The Mathematical Experience |
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Page 326
... example of the changeless , uni- versal 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 ...
... example of the changeless , uni- versal 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 ...
Page 332
... example of such a set was discovered by Russell himself . To state the Russell paradox , we define an " R - set " as " a set which includes itself . " ( An example is " the set of all objects describable in exactly eleven English words ...
... example of such a set was discovered by Russell himself . To state the Russell paradox , we define an " R - set " as " a set which includes itself . " ( An example is " the set of all objects describable in exactly eleven English words ...
Page 370
... example is a counterexample to the law of trichotomy . He gives a real number which , he as- serts , is neither positive , negative , nor zero . Most mathe- maticians , when presented with the example , violently re- ject Brouwer's ...
... example is a counterexample to the law of trichotomy . He gives a real number which , he as- serts , is neither positive , negative , nor zero . Most mathe- maticians , when presented with the example , violently re- ject Brouwer's ...
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