Theory of Probability

1Introduction

1.1 Why a New Book on Probability?

There exist numerous treatments of this topic, many of which are very good, and others continue to appear. To add one more would certainly be a presumptuous undertaking if I thought in terms of doing something better, and a useless undertaking if I were to content myself with producing something similar to the ‘standard’ type. Instead, the purpose is a different one: it is that already essentially contained in the dedication to Beniamino Segre

[who about twenty years ago pressed me to write it as a necessary document for clarifying one point of view in its entirety.]

Segre was with me at the International Congress of the Philosophy of Science (Paris 1949), and it was on the occasion of the discussions developed there on the theme of probability that he expressed to me, in persuasive and peremptory terms, a truth, perhaps obvious, but which only since appeared to me as an obligation, difficult but unavoidable.

‘Only a complete treatment, inspired by a well‐defined point of view and collecting together the different objections and innovations, showing how the whole theory results in coherence in all of its parts, can turn out to be convincing. Only in this way is it possible to avoid the criticisms to which fragmentary expositions easily give rise since, to a person who in looking for a completed theory interprets them within the framework of a different point of view, they can seem to lead unavoidably to contradictions.’