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Mathematical Intuition vs. Mathematical Monsters

Solomon Feferman
Synthese
Vol. 125, No. 3 (Dec., 2000), pp. 317-332
Published by: Springer
Stable URL: http://www.jstor.org/stable/20117089
Page Count: 16
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Mathematical Intuition vs. Mathematical Monsters
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Abstract

Geometrical and physical intuition, both untutored and cultivated, is ubiquitous in the research, teaching, and development of mathematics. A number of mathematical "monsters", or pathological objects, have been produced which -- according to some mathematicians -- seriously challenge the reliability of intuition. We examine several famous geometrical, topological and set-theoretical examples of such monsters in order to see to what extent, if at all, intuition is undermined in its everyday roles.

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