Generalized Carnapian Systems

Abstract

Carnap has always considered the problem of explication of rational (degree of) belief as the problem of the determination of the ‘logical probability’ of a hypothesis in the light of evidence (see, e.g., [2] and [7]). However, he does not make assumptions about the way in which evidence is obtained. More precisely, Carnap presupposes that the logical probability can be determined as soon as the non-logical constants of the language in which hypothesis and evidence are formulated are known. A consequence of this approach is that Carnap’s famous continuum of inductive methods for monadic predicate language (Carnap [3], see also Kemeny [21]) is a purely mathematical probability system presented in the form of a particular application.