The Mathematical Experience |
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Page 46
... constructing models . The models that one constructs are of course dependent upon one's state of knowledge . Ideally , a model should have predictive value . Therefore it is no good to construct a model which is too complex to support ...
... constructing models . The models that one constructs are of course dependent upon one's state of knowledge . Ideally , a model should have predictive value . Therefore it is no good to construct a model which is too complex to support ...
Page 235
... constructed — and our a precisely lacks any such individuality . To construct a model in which the continuum hypoth- esis is false we must add to M not just one new element a but a great many new elements . In fact , we must add an ...
... constructed — and our a precisely lacks any such individuality . To construct a model in which the continuum hypoth- esis is false we must add to M not just one new element a but a great many new elements . In fact , we must add an ...
Page 236
... constructed with a par- ticular purpose in mind . Perhaps more important than any of the models is the technique that enables one to construct them all : the notion of “ generic " and the related notion of " forcing . " Very roughly ...
... constructed with a par- ticular purpose in mind . Perhaps more important than any of the models is the technique that enables one to construct them all : the notion of “ generic " and the related notion of " forcing . " Very roughly ...
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