Blackwell Reference Online

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The true logic of the world is in the calculus of probabilities. James Clerk Maxwell ‘Probability logic’ might seem like an oxymoron. Logic traditionally concerns matters immutable, necessary and certain, while probability concerns the uncertain, the random, the capricious. Yet our subject has a distinguished pedigree. Ramsey begins his classic “Truth and Probability” (1980 [1931]) with the words: “In this essay the Theory of Probability is taken as a branch of logic. … “ De Finetti (1980) speaks of “the logic of the probable.” And more recently, Jeffrey (1992) regards probabilities as estimates of truth values, and thus probability theory as a natural outgrowth of two-valued logic—what he calls “probability logic.” However the point is put, probability theory and logic are clearly intimately related. This chapter explores some of the multifarious connections between probability and logic, and focuses on various philosophical issues in the foundations of probability theory. The survey begins in section 16.2 with the probability calculus, what Adams (1975 , p. 34) calls “pure probability logic.” As will be seen, there is a sense in which the axiomatization of probability presupposes deductive logic. Moreover, some authors see probability theory as the proper framework for inductive logic—a formal apparatus for codifying the degree of support a piece of evidence lends a hypothesis, ... log in or subscribe to read full text