This chapter describes the problem for a polycriterial theory of probability. Recent philosophical theories about probability have tended to be polycriterial rather than monocriterial. The identification of mathematical structure does not suffice to explain why such-and-such criteria are all criteria of probability. Nor can a family-resemblance theory explain this (or any other) conceptual unity. The chapter also discusses the mathematicist theory. A formal axiomatization of probability is in principle open to non-standard interpretations. It then evaluates family-resemblance theory. The...

This chapter describes the problem for a polycriterial theory of probability. Recent philosophical theories about probability have tended to be polycriterial rather than monocriterial. The identification of mathematical structure does not suffice to explain why such-and-such criteria are all criteria of probability. Nor can a family-resemblance theory explain this (or any other) conceptual unity. The chapter also discusses the mathematicist theory. A formal axiomatization of probability is in principle open to non-standard interpretations. It then evaluates family-resemblance theory. The family-resemblance account imposes an all-too-familiar kind of gloss on the data, but cannot be relied on to lead to anything new.