The Mathematical Experience |
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Page 246
... logic . More recently it has been found that mathematical logic provides a conceptual foundation for the theory of com- puting machines and computer programs . Hence this pro- totype of purity in mathematics now has to be regarded as ...
... logic . More recently it has been found that mathematical logic provides a conceptual foundation for the theory of com- puting machines and computer programs . Hence this pro- totype of purity in mathematics now has to be regarded as ...
Page 354
... logic . Worrall and Zahar are asserting that a formal derivation in first order logic is not fallible in any serious sense . But they fail to make clear that such derivations are purely hy- pothetical activities ( except for " toy ...
... logic . Worrall and Zahar are asserting that a formal derivation in first order logic is not fallible in any serious sense . But they fail to make clear that such derivations are purely hy- pothetical activities ( except for " toy ...
Page 357
... logic would not be a constructive proof . Would a constructivist find it illuminating ? Perhaps it might encourage him , in some cases , to look for a con- structive proof of something proved in B. ) Such modest claims for logic ...
... logic would not be a constructive proof . Would a constructivist find it illuminating ? Perhaps it might encourage him , in some cases , to look for a con- structive proof of something proved in B. ) Such modest claims for logic ...
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 |
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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