Intuitionistic Logic: A Philosophical Challenge

Abstract

There is a tendency in recent discussions to try to reconciliate the differences between intuitionistic and classical logic by saying that each logic has its interest and is correct from its own point of view when suitably interpreted. But this is to overlook the fact that there is a real conflict between two positions of which at most one can be correct: classical logic is set forth as a system of universally valid canons of reasoning and intuitionistic logic was formulated in response to Brouwer’s criticism of the classical claim and as a revision of this allegedly erroneous classical logic. In our deductive practice, we take, in fact, a stand on this conflict; even if we try to reconcile the two logics, our actual reasoning will usually show a clear preference for one of them. In philosophy, furthermore, we should reflect on our deductive practice and should be able to formulate explicitly what kind of reasoning is correct.