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) conclusions are statements which are accepted on the basis of unusually strong evidence;
(2) conclusions are to remain accepted unless and until unusually strong evidence to the contrary arises;
(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.