Two Problems of Direct Inference
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The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have postponed treatment of the problem associated with gerrymandered reference classes by appealing to an unexplicated notion of projectability. I address the lacuna in past theories by introducing criteria for being a relevant statistic. The prescription that only relevant statistics play a role in direct inference corresponds to the sort of projectability constraints envisioned by past theories.
This work was supported by the LogiCCC EUROCORES program of the ESF and DFG. For helpful comments on earlier presentations of this paper, I thank audiences at the University of Arizona, the University of Düsseldorf, and the Third Formal Epistemology Festival at the University of Toronto. I also thank Terry Horgan, Shaughan Lavine, Gerhard Schurz, and especially John Pollock and two anonymous referees for Erkenntnis for helpful comments on earlier drafts of the paper.
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