Direct Inference from Imprecise Frequencies

In Michela Massimi, Jan-Willem Romeijn & Gerhard Schurz (eds.), EPSA15 Selected Papers: The 5th conference of the European Philosophy of Science Association in Düsseldorf. Cham: Springer. pp. 347-358 (2017)
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Abstract

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'.

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Author's Profile

Paul D. Thorn
Heinrich Heine University Düsseldorf

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References found in this work

The theory of probability.Hans Reichenbach - 1949 - Berkeley,: University of California Press.
The logic of chance.John Venn - 1876 - Mineola, N.Y.: Dover Publications.
Nomic Probability and the Foundations of Induction.John L. Pollock - 1990 - New York, NY, USA: Oxford University Press.
Uncertain Inference.Henry E. Kyburg Jr & Choh Man Teng - 2001 - Cambridge University Press.
The Logic of Chance.John Venn - 1866 - British Journal for the Philosophy of Science 14 (53):73-74.

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