Brouwer has, as is well known, put up the claim that the law of excluded middle is no reliable means of proof in mathematics. His justification is that for many a mathematical proposition, it is today completely out of the question to decide whether it is true or false – and such a decision is perhaps impossible in general. The claim that each proposition should be either true or false, completely disregarding whether one can determine the one or the other, that Brouwer holds to be senseless. Brouwer has later drawn various conclusions from his claim, in a more or less systematic way. It is only with his student Heyting that this question has been engaged with axiomatically. Namely, he has put up an axiom system for logic, more precisely the narrowest part of logic, the propositional calculus, from which the law of excluded middle cannot be derived.