Axioms for typefree subjective probability

TL;DR

This paper develops two foundational axiomatic systems for typefree subjective probability, one finitely additive and one infinitely additive, to provide a formal basis for analyzing controversial principles in the field.

Contribution

It introduces and compares two axiomatic frameworks for typefree subjective probability, offering a formal foundation for future theoretical investigations.

Findings

Finitely additive probability system suitable for controversial principles

Infinitely additive probability system explicated and contrasted

Frameworks facilitate formal analysis of subjective probability principles

Abstract

We formulate and explore two basic axiomatic systems of typefree 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 typefree subjective probability.