Correcting The Guide to Objective Chance

Abstract

In his A Subjectivist's Guide to Objective Chance, David Lewis argues persuasively that a certain relationship holds between reasonable credence and objective chance (I 980).l Both items involve varieties of probability: in the case of credence, we use subjective probability to describe gradations in degree of belief; in the case of chance, we use objective probability to describe irreducibly indeterministic processes (e.g., radioactive decay). While these two uses are not to be conflated, Lewis points out an important connection between them: roughly, rationality requires conforming one's subjective credence in a proposition to one's estimate of the objective chance that the proposition will come true. As a precise statement of this connection, Lewis offers his Principle-only to find that it conflicts with his cherished thesis of reductionist metaphysics dubbed Humean Supervenience. So we seem to face a dilemma: either we abandon an attractive and plausible principle relating credence and chance, or we give up the reductionist thesis. Wrong. The Principal Principle (hereafter: the Principle) does not adequately formulate the connection between credence and chance. Close inspection reveals that it embodies a crucial oversight for which there is, happily, a natural repair. Undertaking this repair, we arrive at a New Principle which all parties, regardless of their metaphysical commitments, should find compelling. This New Principle functions much better than the Old: it is more precise, holds without qualification, explains the initial plausibility of the Old Principle while yielding that Principle as an approximation, is perfectly immune to the problem raised in Lewis (1980) and provides an analysis of an important range of cases about which the Old Principle fell silent. In what follows, I rehearse the Old Principle together with familiar problems confronting it, paying special attention to the notion of admissibility required for its formulation. This notion is, ultimately, dispensable: where inadmissible information was taken to break the connection between credence and chance, I show that on the contrary there is a perfectly straightforward way to incorporate such information into the connection. Following this line of thought leads directly to the New Principle. All of which will require some background, which follows.