Volume 31, Number 2 · February 16, 1984
Where Does Math Come From?
By Ian Hacking
The Nature of Mathematical Knowledge
by Philip Kitcher
Oxford University Press, 287 pp., $25.00
Philip Kitcher thinks that mathematics is surprisingly like empirical science. Few mathematicians would agree; philosophers too, from Socrates on, have held the opposite opinion. In mathematics, they have said, we are able to solve problems and construct proofs by pure thought, without any need to check out how the land lies. Yet we can use geometry for surveying; hence, somewhat mysteriously, the products of reasoning apply to the world. Philosophers have also said that anything that you prove in pure mathematics must be true. To put it metaphorically, not even God could create a world in which a theorem that we have demonstrated is false. Men such as Plato, Aquinas, Leibniz, Kant, Russell, and Wittgenstein have said such things. Almost the only famous dissenters from this established tradition were (until recently) Descartes and John Stuart Mill. Kitcher is on their side.
Review, 3233 words
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