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(1995) Mexican studies in the history and philosophy of science, Dordrecht, Springer.
It is often said that mathematics are a deductive science. Inasmuch as this claim puts forward its demonstrative character, it has two failures: first, it does not account for the creative or heuristic side of mathematics (for example, how are theorems discovered?); second, it omits the fact that a great part of mathematical knowledge is based upon sense evidence, not on proof. With this we mean that there are — in the last instance, for in practice the process is quite mixed — two kinds of "truth" in mathematics: those based on sense-perception and those inferred from other propositions by logical deduction. Those, we say, are shown , the latter are proven.
Publication details
DOI: 10.1007/978-94-009-0109-4_16
Full citation:
Torres, C. , Falcon Vege, J.O. (1995)., To show and to prove, in R. S. Cohen (ed.), Mexican studies in the history and philosophy of science, Dordrecht, Springer, pp. 249-264.
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