Notre Dame Journal of Formal Logic 41 (3):187-209 (2000)

Authors
Richard Kimberly Heck
Brown University
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
Keywords Frege   logicism   counting   arithmetic
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DOI 10.1305/ndjfl/1038336841
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References found in this work BETA

Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
Frege's Theory of Numbers.Charles Parsons - 1965 - In M. Black (ed.), Philosophy in America. Cornell University Press. pp. 180-203.
Frege on Knowing the Foundation.Tyler Burge - 1998 - Mind 107 (426):305-347.
Finitude and Hume’s Principle.Richard Heck - 1997 - Journal of Philosophical Logic 26 (6):589-617.

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Citations of this work BETA

Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.

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