The Mathematical Experience |
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Page 51
... sense that he believes that mathematical concepts exist in the world apart from the people that do mathematics . He replied that he was , but in a limited sense . Certainly not in a “ theological ” sense . He believed that certain ...
... sense that he believes that mathematical concepts exist in the world apart from the people that do mathematics . He replied that he was , but in a limited sense . Certainly not in a “ theological ” sense . He believed that certain ...
Page 349
Philip J. Davis, Reuben Hersh. import only in the critical sense , especially in an all - out tooth - and - nail attack on formalism . But what is its import in the positive sense ? First of all , we need to know what mathematics is ...
Philip J. Davis, Reuben Hersh. import only in the critical sense , especially in an all - out tooth - and - nail attack on formalism . But what is its import in the positive sense ? First of all , we need to know what mathematics is ...
Page 368
... sense from a constructivist or formalist point of view . The constructivist says that the Riemann hypothesis will become true or false only when a constructive proof one way or the other is given . It makes no sense to discuss whether ...
... sense from a constructivist or formalist point of view . The constructivist says that the Riemann hypothesis will become true or false only when a constructive proof one way or the other is given . It makes no sense to discuss whether ...
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