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(2017) Rethinking knowledge, Dordrecht, Springer.
Contrary to the belief of several mathematicians that philosophy is irrelevant to mathematics, this chapter argues that philosophy is relevant to it, because it may expose the inadequacy of some basic mathematical concepts, it may provide an analysis of some basic mathematical concepts, and may help to formulate new rules of discovery. What is relevant to mathematics, however, is not classical philosophy of mathematics, which has basic limitations, but an alternative approach to the philosophy of mathematics according to which, like all other knowledge, mathematics is problem solving by the analytic method. In this perspective, the chapter argues that the aim of mathematics is not truth but plausibility, and that intuition has no role in mathematics.
Publication details
DOI: 10.1007/978-3-319-53237-0_18
Full citation:
Cellucci, C. (2017). Mathematics as problem solving, in Rethinking knowledge, Dordrecht, Springer, pp. 235-249.
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