The conceptual basis of numerical abilities: One-to-one correspondence versus the successor relation
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophical Psychology 21 (4):459 – 473 (2008)
In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Elizabeth M. Brannon (2002). The Development of Ordinal Numerical Knowledge in Infancy. Cognition 83 (3):223-240.
Gottlob Frege (1964). The Basic Laws of Arithmetic. Berkeley, University of California Press.
Rochel Gelman & Brian Butterworth (2005). Number and Language: How Are They Related? Trends in Cognitive Sciences 9 (1):6-10.
Dedre Getner & Susan Goldin-Meadow (eds.) (2003). Language in Mind: Advances in the Study of Language and Thought. Mit Press.
Jennifer S. Lipton & Elizabeth S. Spelke (2006). Preschool Children Master the Logic of Number Word Meanings. Cognition 98 (3):57-66.
Citations of this work BETA
Helen De Cruz & Johan De Smedt (2010). The Innateness Hypothesis and Mathematical Concepts. Topoi 29 (1):3-13.
Wojciech Krysztofiak (2012). Indexed Natural Numbers in Mind: A Formal Model of the Basic Mature Number Competence. [REVIEW] Axiomathes 22 (4):433-456.
Similar books and articles
Eric Bush (1977). Berkeley, Truth, and the World. Inquiry 20 (1-4):205 – 225.
Chris Pincock (2008). Russell's Last (And Best) Multiple-Relation Theory of Judgement. Mind 117 (465):107 - 139.
Ingvar Johansson (2004). Truthmaking: A Cognition-Independent Internal Relation with Heterogeneous Relata. In Johann Christian Marek & Maria Elisabeth Reicher (eds.), Experience and Analysis: Papers of the 27th International Wittgenstein Symposium. Austrian Ludwig Wittgenstein Society. 154--56.
Lieven Decock (2008). Neo-Fregeanism Naturalized: The Role of One-to-One Correspondence in Numerical Cognition. Behavioral and Brain Sciences 31 (6):648-649.
Hans Radder (1991). Heuristics and the Generalized Correspondence Principle. British Journal for the Philosophy of Science 42 (2):195-226.
Hans Johann Glock (2006). Truth in the Tractatus. Synthese 148 (2):345 - 368.
Marian David, The Correspondence Theory of Truth. Stanford Encyclopedia of Philosophy.
David Pearce & Veikko Rantala (1983). Correspondence as an Intertheory Relation. Studia Logica 42 (2-3):363 - 371.
Michael J. Shaffer (2008). Re-Formulating the Correspondence Principle: Problems and Prospects. Polish Journal of Philosophy 2 (1):99-115.
Stephan Hartmann (2008). Modeling High-Temperature Superconductors: Correspondence at Bay? In Lena Soler (ed.), Rethinking Scientific Change. Stabilities, Ruptures, Incommensurabilities? Springer. 107--128.
Added to index2009-01-28
Total downloads16 ( #102,826 of 1,101,679 )
Recent downloads (6 months)2 ( #178,427 of 1,101,679 )
How can I increase my downloads?