Plausible inference from the idea of estimation

Abstract

The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that one can start from an alternative point of view, postulating the existence of an operation for \textit{estimating magnitudes given a state of knowledge}. The properties of this operation can be established through basic consistency requirements. Application of this estimation operation to the truth values of propositions in an integer representation directly yields non-negative, normalized quantities following the sum and product rules of probability.