Mathematical Discourse vs. Mathematical Intuition
In Carlo Cellucci & Donald Gillies (eds.), Mathematical Reasoning and Heuristics, 137-165. College Publications (2005)
| Abstract | In this paper it is argued that the opposition between the two main methods of mathematics, the axiomatic and the analytic method, is first of all an opposition between intuition and <span class='Hi'>discourse</span>, and, in addition, an opposition between the socalled demonstrative and non-demonstrative reasoning. These two methods, however, are not on a par because the view that the method of mathematics is the axiomatic method is refuted by Goedel's incompleteness results, which on the contrary do not affect the view that the method of mathematics is the analytic method. | |||||||||
| Keywords | axiomatic method analytic method intuition discourse incompleteness | |||||||||
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