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Intuitionism - The Philosophy of L. E. J. Brouwer

by Dirk Schlimm
1997-1998

Heyting's formalization of intuitionistic logic in 1930 was an important step in making Intuitionism accessible to the mathematical community. However, the price of this formalization was the abandonment of L.E.J. Brouwer's philosophical ideas. These ideas have only been expressed rather obscurely in his writings, and most early papers were not available until the early 1980s, long after the dispute between Intuitionism and Formalism had ceased.

In this talk Brouwer's motivations for developing Intuitionism as a philosophy of mathematics will be presented, in order to throw some light on his otherwise obscure writings. The conclusion of the debate about the foundations of mathematics will be discussed, and reasons will be offered to explain the outcome, namely, the defeat of Intuitionism.