By Reuben Hersh

ISBN-10: 0387257179

ISBN-13: 9780387257174

Collection of the main attention-grabbing contemporary writings at the philosophy of arithmetic written by means of hugely revered researchers from philosophy, arithmetic, physics, and chemistry

Interdisciplinary booklet that may be worthwhile in different fields—with a cross-disciplinary topic quarter, and contributions from researchers of assorted disciplines

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SOCRATES In poetry that would be impossible. Now you see that there is a problem. But let us continue. How do you explain that the mathematicians of different countries can usually agree about the truth, while about questions concerning the state, for example, the Persians and the Spartans have quite opposite views from ours in Athens, and, moreover, we here do not often agree with each other? HIPPOCRATES I can answer that last question. In matters concerning the state everybody is personally interested, and these personal interests are often in contradiction.

87. Lang 1985, p. 19. 26 Carlo Cellucci rather the arrival point of a theory”, and “the occasions where one started from the axioms are rather the exception than the rule”46. Hersh points out that, “in developing and understanding a subject, axioms come late”, and even if “sometimes someone tries to invent a new branch of mathematics by making up some axioms and going from there”, still “such efforts rarely achieve recognition or permanence. Examples, problems, and solutions come first. Later come axiom sets on which the existing theory can be ‘based’.

Maddy 1997, p. 163. “Introduction” to Filosofia e matematica 31 As regards certainty, mathematics has no privilege and is as risky as any other human creation. e. compatible with the existing knowledge, and plausibility does not grant certainty, because the existing knowledge is not absolutely certain, but only plausible. For centuries mathematics was considered a body of absolutely certain truths, but now this is increasingly perceived as an illusion. Uncertainty and doubt have replaced the self-complacent certainty of the past.

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18 Unconventional Essays on the Nature of Mathematics by Reuben Hersh

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