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Mathematical induction and its formation during childhood

Published online by Cambridge University Press:  11 December 2008

Leslie Smith
Affiliation:
Freelance Researcher, Lake District, United Kingdom; Professor Emeritus, Lancaster University, Lancaster LA1 4YD, United Kingdoml.smith@lancaster.ac.ukhttp://www.2.clikpic.com/ls99/http://www.lancs.ac.uk/fass/edres/profiles/Leslie-Smith/

Abstract

I support Rips et al.'s critique of psychology through (1) a complementary argument about the normative, modal, constitutive nature of mathematical principles. I add two reservations about their analysis of mathematical induction, arguing (2) for constructivism against their logicism as to its interpretation and formation in childhood (Smith 2002), and (3) for Piaget's account of reasons in rule learning.

Type
Open Peer Commentary
Copyright
Copyright © Cambridge University Press 2008

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References

Frege, G. (1979) Posthumous papers. Blackwell.Google Scholar
Inhelder, B. & Piaget, J. (1963) Itération et récurrence. In: La formation des raisonnements récurrentiels, ed. Gréco, P., Inhelder, B., Matalon, B. & Piaget, J.. Presses Universitaires de France.Google Scholar
Kant, I. (1787/1933) Critique of pure reason. 2nd edition.Macmillan (Original work published in 1787).Google Scholar
Kant, I. (1790/2002) Theoretical philosophy after 1781. Cambridge University Press (Original work published in 1790).Google Scholar
Leibniz, G. (1996) New essays on human understanding. Cambridge University Press.CrossRefGoogle Scholar
Piaget, J. (1942) Classes, relations, nombres. Vrin.Google Scholar
Piaget, J. (2006) Reason. New Ideas in Psychology 24:129.CrossRefGoogle Scholar
Poincaré, H. (1905) Science and hypothesis. Walter Scott.Google Scholar
Poincaré, H. (1952) Science and method. Dover.Google Scholar
Rips, L. J. & Asmuth, J. (2007) Mathematical induction and induction in mathematics. In: Induction, ed. Feeney, A. & Heit, E.. Cambridge University Press.Google ScholarPubMed
Smith, L. (1999) Epistemological principles for developmental psychology in Frege and Piaget. New Ideas in Psychology 17:83147.CrossRefGoogle Scholar
Smith, L. (2002) Reasoning by mathematical induction in children's arithmetic. Pergamon.Google Scholar
Smith, L. (in press a) Piaget's developmental epistemology. In: Cambridge companion to Piaget, ed. Müller, U., Carpendale, J. & Smith, L.. Cambridge University Press.Google Scholar
Smith, L. (in press b) Wittgenstein's rule-following paradox: How to resolve it with lessons for psychology. New Ideas in Psychology 26.Google Scholar
Wittgenstein, L. (1978) Remarks on the foundations of mathematics, 3rd edition.Blackwell.Google Scholar