Theory of Probability

3Prevision and Probability

3.1 From Uncertainty to Prevision

3.1.1. So far, even in the way we presented the preceding examples, we have limited ourselves to depicting and representing the situation facing You, when You are interested in distinguishing among a more or less extensive class of alternatives (all those which, in the present state of your information, appear possible to You). This preliminary topic, which we will have to consider more deeply in what follows, is still within the ambit of ordinary logic, the logic of certainty. One should always be careful to distinguish clearly between those things belonging to this domain and those belonging to the probabilistic domain – the ambit of the logic of uncertainty, the logic of prevision – to which we must now turn our attention. It was precisely in order to pin‐point this distinction that we decided upon this form of exposition, presenting concepts and related examples which reveal the situation as it is, while leaving undetermined all questions concerning the possible introduction of probability, its conceptual basis and its evaluation. It would certainly be easier, and seemingly more instructive, to go right ahead and take the two steps together, instead of just the one. In other words, we could present right away, fused together in the examples and definitions, both the probability (which answers the need) and the uncertainty (from which the need arises), without first making such a need ‘felt’, and then pausing ...