Book contents
Chapter 2 - What makes mathematics mathematics?
Published online by Cambridge University Press: 05 June 2014
Summary
We take it for granted
Philosophers, like most other people who think about it at all, tend to take ‘mathematics’ for granted. We seldom reflect on why we so readily recognize a problem, a conjecture, a fact, a proof idea, a piece of reasoning, a definition, or a sub-discipline, as mathematical. Some philosophers ask sophisticated questions about which parts of mathematics are constructive, or about set theory. Others debate ‘platonism’ versus ‘nominalism’, or, nowadays, versus ‘naturalism’ or ‘structuralism’. But we seem to shy away from the naïve question of why so many diverse topics addressed by real-life mathematicians are immediately recognized as ‘mathematics’. And what have those increasingly esoteric matters got to do with the common-or-garden mathematics of carpenters and shopkeepers; or, to move up a few social classes, of architects and stockbrokers?
Richard Courant published his classic What is Mathematics? in 1941. The Introduction ends with these words. ‘For scholars and laymen alike it is not philosophy but active experience in mathematics itself that alone can answer the question: What is mathematics?’ (Courant and Robbins 1996: n.p.). Courant was surely right: you learn what mathematics is by doing it.
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- Why Is There Philosophy of Mathematics At All? , pp. 41 - 78Publisher: Cambridge University PressPrint publication year: 2014