The Mathematical Experience |
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Page 136
... formal language . This language is the language of formal set theory . Every text on mathematical logic explains the rules of syntax for this language . The picture on page 138 shows the axioms of Zermelo - Fraenkel - Skolem , the most ...
... formal language . This language is the language of formal set theory . Every text on mathematical logic explains the rules of syntax for this language . The picture on page 138 shows the axioms of Zermelo - Fraenkel - Skolem , the most ...
Page 139
... formal lan- guage , we can construct a mathematical theory about mathematics . For the purpose of logical analysis of mathe- matics , it is necessary to conceive of mathematics as ex- pressed in a formal language . On this supposition ...
... formal lan- guage , we can construct a mathematical theory about mathematics . For the purpose of logical analysis of mathe- matics , it is necessary to conceive of mathematics as ex- pressed in a formal language . On this supposition ...
Page 246
... formal language , which is the kind of language machines understand . And it is the notion of a formal language that enabled Robinson to make precise Leibniz ' claim that one could without error reason as if in- finitesimals existed ...
... formal language , which is the kind of language machines understand . And it is the notion of a formal language that enabled Robinson to make precise Leibniz ' claim that one could without error reason as if in- finitesimals existed ...
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