The Mathematical Experience |
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Page 328
... knowledge is not problem- atical , even if all other knowledge is . Hume exempted only books of mathematics and of natural science from his cele- brated instruction to " commit it to the flames . " Even he did not perceive a problem in ...
... knowledge is not problem- atical , even if all other knowledge is . Hume exempted only books of mathematics and of natural science from his cele- brated instruction to " commit it to the flames . " Even he did not perceive a problem in ...
Page 329
... knowledge . Kant wanted to rebut Hume's critique of the possibility of certainty in human knowledge . He made a sharp distinction between the nou- mena , the things in themselves , which we can never know , and the phenomena , the ...
... knowledge . Kant wanted to rebut Hume's critique of the possibility of certainty in human knowledge . He made a sharp distinction between the nou- mena , the things in themselves , which we can never know , and the phenomena , the ...
Page 384
... knowledge " -things everybody knows and which I believe because I accept " what everybody knows . " In this way , mathematical knowledge is reduced to the level of common knowledge . But common knowledge does not claim to be based on ...
... knowledge " -things everybody knows and which I believe because I accept " what everybody knows . " In this way , mathematical knowledge is reduced to the level of common knowledge . But common knowledge does not claim to be based on ...
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