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Intuition and Logic
Journal Title: PARADIGMI 
Author/s: Gabriele Lolli 
Year:  2011 Issue: Language: Italian 
Pages:  13 Pg. 45-57 FullText PDF:  523 KB
DOI:  10.3280/PARA2011-003004
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The early twentieth century discussions on the principle of choice and related arguments, especially those around Zermelo’s 1904 proof of the well-ordering theorem, make an interesting example of the relationship of intuition and logic in the growth of mathematics. There are two opposed views confronting themselves: mathematics as a human construction, where constraints are determined by the supposed limitations of the effective capabilities, even if idealized, of the subjects; and mathematics as an objective reality. But in the case of the infinite process of choices, there is a paradox: those insisting on the human construction conception are wary of intuition, in so far as it tends to push the process beyond effective feasibility, while Zermelo with his logical formulation of the principle is the one willing to recognize the soundness of the original pre-mathematical intuition.
Keywords: Choice principle, Construction, Intuition, Logic, Objectivity

Gabriele Lolli, Intuition and Logic in "PARADIGMI" 3/2011, pp. 45-57, DOI:10.3280/PARA2011-003004

   

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