By Reuben Hersh
Collection of the main fascinating contemporary writings at the philosophy of arithmetic written by means of hugely revered researchers from philosophy, arithmetic, physics, and chemistry
Interdisciplinary ebook that might be beneficial in different fields—with a cross-disciplinary topic zone, and contributions from researchers of assorted disciplines
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Extra info for 18 Unconventional Essays on the Nature of Mathematics
The logic of mathematics is not, therefore, that studied by mathematical logic, which is simply a branch of mathematics, but consists of a set of non-deductive methods and techniques in addition to deductive methods and techniques, and hence is not a theory but a set of tools. To claim that the logic of mathematics is deductive logic because theorems are justified by deductive inference, restricts mathematical experience to ways of reasoning found only in textbooks of mathematical logic, and neglects those that are really used in mathematical activity.
158. 86 Pólya 1954, I, p. vi. , I, p. v. , I, p. vi. 89 See, for example, Cellucci 1998a, 1998b, 2000, 2002b. 81 34 Carlo Cellucci because that would require far more space than is available. To my mind, however, the questions discussed here should be dealt with in any investigation concerning the nature of mathematics. The book consists of a number of short chapters, each of which can be read independently of the others, although its full meaning will emerge only within the context of the whole book.
Similarly, to claim that, when it comes to explaining the remarkable phenomenon that work on a mathematical problem may end in a result that everyone finds definitive and conclusive, the notion of deduction is a central one, overlooks the fact that, according to the dominant view, several Euclid’s proofs are flawed. Thus, in this view, the fact that everyone finds Euclid’s results definitive and conclusive cannot depend on Euclid’s proofs. The same applies to contemporary mathematics, where 55 56 57 Franks 1989a, p.