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To show and to prove
pp. 249-264
Résumé
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.
Détails de la publication
Publié dans:
Cohen Robert S (1995) Mexican studies in the history and philosophy of science. Dordrecht, Springer.
Pages: 249-264
DOI: 10.1007/978-94-009-0109-4_16
Citation complète:
Torres Carlos, Falcon Vege Jaime Oscar, 1995, To show and to prove. In R.S. Cohen (ed.) Mexican studies in the history and philosophy of science (249-264). Dordrecht, Springer.