On confirmation

Abstract

Taking for the relation of confirmation the following obvious axioms, we obtain several more or less well-known theorems and are able to solve in a definite and strict manner several problems concerning confirmation. Let a, b , and c be variable names of sentences belonging to a certain class, the operations a · b , a + b , and ā the (syntactical) product, the sum, and the negation of them. Let us further assume the existence of a real non-negative function c ( a, b ) of a and b , when b is not self-contradictory. Let us read ‘ c ( a, b )’ ‘degree of confirmation of a with respect to b ' and take the following axioms: Axiom I. If a is a consequence of b, c ( a, b ) = 1 . Axiom II. If is a consequence of c , Axiom III. c ( a · b , c ) = c ( a, c )· c ( b , a · c ). Axiom IV. If b is equivalent to c, c ( a, b ) = c ( a, c ). As may be easily seen, the interval of variation for c is ( 0, 1 ); this is quite conventional.