The Mathematical Experience |
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Page 46
... Questions as to the truth or the indubitability of mathemat- ics are not important to him because all scientific work of every kind is of a provisional nature . The question should be not how true it is but how good it is . In the ...
... Questions as to the truth or the indubitability of mathemat- ics are not important to him because all scientific work of every kind is of a provisional nature . The question should be not how true it is but how good it is . In the ...
Page 161
... question of infinite divisibility was undecidable . By the twentieth century , the weight of two hundred years of successful practice of mathematical analysis has settled the question . " Between any two distinct points on the line ...
... question of infinite divisibility was undecidable . By the twentieth century , the weight of two hundred years of successful practice of mathematical analysis has settled the question . " Between any two distinct points on the line ...
Page 342
... questions , to the formalist , are premathematical . If they are admitted at all to his text or his course , it will be ... question . One reason for the dominance of formalism was its con- nection with logical positivism . This was the ...
... questions , to the formalist , are premathematical . If they are admitted at all to his text or his course , it will be ... question . One reason for the dominance of formalism was its con- nection with logical positivism . This was the ...
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