By Reuben Hersh
Collection of the main attention-grabbing contemporary writings at the philosophy of arithmetic written through hugely revered researchers from philosophy, arithmetic, physics, and chemistry
Interdisciplinary e-book that would be important in different fields—with a cross-disciplinary topic region, and contributions from researchers of assorted disciplines
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Additional resources for 18 Unconventional Essays on the Nature of Mathematics
Philosophy of mathematics. Selected readings, Cambridge University Press, Cambridge. [First published 1964]. Beth, Evert Willem, 1957. La crise de la raison et la logique, Gauthier-Villars, Paris, and Nauwelaerts, Louvain. Cellucci, Carlo, 1998a. Le ragioni della logica, Laterza, Bari. [Reviewed by Donald Gillies, Philosophia Mathematica, vol. 7 (1999), pp. 213-222]. Cellucci, Carlo, 1998b. ‘The scope of logic: deduction, abduction, analogy’, Theoria, vol. 64, pp. 217-242. Cellucci, Carlo, 2000.
Franks 1989b, p. 12. Monk 1976, p. 4. 24 Carlo Cellucci tial feature of mathematics. Problem solving, however, does not concern single separated problems nor leads to a final solution. For each solution generates new problems, and depends on the solutions found for these new problems. Thus, no solution is final but is always subject to further reconsideration. 7. According to the dominant view, the method of mathematics is the axiomatic method. For “proof must begin from axioms that are not themselves proved”37.
Compatible with the existing knowledge, in the sense that, if one compares the reasons for and against the hypotheses, the reasons for prevail. 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.