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A Theory of Conclusions

Published online by Cambridge University Press:  01 April 2022

Raymond Dacey
Raymond Dacey*
Affiliation:
University of Oklahoma
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Abstract

This paper presents a theory of conclusions based upon the suggestions of Tukey [21]. The logic offered here is based upon two rules of detachment that occur naturally in probabilistic inference, a traditional rule of acceptance, and a rule of rejection. The rules of detachment provide flexibility: the theory of conclusions can account for both statistical and deductive arguments. The rule of acceptance governs the acceptance of new conclusions, is a variant of the rule of high probability, and is a limiting case of a decision-theoretic rule of acceptance. The rule of rejection governs the removal of previously accepted conclusions on the basis of new evidence. The resulting theory of conclusions is not a decision-theoretic logic but does, through the aforementioned limiting property, provide a line of demarcation between decision and conclusion (i.e., nondecision) logics of acceptance. The theory of conclusions therefore complements decision-theoretic inference.

The theory of conclusions presented here satisfies Tukey's desiderata, specifically:

  1. (1) conclusions are statements which are accepted on the basis of unusually strong evidence;

  2. (2) conclusions are to remain accepted unless and until unusually strong evidence to the contrary arises;

  3. (3) conclusions are subject to future rejection, when and if the evidence against them becomes strong enough.

Finally, the preferred theory of conclusions has a strong conservative bias, reflecting Tukey's aims.

Type
Research Article
Information
Philosophy of Science , Volume 45 , Issue 4 , December 1978 , pp. 563 - 574
Copyright
Copyright © Philosophy of Science Association 1978

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Footnotes

†

I would like to thank C. Glymour, K. Lehrer, J. Pitt, S. Spielman, P. Suppes, and an anonymous referee for their criticisms and suggestions.

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