David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 41 (3):187-209 (2000)
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Sean Walsh (2014). Logicism, Interpretability, and Knowledge of Arithmetic. Review of Symbolic Logic 7 (1):84-119.
Richard Heck (2011). Ramified Frege Arithmetic. Journal of Philosophical Logic 40 (6):715-735.
Sean Walsh (2012). Comparing Peano Arithmetic, Basic Law V, and Hume's Principle. Annals of Pure and Applied Logic 163 (11):1679-1709.
John MacFarlane (2009). Double Vision: Two Questions About the Neo-Fregean Program. Synthese 170 (3):443 - 456.
Aaron Barth (2012). A Refutation of Frege's Context Principle? Thought 1 (1):26-35.
Similar books and articles
Massimiliano Carrara & Elisabetta Sacchi (2007). Cardinality and Identity. Journal of Philosophical Logic 36 (5):539 - 556.
G. Aldo Antonelli (2010). Numerical Abstraction Via the Frege Quantifier. Notre Dame Journal of Formal Logic 51 (2):161-179.
Matthias Schirn (2006). Hume's Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters. Synthese 148 (1):171 - 227.
Boudewijn de Bruin (2008). Wittgenstein on Circularity in the Frege-Russell Definition of Cardinal Number. Philosophia Mathematica 16 (3):354-373.
Marco Ruffino (2003). Why Frege Would Not Be a Neo-Fregean. Mind 112 (445):51-78.
Clinton Tolley (2011). Frege's Elucidatory Holism. Inquiry 54 (3):226-251.
Matthias Schirn (2003). Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic. Erkenntnis 59 (2):203 - 232.
Joongol Kim (2013). What Are Numbers? Synthese 190 (6):1099-1112.
Gregory Landini (2006). Frege's Cardinals as Concept-Correlates. Erkenntnis 65 (2):207 - 243.
Matthew W. Parker (2009). Philosophical Method and Galileo's Paradox of Infinity. In Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics : Brussels, Belgium, 26-28 March 2007. World Scientfic.
Richard Heck (1999). Frege's Theorem: An Introduction. The Harvard Review of Philosophy 7 (1):56-73.
Ari Maunu (2002). Frege's Gedanken Are Not Truth Conditions. Facta Philosophica 4 (2):231-238.
William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
Saharon Shelah & Pauli Vaisanen (2000). On Inverse Γ-Systems and the Number of L∞Λ- Equivalent, Non-Isomorphic Models for Λ Singular. Journal of Symbolic Logic 65 (1):272 - 284.
Added to index2010-08-24
Total downloads38 ( #49,978 of 1,139,887 )
Recent downloads (6 months)9 ( #22,168 of 1,139,887 )
How can I increase my downloads?