A Formal Solution to Reichenbach's Reference Class Problem

Abstract

Following Reichenbach, it is widely held that in making a direct inference, one should base one's conclusion on a relevant frequency statement concerning the most specific reference class for which one is able to make a warranted and relatively precise-valued frequency judgment. In cases where one has accurate and precise-valued frequency information for two relevant reference classes, R 1 and R 2 , and one lacks accurate and precise-valued frequency information concerning their intersection, R 1 ∩R 2 , it is widely held, following Reichenbach, that no inference may be drawn. In contradiction to Reichenbach and the common wisdom, I argue for the view that it is often possible to draw a reasonable informative conclusion in such circumstances. As a basis for drawing such a conclusion, I show that one is generally in a position to formulate a reasonable direct inference for a reference class that is more specific than either of R 1 and R 2 . Direct Inference DI½ :c∈R and freq TjR ð Þ¼r is a reason for concluding that PROB c∈T ð Þ¼r: 1 assumed that the proper major premises for direct inference are statements of frequency or limiting frequency, other proposals have been made, by Bacchus (1990), Pollock (1990) and Thorn (2012Thorn ( , 2017. The modest assumption that point-valued frequency statements may serve as major premises for direct inference will be sufficient for the present paper. bs_bs_banner dialectica Following Reichenbach, it is widely held that in making a direct inference, we should base our conclusion on a relevant frequency statement concerning the most specific reference class for which we are able to make a warranted and (relatively) precise-valued frequency judgment where we have accurate and precise-valued frequency information for two relevant reference classes, R 1 and R 2 , and we lack accurate and precise-valued frequency information concerning their intersection, it is widely held, following Reichenbach, that no inference may be drawn. In such cases, Reichenbach holds that there is no formal solution to the problem, and that our only course, if we hope to make an inference, is to gather more information concerning the intersection of the two reference classes (Reichenbach 1949, 375). 2 In contradiction to Reichenbach and the common wisdom, I follow in the footsteps of Kyburg and Teng (2001) and Pollock (2011), and argue that it is often possible to draw a reasonable informative conclusion, in such circumstances. As a basis for drawing such a conclusion, I show that one is generally in a position to formulate a reasonable direct inference for a reference class that is more specific than either of R 1 and R 2 . After presenting my approach in Section 3, I compare it to the approaches of Kyburg and Teng (2001) and Pollock (2011), in Section 4. Preliminary discussionBefore proceeding, it will be helpful to get a bit clearer about the sorts of conditions under which direct inferences are defeated. There are two plausible principles that provide a partial specification of the conditions under which...

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