The term ‘probability’ and its cognates occur frequently in both everyday and philosophical discourse. Unlike many other concepts, it is unprofitable to view ‘probability’ as having a unique meaning. Instead, there exist a number of distinct, albeit related, concepts, of which we here mention five: the classical or equiprobable view, the relative frequency view, the subjectivist or personalist view, the propensity view, and the logical probability view. None of these captures all of our legitimate uses of the term ‘probability’, which range from the clearly subjective, as in our assessment of the likelihood of one football team beating another, through the inferential, as when one set of sentences lends a degree of inductive support to another sentence, to the obviously objective, as in the physical chance of a radioactive atom decaying in the next minute. It is often said that what all these interpretations have in common is that they are all described by the same simple mathematical theory – ‘the theory of probability’ to be found in most elementary probability textbooks – and it has traditionally been the task of any interpretation to conform to that theory. But this saying does not hold up under closer examination, and it is better to consider each approach as dealing with a separate subject matter, the structure of which determines the structure of the appropriate calculus.
Introduction to Quantum Logical Information Theory: Talk