The Mathematical Experience |
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Page 318
... Platonism , formal- ism , and constructivism . According to Platonism , mathematical objects are real . Their existence is an objective fact , quite independent of our knowledge of them . Infinite sets , uncountably infinite sets ...
... Platonism , formal- ism , and constructivism . According to Platonism , mathematical objects are real . Their existence is an objective fact , quite independent of our knowledge of them . Infinite sets , uncountably infinite sets ...
Page 319
... Platonist , who sees the world of the actual infinite spread out before him and believes that he can compre- hend the incomprehensible . ( A. Robinson , 1969 ) According to formalism , on the other ... Platonism , Formalism , Constructivism.
... Platonist , who sees the world of the actual infinite spread out before him and believes that he can compre- hend the incomprehensible . ( A. Robinson , 1969 ) According to formalism , on the other ... Platonism , Formalism , Constructivism.
Page 393
... Platonism , formalism , and constructivism . It will be suffi- cient to characterize each viewpoint crudely with a ... Platonist regards mathematical objects , not as things which we construct , but as things already existing , once and ...
... Platonism , formalism , and constructivism . It will be suffi- cient to characterize each viewpoint crudely with a ... Platonist regards mathematical objects , not as things which we construct , but as things already existing , once and ...
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