Read e-book online 18 Unconventional Essays on the Nature of Mathematics PDF

By Reuben Hersh

ISBN-10: 0387257179

ISBN-13: 9780387257174

Selection of the main attention-grabbing fresh writings at the philosophy of arithmetic written via hugely revered researchers from philosophy, arithmetic, physics, and chemistry Interdisciplinary publication that may be necessary in different fields—with a cross-disciplinary topic quarter, and contributions from researchers of assorted disciplines

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Bacon, after all, thought it better to invent a means by which everything could easily be discovered than to discover particular truths, and all steps of scientific progress in recent times have had their origin in an improvement of method”16. That the reflection on mathematics can contribute to the progress of mathematics entails that mathematics does not come first, with philosophizing about it following. On the contrary, they proceed together, both contributing to the advancement of learning.

The view expressed in this book is instead that mathematics is problem solving. That does not mean that mathematics is only problem solving. First one must pose problems, then one can refine them, exhibit them, dismiss them or even dissolve them. But problem solving is the core of mathematical activity, so it seems justified to maintain that it is an essen- 29 30 31 32 33 34 35 36 Lukasiewicz 1970, p. 112. Beth 1957, pp. 8-9. Kreisel 1984, p. 82. Kreisel 1967, p. 201. Mac Lane 1981, p. 462. Takeuti 1987, p.

But what is the use of knowledge of non-existing things such as that which mathematics offers? Even if it is complete and beyond any doubt, what is the use of knowledge concerning things which do not exist in reality? SOCRATES My dear friend, I am quite sure you know the answer, only you want to examine me. HIPPOCRATES By Heracles, I do not know the answer. Please help me. SOCRATES Well, let us try to find it. We have established that the notions of mathematics are created by the mathematician himself.

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18 Unconventional Essays on the Nature of Mathematics by Reuben Hersh


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