No CrossRef data available.
Article contents
Neo-Fregeanism naturalized: The role of one-to-one correspondence in numerical cognition
Published online by Cambridge University Press: 11 December 2008
Abstract
Rips et al. argue that the construction of math schemas roughly similar to the Dedekind/Peano axioms may be necessary for arriving at arithmetical skills. However, they neglect the neo-Fregean alternative axiomatization of arithmetic, based on Hume's principle. Frege arithmetic is arguably a more plausible start for a top-down approach in the psychological study of mathematical cognition than Peano arithmetic.
- Type
- Open Peer Commentary
- Information
- Copyright
- Copyright © Cambridge University Press 2008
References
Boolos, G. (1997) Is Hume's principle analytic? In: Language, thought, and logic: Essays in honor of Michael Dummett, ed. Heck, R.. Oxford University Press.Google Scholar
Demopoulos, W. (1998) The philosophical basis of our knowledge of number. Noûs 32:481–503.CrossRefGoogle Scholar
Frege, G. (1893/1967) The basic laws of arithmetic. University of California Press. (Original work published 1893).Google Scholar
Frege, G. (1884/1974) The foundations of arithmetic. Blackwell. (Original work published 1884).Google Scholar
Gelman, R. & Gallistel, C. R. (1978) The child's understanding of number. Harvard University Press/MIT Press. (Second printing, 1985. Paperback issue with new preface, 1986).Google Scholar
Gelman, R. & Greeno, J. G. (1989) On the nature of competence: Principles for understanding in a domain. In: Knowing and learning: Issues for a cognitive science of instruction: Essays in honor of Robert Glaser, ed. Resnick, L. B., pp. 125–86. Erlbaum.Google Scholar
Gelman, R. & Meck, E. (1983) Preschoolers' counting: Principles before skill. Cognition 13:343–59.CrossRefGoogle ScholarPubMed
Gelman, R., Meck, E. & Merkin, S. (1986) Young children's numerical competence. Cognitive Development 1:1–29.CrossRefGoogle Scholar
Gordon, P. (2004) Numerical cognition without words: Evidence from Amazonia. Science 306:496–99.CrossRefGoogle ScholarPubMed
Heck, R. (1993) The development of arithmetic in Frege's Grundgesetze der Arithmetic. Journal of Symbolic Logic 58(2):579–600.CrossRefGoogle Scholar
Heck, R. G. Jr. (2000) Cardinality, counting, and equinumerosity. Notre Dame Journal of Formal Logic 41(3):187–209.CrossRefGoogle Scholar
Jordan, K. & Brannon, E. (2006) The multisensory representation of number in infancy. Proceedings of the National Academy of Sciences USA 103:3486–89.CrossRefGoogle ScholarPubMed
Wright, C. (1983) Frege's conception of numbers as objects. Aberdeen University Press.Google Scholar
Zalta, E. N. (2008) Frege's logic, theorem, and foundations for arithmetic. In: The Stanford encyclopedia of philosophy (Summer 2008 edition), ed. Zalta, E. N.. Available at: http://plato.stanford.edu/archives/sum2008/entries/frege-logic/.Google Scholar