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Beyond Wittgenstein's remarks on the foundation of mathematics: Explication of Piaget's suggestion of a biological foundation

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Abstract

Knowing about the axiomatic aspects of mathematics, Wittgenstein asked the more fundamental question: ‘But then what does the peculiar inexorability of mathematics consist in?’. He answers the question partially by saying: ‘Then do you want to say that “being true” means: being usable (or useful)? — No, not that; but that it can't be said of the series of natural numbers — any more than of our language —that it is true, but: that it is usable, and, above all, it is used’. Here it will be demonstrated that there is another aspect ‘to be said of the series of natural numbers’, besides the mere fact that they are used or usable, namely a biological one, as has been suggested, though not explicated, by Piaget.

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  1. Institute of Theoretical Physics, University of Bremen, D2800, Bremen 33, Germany

    Hans-Otto Carmesin

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  1. Hans-Otto Carmesin
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Carmesin, HO. Beyond Wittgenstein's remarks on the foundation of mathematics: Explication of Piaget's suggestion of a biological foundation. Sci Educ 1, 205–215 (1992). https://doi.org/10.1007/BF00572840

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  • DOI: https://doi.org/10.1007/BF00572840

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