Abstract

The limitations of mathematical logic either as a tool for the foundations of mathematics, or as a branch of mathematics, or as a tool for artificial intelligence, raise the need for a rethinking of logic. In particular, they raise the need for a reconsideration of the many doors the Founding Fathers of mathematical logic have closed historically. This paper examines three such doors, the view that logic should be a logic of discovery, the view that logic arises from method, and the view that logic is not the whole of reason, and on this basis proposes an alternative approach to logic.