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2000 Cardinality, Counting, and Equinumerosity
Richard G. Heck Jr.
Notre Dame J. Formal Logic 41(3): 187-209 (2000). DOI: 10.1305/ndjfl/1038336841

Abstract

Frege, famously, held that there is a close connection between our concept of cardinal number and the notion of one-one correspondence, a connection enshrined in Hume's Principle. Husserl, and later Parsons, objected that there is no such close connection, that our most primitive conception of cardinality arises from our grasp of the practice of counting. Some empirical work on children's development of a concept of number has sometimes been thought to point in the same direction. I argue, however, that Frege was close to right, that our concept of cardinal number is closely connected with a notion like that of one-one correspondence, a more primitive notion we might call just as many.

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Richard G. Heck Jr.. "Cardinality, Counting, and Equinumerosity." Notre Dame J. Formal Logic 41 (3) 187 - 209, 2000. https://doi.org/10.1305/ndjfl/1038336841

Information

Published: 2000
First available in Project Euclid: 26 November 2002

zbMATH: 1009.03009
MathSciNet: MR1943492
Digital Object Identifier: 10.1305/ndjfl/1038336841

Subjects:
Primary: 03A05

Rights: Copyright © 2000 University of Notre Dame

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