By Reuben Hersh

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

Interdisciplinary publication that might be beneficial in different fields—with a cross-disciplinary topic region, and contributions from researchers of varied 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.

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. To illustrate my view, I often use fairly simple mathematical examples, which can be presented briefly and do not require elaborate preliminary explanations.

It is often claimed that ‘plausible’ has a subjective, psychological connotation, so that it is almost equivalent to ‘rhetorically persuasive’, hence plausible arguments are of little interest in mathematics. But ‘plausible’, in the sense explained above, has nothing subjective or psychological about it. To assess whether a given hypothesis is plausible, one examines the reasons for and against it. This examination is carried out using facts which confirm the hypothesis or refute it, where these facts belong to the existing knowledge.

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