Abstract

This paper addresses two central questions within the philosophy of mathematics: (1) What is the ground of the necessity of mathematical theorems? and (2) How is our belief in the existence of the objects of the fundamental mathematical theories to be justified? Frege's logicist answer to these questions is analyzed in detail, as well as Crispin Wright's attempt to refashion it. Hardly anyone else, claims the author, has even tried to address these questions. The author argues that those mathematical theorems that are genuinely applicable to reality hold of analytical necessity, since (he conjectures) it is possible to reformulate them so that the objects assumed are not purely mathematical objects, but ones abstracted from empirical reality