By Reuben Hersh
Collection of the main attention-grabbing contemporary writings at the philosophy of arithmetic written by way of hugely revered researchers from philosophy, arithmetic, physics, and chemistry
Interdisciplinary e-book that might be priceless in numerous fields—with a cross-disciplinary topic region, and contributions from researchers of assorted disciplines
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Extra resources for 18 Unconventional Essays on the Nature of Mathematics
Given the close connection between philosophy and mathematics, it is hardly surprising that some major philosophers, such as Descartes, Leibniz, Pascal and Lambert, have also been major mathematicians. In the history of philosophy the reflection on mathematics has taken several forms. Since it is impossible to deal with all of them in a single volume, in this book I will present what seems to me the most satisfactory form today. My own view, however, differs considerably from the dominant view, and on a number of accounts.
SOCRATES If you still have patience, let us try it together. Tell me, what is the difference between the sailor who finds an uninhabited island and the painter who finds a new color, one which no other painter has used before him? HIPPOCRATES I think that the sailor may be called a discoverer, and the painter an inventor. The sailor discovers an island which existed before him, only it was unknown, while the painter invents a new color which before that did not exist at all. SOCRATES Nobody could answer the question better.
P. 35. Ibid. Maddy 1984, p. 49. Dummett 1991, p. 305. Prawitz 1998, p. 332. Ibid. “Introduction” to Filosofia e matematica 27 deductive logic is the sole arbiter of truth. As a result mathematical truths established at the time of Euclid are still held valid today and are still taught. No other science can make this claim”55. ) inferences in addition to deductive inferences. It is by non-deductive inferences that one finds the hypotheses by which mathematical problems are solved. 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.