Objective bayesianism with predicate languages

Synthese 163 (3):341 - 356 (2008)
Abstract
Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to first-order logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequency-induced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.
Keywords Bayesianism  Objective Bayesianism  Bayesian epistemology  Formal epistemology  Inductive logic  Probabilistic logic
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    Rudolf Carnap (1952). The Continuum of Inductive Methods. [Chicago]University of Chicago Press.

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