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The theory of probability and statistical inference is various things to various people. To the mathematician, it is an intricate formal calculus, to be explored and developed with little professional concern for any empirical significance that might attach to the terms and propositions involved. To the philosopher, it is an embarrassing mystery whose justification and conceptual clarification have remained stubbornly refractory to philosophical insight. (A famous philosophical epigram has it that induction [a special case of statistical
William W. Rozeboom (Thu,) studied this question.