The Mathematical Experience |
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Page 70
... Truth has abdicated and expediency reigns . Some Simple Instances of Mathematics by Fiat Of course , hardly any scientists live by a consistent creed . Scientists believe simultaneously both in theories and in models , in truth and in ...
... Truth has abdicated and expediency reigns . Some Simple Instances of Mathematics by Fiat Of course , hardly any scientists live by a consistent creed . Scientists believe simultaneously both in theories and in models , in truth and in ...
Page 326
... truths which , indeed , we can perceive and recog- nize . 3. Thus there must exist a realm of absolute , unchanging truth , the source and the basis for our knowledge of the Good . Plato's conception of geometry was a key element in his ...
... truths which , indeed , we can perceive and recog- nize . 3. Thus there must exist a realm of absolute , unchanging truth , the source and the basis for our knowledge of the Good . Plato's conception of geometry was a key element in his ...
Page 406
... truth , like other kinds of truth , is fallible and corrigible . Do we really have to choose between a formalism that is falsified by our everyday experience , and a Platonism that postulates a mythical fairyland where the uncountable ...
... truth , like other kinds of truth , is fallible and corrigible . Do we really have to choose between a formalism that is falsified by our everyday experience , and a Platonism that postulates a mythical fairyland where the uncountable ...
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