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Commentary on Menger and Intuitionism

  • Dirk van Dalen
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Abstract

Of all the enigmas with which intuitionism confronted the world, that of “spread” was the most perplexing. Brouwer’s first definition [3], 13 lines long, was so exotic that hardly anyone could grasp it. When he returned to the definition in [4, 5], he apologetically remarked, “The circumstances that the definition of spread is long-winded can unfortunately not be helped”. The notion indeed suffered from a number of pedagogical deficiencies. The worst one seems to be the choice of terminology; in his German presentation Brouwer used the term “Menge”, thereby almost inviting confusion. In order to understand Brouwer’s terminology, one has to bear in mind that ever since his dissertation (1907), he sought to characterise the “possible sets” of the constructive universe [1, 2].

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© Springer-Verlag Wien 2003

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  • Dirk van Dalen

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