Abstract
In this chapter I want to give one or two examples of the convergence between genetic and axiomatic investigations, since such examples can show how certain general results of formal analysis are psychologically explicable if based on what we know of the subject’s activities.
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References
P. Gréco has further shown that between general non-conservation (the beginning of stage II) and conservation (stage III) there is an intermediate stage where the child expects to find the same number (in the case where visual correspondence is destroyed), but continues to deny that the quantity is the same. See ‘Quantité et quotité’, in Etudes épist. génét., vol. XIII, Etude 1.
See Inhelder and Piaget, La genèse des structures logiques élémentaires,Neuchâtel—Paris, 1959, Chapter 1.
Inhelder and Piaget, loc. cit.
See A. Morf, `Recherches sur l’origine de la connexité de la suite des nombres’, in Etudes épist. génét., Vol. XIII, Etude I I.
P. Gréco, toc. cit.
See Grize, loc. cit.,p. 95.
On the difficulties of logical reductionism in general, see S. Papert, `Sur le réductionnisme logique’, in Etudes épist. génét., Vol. XI, Etude I II.
We will say that we have interpreted the semantics of A in A if X being any proposition of Sem(A) and X’being the result obtained by replacing in X all the concepts of Sem(A) by their definition, X’ is true (or false) at the same time as X.
E. W. Beth, The Foundations of Mathematics, Amsterdam, 1959, p. 340.
Grundlagen der Mathematik,Berlin, 1939, Volume II, p. 268.
J. B. Grize, Remarques sur les limitations des formalismes’, in Etudes épist. génét., Vol. XVI, pp. 69–97.
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Beth, E.W., Piaget, J. (1974). Some Convergences between Formal and Genetic Analyses. In: Mathematical Epistemology and Psychology. Synthese Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2193-6_11
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