The Mathematical Experience |
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Page 322
... Platonists , 30 % formalists , and 5 % con- structivists . Our own impression is that the Cohen - Dieu- donné picture is closer to the truth . The typical mathematician is both a Platonist and a formalist- -a secret Platonist with a ...
... Platonists , 30 % formalists , and 5 % con- structivists . Our own impression is that the Cohen - Dieu- donné picture is closer to the truth . The typical mathematician is both a Platonist and a formalist- -a secret Platonist with a ...
Page 349
... Platonist ( in particular , the logical Platonist such as Frege or the early Russell ) would say it is about objectively existing ideal entities , which a certain intellectual faculty permits us to perceive or intuit directly , just as ...
... Platonist ( in particular , the logical Platonist such as Frege or the early Russell ) would say it is about objectively existing ideal entities , which a certain intellectual faculty permits us to perceive or intuit directly , just as ...
Page 393
... Platonist regards mathematical objects , not as things which we construct , but as things already existing , once and for all , in some ideal and timeless ( or " tenseless " ) sense . We do not create , we only discover what is already ...
... Platonist regards mathematical objects , not as things which we construct , but as things already existing , once and for all , in some ideal and timeless ( or " tenseless " ) sense . We do not create , we only discover what is already ...
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