The generative basis of natural number concepts

Trends in Cognitive Sciences 12 (6):213-218 (2008)
  Copy   BIBTEX

Abstract

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,509

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Linguistics and Natural Logic.George Lakoff - 1970 - Synthese 22 (1-2):151 - 271.
From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
Natural Number Concepts: No Derivation Without Formalization.Paul Pietroski & Jeffrey Lidz - 2008 - Behavioral and Brain Sciences 31 (6):666-667.
Why Cardinalities Are the “Natural” Natural Numbers.Mathieu Le Corre - 2008 - Behavioral and Brain Sciences 31 (6):659-659.
Math Schemata and the Origins of Number Representations.Susan Carey - 2008 - Behavioral and Brain Sciences 31 (6):645-646.
Mental Magnitudes and Increments of Mental Magnitudes.Matthew Katz - 2013 - Review of Philosophy and Psychology 4 (4):675-703.
Number and Natural Language.Stephen Laurence & Eric Margolis - 2005 - In Peter Carruthers, Stephen Laurence & Stephen P. Stich (eds.), The Innate Mind: Structure and Contents. New York: Oxford University Press New York. pp. 1--216.
Recursive Reminding and Children's Concepts of Number.Douglas L. Hintzman - 2008 - Behavioral and Brain Sciences 31 (6):656-657.
Dworkin on the Semantics of Legal and Political Concepts.Dennis M. Patterson - 2006 - Oxford Journal of Legal Studies 26 (3):545-557.

Analytics

Added to PP
2013-12-01

Downloads
157 (#79,068)

6 months
1 (#417,896)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Alan M. Leslie
Rutgers University - New Brunswick