Cardinality, Counting, and Equinumerosity

Notre Dame Journal of Formal Logic 41 (3):187-209 (2000)
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
Categories (categorize this paper)
DOI 10.1305/ndjfl/1038336841
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,167
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Logicism, Interpretability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Review of Symbolic Logic 7 (1):84-119.
Comparing Peano Arithmetic, Basic Law V, and Hume's Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.

View all 12 citations / Add more citations

Similar books and articles
Frege's Elucidatory Holism.Clinton Tolley - 2011 - Inquiry 54 (3):226-251.
What Are Numbers?Joongol Kim - 2013 - Synthese 190 (6):1099-1112.
Frege's Cardinals as Concept-Correlates.Gregory Landini - 2006 - Erkenntnis 65 (2):207 - 243.
Frege's Theorem: An Introduction.Richard Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
Frege's Gedanken Are Not Truth Conditions.Ari Maunu - 2002 - Facta Philosophica 4 (2):231-238.
Frege, Hilbert, and the Conceptual Structure of Model Theory.William Demopoulos - 1994 - History and Philosophy of Logic 15 (2):211-225.

Monthly downloads

Added to index

2010-08-24

Total downloads

272 ( #11,310 of 2,153,472 )

Recent downloads (6 months)

5 ( #162,759 of 2,153,472 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums