Wednesday, July 29, 2009

Alfred North Whitehead

[In Principia Mathematica] Russell and Whitehead suggested no new numbers or arithmetical rules, but they did try to show how the simplest numbers—integers—could be built using the principles of logic. But the methods they proposed for even the simplest sums were desperately cumbersome. And for the proof that 1+1=2, readers had to wait until volume II, page 83. --The Economist, When 1, 2, 3... is not enough: Arguments over what counts as a number, December 30, 2008

Logicism posits that the vast edifice of mathematics is nothing but a working out of logic, of the rules of reasoning. This was Bertrand Russell’s view, famously worked out with Alfred North Whitehead in Principia Mathematica. Most mathematicians and most philosophers of mathematics found the book unreadable and the argument unpersuasive. --Fernando Q. Gouvea, The Book of Numbers, First Things, February 2009, review of Is God a Mathematician? by Mario Livio

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