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Tests of Significance Violate the Rule of Implication

Published online by Cambridge University Press:  28 February 2022

Davis Baird
Davis Baird*
Affiliation:
University of South Carolina
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Extract

Here follows a puzzle for those attempting to explain inductive inference. Suppose one hypothesis, H, implies another, I. Suppose further we obtain evidence, E, deemed sufficient to warrant the rejection of I. Is this evidence sufficient to warrant the rejection of H as well?

It is very tempting to answer this question affirmatively. The inference in question appears to be justified by a single use of modus tollens or denying the consequent:

A testament to the obvious plausibility of this sort of inference is the ubiquity of its endorsement in treatises on inductive inference. See, for example, Popper (Popper 1935, p. 76), Hempel (Hempel 1945, p. 31), Hacking (Hacking 1976, p. 33), or Savage (Savage 1954, p. 32). Indeed, a referee reporting on another paper called the following “rule of implication”:

(+) If hypothesis H implies hypothesis I, then evidence sufficient to warrant the rejection of I, in turn warrants the rejection of H.

Type
Part III. Statistical Hypotheses and Statistical Testing
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1984 , Issue 1: Volume One: Contributed Papers 1984 , 1984 , pp. 81 - 92
Copyright
Copyright © Philosophy of Science Association 1984

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References

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