The Mathematical Experience |
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Page 142
... fact there are severe logical and psychological difficulties associated with it . A conception of small integers such as 1 , 2 , 3 , etc. may come about as an act of abstraction . But what shall we say to the number ...
... fact there are severe logical and psychological difficulties associated with it . A conception of small integers such as 1 , 2 , 3 , etc. may come about as an act of abstraction . But what shall we say to the number ...
Page 407
... fact goes against common sense , and we are nevertheless com- pelled to accept and deal with this fact , we learn to alter our notion of common sense . There are two pieces of information which we have about the nature of mathematics . Fact ...
... fact goes against common sense , and we are nevertheless com- pelled to accept and deal with this fact , we learn to alter our notion of common sense . There are two pieces of information which we have about the nature of mathematics . Fact ...
Page 408
... facts about imaginary objects . From the Platonist point of view , Fact 1 is unacceptable . Since mathematical objects are what they are , in defiance of our ignorance or preferences , they must be real in a sense independent of human ...
... facts about imaginary objects . From the Platonist point of view , Fact 1 is unacceptable . Since mathematical objects are what they are , in defiance of our ignorance or preferences , they must be real in a sense independent of human ...
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