Behavioral and Brain Sciences

Open Peer Commentary

Mathematical induction and its formation during childhood

Leslie Smitha1

a1 Freelance Researcher, Lake District, United Kingdom; Professor Emeritus, Lancaster University, Lancaster LA1 4YD, United Kingdom l.smith@lancaster.ac.uk http://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.

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