Two Mistakes About Credence and Chance

Abstract 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. David Lewis’s conception of the challenges involved in giving a philosophical account of objective chance [Lewis 1980; 1994] has shaped that of almost every other philosopher working in the field. (For a sampling, see Black [1998], Halpin [1998], Hoefer [1997], Ismael [1996], Roberts [2001], Strevens [1995; 1999], Sturgeon [1998], and Vranas [2002].) I think this conception embodies two key mistakes. The first concerns an alleged cost incurred by Lewis and other philosophers who advocate reductionism about chance. The second concerns an alleged cost incurred by their non-reductionist opponents. A summary: Lewis recognized early on that objective chance and subjective probability-the sort of probability that measures rational degree of belief-exhibit an important connection: a rational agent’s degrees of belief should conform in a certain way to her degrees of belief about the chances. Other philosophers had also recognized this connection; but Lewis provided perhaps the most sophisticated presentation of it, in the form of his famous ‘Principal Principle’ [1986b]. At the same time, Lewis’s reductionism about chance held that facts about chance at a world somehow reduce to-and so, supervene on-the totality of categorical (i.e., non-modal) facts about that world.