  Brouwer was prepared to follow his philosophy of mind to its ultimate conclusions; whether the reconstructed mathematics was compatible or incompatible with classical mathematics was a secondary question, and never decisive. In thus granting philosophy priority over traditional mathematics, he showed himself a revisionist. And indeed, whereas intuitionistic arithmetic is a subsystem of classical arithmetic, in analysis the situation is different: not all of classical analysis is intuitionistically acceptable, but neither is all of intuitionistic analysis classically acceptable. Brouwer accepted this consequence wholeheartedly.