Jan Harald Alnes: Features of Frege’s logicism: Concept, Logical Object and Axiom V

Frege’s method for forming logical proper names that mean individual numbers in Die Grundlagen der Arithmetik is contextualized within the framework of his contemporary mathematics. Originally, Frege thought that the numbers could be constructed by way of contextual definitions, but due to the so-called Julius Caesar problem, he had to invoke extensions or courses-of-values. This move away from construing names directly from given concepts, had the consequence that it became difficult to find persuasive arguments in favour of the claim that arithmetic is an analytic science and not a synthetic a priori one, as is geometry. It is maintained, among other things, that Frege introduced his celebrated distinction between sense [Sinn] and meaning [ Bedeutung] due to reflections on the epistemic status of arithmetic. Frege’s well-known doubts about Basic law V is said to concern this question and not its truth-value. The originality of the article consists mainly in the internal connections seen in Frege’s work and the way his philosophical writings are related to the grand project of determining the status of arithmetic.

Keywords: Gottlob Frege, logicism, concept, function, extension, logical object, conceptual notation, Basic law V, sense, meaning