Research project Frege tried to explain our knowledge of the natural numbers by reducing arithmetic to logic. This program, however, could not be carried out. The main reason was that the theory of classes that Frege used in defining the natural numbers turned out to be inconsistent.
For a long time, therefore, Frege´s philosophy of mathematics came to be regarded as hopelessly passé. Recently, however, the situation has changed, mainly due to the revision of Frege´s program by Crispin Wright and Bob Hale and logical investigations carried out by the late George Boolos, Richard Heck, and others. The project concerns the semantics, metaphysics and epistemology of mathematics. If we take mathematical statements at face value, they assert the existence of various kinds of mathematical objects such as numbers, sets, functions etc. This gives rise to different philosophical questions: Should we accept mathematics as being literally true and thereby commit ourselves to the existence of mathematical objects? Or should we rather think of mathematics as some kind of useful fiction? If there are mathematical objects, what is their nature and how can we gain knowledge about them?
Finansår , 2005, 2006
huvudman: Sten Lindström, finansiar: Riksbankens jubileumsfond, y2005: 500, y2006: 500,