Vindicating Chance: On the Reductionism/Non-Reductionism Debate

Abstract

One of the issues concerning a strictly objective interpretation of probability is the debate between reductionist and non-reductionist accounts of chance. In section 1, we introduce the debate between these two camps, and identify the main challenges each of them face. As is well known, the discovery of the incompatibility between reductionist positions concerning chance and an intuitive credence-chance principle, namely Lewis [1980]'s Principal Principle, generated a new, two-pronged way of addressing this debate. Reductionists face the motivation problem: they are required to provide motivation for alternative credence-chance principles compatible with their metaphysical assumptions. Non-reductionists face the explanation problem: they are required explain why it is rational for us to let chance guide credence in the way specified by her favored credence-chance norm. In section 2, we revisit some known background in order to set the scene for the discussion to follow. In section 3, we follow Briggs [2009] in identifying further problems for the reductionist, and argue that, in view of these, the reductionist's prospects of being able to meet the motivation problem are slim at best. In section 4, we turn to a fuller discussion of the explanation problem. As Hall [2004] argues, it turns out that the reductionist faces this problem too. In 4.1, we delineate a formal strategy for justifying any favored credence-chance norm. In 4.2, we show how the anti-reductionist is able to put in motion this formal strategy by providing a motivation for a key assumption upon which the strategy relies. In 4.3, we argue that the reductionist's prospects of being able to provide a similar justification of the assumption are also slim. We claim that these considerations provide a dialectical advantage to the anti-reductionist camp. 1. Reductionism and anti-reductionism about chance According to a broad class of reductionist views on chance, facts about chance at a world supervene upon (or at any rate are reducible to) the global distribution of categorical facts throughout the entire history of that world. Variation with respect to the nature of the supervenience base is possible, as long as no modal facts, no primitive dispositions or propensities are allowed among the fundamental properties of the