Intuitionism in Mathematics

D. C. McCarty

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print June 2007 | ISBN: 9780195325928
Published online September 2009 | e-ISBN: 9780199892082 | DOI:

Series: Oxford Handbooks

Intuitionism in Mathematics

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The extent to which practicing mathematicians of a conventional tendency are already intuitionists is reassuring. Today's mathematicians treat mathematical claims much as Brouwer once did: as independently meaningful efforts to record mathematical facts which are, when true, demonstrable from proofs rooted in basic assumptions or principles. Until they are proven, those assumptions rest upon intuitions: illuminating, at times fallible, insights into the dynamical behaviors of numbers, sets, functions, and operations on them.

Keywords: intuitionism; Brouwer; mathematical claims; mathematics; mathematical facts; intuitions; numbers

Article.  13462 words. 

Subjects: Philosophy of Mathematics and Logic

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