Axioms for Type-Free subjective Probability

Cezary Cieslinski, Leon Horsten, Hannes Leitgeb

Abstract: We formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles about type-free subjective probability.