Logic of subjective probability

TL;DR

This paper explores the syntax and semantics of subjective probability, examining how different types relate to objectivity, and discusses Jeffreys's law and links to frequentist probability.

Contribution

It offers a comprehensive analysis of subjective probability, including intersubjective and impersonal types, and argues for the objectivity of well-tested impersonal probabilities.

Findings

Impersonal probabilities can acquire features of objective probabilities.

Jeffreys's law supports the idea of objective probabilities.

Connections between subjective and frequentist probability are discussed.

Abstract

In this paper I discuss both syntax and semantics of subjective probability. The semantics determines ways of testing probability statements. Among important varieties of subjective probabilities are intersubjective probabilities and impersonal probabilities, and I will argue that well-tested impersonal probabilities acquire features of objective probabilities. Jeffreys's law, my next topic, states that two successful probability forecasters must issue forecasts that are close to each other, thus supporting the idea of objective probabilities. Finally, I will discuss connections between subjective and frequentist probability.