 In classical logic, these principles are valid. The logic of intuitionistic mathematics is obtained by removing the principle of excluded third (and its equivalents) from classical logic. This of course leads to a revision of mathematical knowledge. For instance, the classical theory of elementary arithmetic, Peano Arithmetic, can no longer be accepted. Instead, an intuitionistic theory of arithmetic (called Heyting Arithmetic) is proposed which does not contain the principle of excluded third. Although intuitionistic elementary arithmetic is weaker than classical elementary arithmetic, the difference is not all that great. There exists a simple syntactical translation which translates all classical theorems of arithmetic into theorems which are intuitionistically provable.