  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.
