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- W2895738497 abstract "This chapter discusses the intuitionism and formalism. In Kant, one find an old form of intuitionism almost completely abandoned in which time and space are taken to be the forms of conception inherent in human reason. For Kant, the axioms of arithmetic and geometry were synthetic a priori judgments, that is, judgments independent of experience and not capable of analytical demonstration and this explained their apodictic exactness in the world of experience as well as in abstracto. Diametrically opposed to this is the view of formalism which maintains that human reason does not have at its disposal exact images either of straight lines or of numbers larger than ten, for example; therefore, these mathematical entities do not have existence in conception of nature any more than in nature itself. It is true that from certain relations among mathematical entities, which one assume as axioms, one deduce other relations according to fixed laws, in the conviction that in this way one derive truths from truths by logical reasoning, but this nonmathematical conviction of truth or legitimacy has no exactness." @default.
- W2895738497 created "2018-10-12" @default.
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- W2895738497 date "1975-01-01" @default.
- W2895738497 modified "2023-10-16" @default.
- W2895738497 title "INTUITIONISM AND FORMALISM††Translated for the BULLETIN by Professor ARNOLD DRESDEN." @default.
- W2895738497 doi "https://doi.org/10.1016/b978-0-7204-2076-0.50012-x" @default.
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