Logic of subjective probability
It addresses foundational issues in probability theory for philosophers and statisticians, but is incremental in nature.
The paper examines the syntax and semantics of subjective probability, proposing that well-tested impersonal probabilities can resemble objective probabilities, and discusses Jeffreys's law to support this idea.
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.