Abstract:

This paper discusses the intuitionistic theory and thought in mathematical philosophy. Intuitionism highly values intuition and personal creative thinking in scientific practice. This is a positive viewpoint. Intuitionism questions the validity of law of excluded middle and the vaildity of indirect proof, and it indicates that classical logic is only a relative truth. Intuitionism stands for constructive and effective methods. These methods promote development of artificial intelligence and computer science. However, an excessive exaggeration of intuitive function is wrong.

Key words: intuitionism, law of excluded middle, paradox, logicism, formalism, indirect proof, constructive