Direct Inference from Imprecise Frequencies

  • Paul ThornEmail author
Conference paper
Part of the European Studies in Philosophy of Science book series (ESPS, volume 5)


It is well known that there are, at least, two sorts of cases where one should not prefer a direct inference based on a narrower reference class, in particular: cases where the narrower reference class is gerrymandered, and cases where one lacks an evidential basis for forming a precise-valued frequency judgment for the narrower reference class. I here propose (1) that the preceding exceptions exhaust the circumstances where one should not prefer direct inference based on a narrower reference class, and (2) that minimal frequency information for a narrower (non-gerrymandered) reference class is sufficient to yield the defeat of a direct inference for a broader reference class. By the application of a method for inferring relatively informative expected frequencies, I argue that the latter claim does not result in an overly incredulous approach to direct inference. The method introduced here permits one to infer a relatively informative expected frequency for a reference class R′, given frequency information for a superset of R′ and/or frequency information for a sample drawn from R′.


Direct inference Statistical syllogism Reference class problem Imprecise probability 



Work on this paper was supported by DFG Grant SCHU1566/9-1 as part of the priority program “New Frameworks of Rationality” (SPP 1516). For comments that motivated the preparation of this paper, I am thankful to participants at EPSA 2015, including Michael Baumgartner, Martin Bentzen, Seamus Bradley, Bert Leuridan, Jan-Willem Romeijn, Gerhard Schurz, and Jon Williamson. I am also grateful for discussions with Christian Wallmann, which motivated the proposal presented in Sect. 28.4.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Philosophy DepartmentUniversity of DuesseldorfDuesseldorfGermany

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