The Mathematical Experience |
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Page 339
... formalist defines mathematics as the science of rig- orous proof . In other fields some theory may be advocated on the basis of experience or plausibility , but in mathemat- ics , he ... Formalist The Formalist Philosophy of Mathe- matics.
... formalist defines mathematics as the science of rig- orous proof . In other fields some theory may be advocated on the basis of experience or plausibility , but in mathemat- ics , he ... Formalist The Formalist Philosophy of Mathe- matics.
Page 341
... formalist view results , in part , from the rejection of the idea that one can start from " self - evident truths . " In our discussion of non - Euclidean geometry in Chapter 5 , we saw how the attempt to prove Euclid's fifth postulate ...
... formalist view results , in part , from the rejection of the idea that one can start from " self - evident truths . " In our discussion of non - Euclidean geometry in Chapter 5 , we saw how the attempt to prove Euclid's fifth postulate ...
Page 344
... formalist style gradually penetrated downward into undergraduate mathematics teaching and , finally , in the name of ... formalist philosophy of mathemat- ics is the intellectual source of the formalist style of mathe- matical work . The ...
... formalist style gradually penetrated downward into undergraduate mathematics teaching and , finally , in the name of ... formalist philosophy of mathemat- ics is the intellectual source of the formalist style of mathe- matical work . 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