The Mathematical Experience |
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Page 60
... positions on the history of dis- covery . The first position holds that individual genius is the wellspring of discovery . The second position is that social and economic forces bring forth discovery . Most people do not hold with the ...
... positions on the history of dis- covery . The first position holds that individual genius is the wellspring of discovery . The second position is that social and economic forces bring forth discovery . Most people do not hold with the ...
Page 278
... position of the bisectors of I and II are identical , but the measure- ment of p ( 180 ° ) is opposite to that of p ( 0 ° ) . Therefore p ( 180 ° ) = −p ( 0 ° ) . Similarly , q ( 180 ° ) = q ( 0 ° ) . Therefore r ( 0 ° ) = p ( 0 ...
... position of the bisectors of I and II are identical , but the measure- ment of p ( 180 ° ) is opposite to that of p ( 0 ° ) . Therefore p ( 180 ° ) = −p ( 0 ° ) . Similarly , q ( 180 ° ) = q ( 0 ° ) . Therefore r ( 0 ° ) = p ( 0 ...
Page 322
... position that much or all of pure mathematics is a meaningless game . It should be obvious that to reject formalism as a philosophy of mathematics by no means implies any cri- tique of mathematical logic . On the contrary , logicians ...
... position that much or all of pure mathematics is a meaningless game . It should be obvious that to reject formalism as a philosophy of mathematics by no means implies any cri- tique of mathematical logic . On the contrary , logicians ...
Other editions - View all
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |
Common terms and phrases
abstract aesthetic algebra algorithmic analysis analytic answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex conjecture construct continuum hypothesis course definition differential equations elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hilbert human hypercube hypersquares idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry non-Riemannian nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line symbols theorem thing tion triangle true truth universe words zero