The Mathematical Experience |
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Page 393
... intuition . ( 2 ) None of them even attempt to explain the nature and meaning of the intuition which they postulate . ( 3 ) A consideration of intuition as it is actually experi- enced leads to a notion which is difficult and complex ...
... intuition . ( 2 ) None of them even attempt to explain the nature and meaning of the intuition which they postulate . ( 3 ) A consideration of intuition as it is actually experi- enced leads to a notion which is difficult and complex ...
Page 395
... intuition , because their philosophical position turns the intuition into an indispensable but unanalyzable faculty . The intuition is for the Platonist what the “ soul ” is for the believer in the hereafter . We know it is there but no ...
... intuition , because their philosophical position turns the intuition into an indispensable but unanalyzable faculty . The intuition is for the Platonist what the “ soul ” is for the believer in the hereafter . We know it is there but no ...
Page 405
... intuition , possibly sorting out the roles played by the visual ( passive observation ) and the kinesthetic ( active manipulation . ) With such study , our un- derstanding of mathematical intuition should increase . There would be less ...
... intuition , possibly sorting out the roles played by the visual ( passive observation ) and the kinesthetic ( active manipulation . ) With such study , our un- derstanding of mathematical intuition should increase . There would be less ...
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