a central role to counterfactuals is well‐suited to fulfill it, and, second, that the most famous pre‐emption‐based counterexamples to a counterfactual account yield an important constraint on a successful account.

David Lewis's influential work on the epistemology and metaphysics of objective chance has convinced many philosophers of the central importance of the following two claims: First, it is a serious cost of reductionist positions about chance (such as that occupied by Lewis) that they are, apparently, forced to modify the Principal Principle--the central principle relating objective chance to rational subjective probability--in order to avoid contradiction. Second, it is a perhaps more serious cost of the rival non-reductionist position that, unlike reductionism, it can give no coherent explanation for why the Principal Principle should hold. I argue that both of these claims are fundamentally mistaken.