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.