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Lines of ThoughtCentral Concepts in Cognitive Psychology$
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Lance Rips

Print publication date: 2011

Print ISBN-13: 9780195183054

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780195183054.001.0001

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Numbers

Numbers

Chapter:
(p.57) 2 Numbers
Source:
Lines of Thought
Author(s):

Lance J. Rips (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195183054.003.0003

This chapter canvasses proposed connections between minds and numbers that might make knowledge of mathematics possible. The goal is to determine whether any promising leads are available in accounting for people's ability to represent math objects. It argues that we have certain primitive concepts (e.g., CAUSE in the case of physical objects, UNIQUENESS in the case of mathematical ones) and certain primitive operations (instantiation, recursion, and other procedures specialized for concept combination) that allow us to form schemas or theories for both physical and mathematical domains. We may then posit that the best of these theories are true—that they correctly describe the nature of our world—and that the objects they describe are elements of that world. Such a schema-based approach has advantages over most current theories of mathematical knowledge.

Keywords:   mathematical objects, number learning, number meaning, concepts of number, math schemas, mathematical knowledge

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