Intuitionism is a philosophy of mathematics which regards the objects of mathematical discourse to be mental constructions based upon intuitively self-evident ideas. Thus, for the intuitionist, mathematical "objects" are purely mental and have no independent physical existence. Founded by the Dutch mathematician L. E. J. Brouwer (1881-1966), the intuitionst philosophy emerged as a reaction to Georg Cantor's theory of infinite sets and the application of standard logic to such sets. In particular, Brouwer required that all mathematical proof be "constructive." By this, he meant that in order to prove the existence of any mathematical object, one must provide the instructions for mentally constructing the object in a finite number of steps. Traditionally, mathematicians have been satisfied to show that a mathematical entity exists by denying its existence and showing that such a denial leads to a contradiction of some known mathematical truth. This method of proof, called indirect...