David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Erkenntnis 71 (2):141 - 155 (2009)
The neo-Fregean account of arithmetical knowledge is centered around the abstraction principle known as Hume’s Principle: for any concepts X and Y , the number of X ’s is the same as the number of Y ’s just in case there is a 1–1 correspondence between X and Y . The Caesar Problem, originally raised by Frege in §56 of Die Grundlagen der Arithmetik , emerges in the context of the neo-Fregean programme, because, though Hume’s Principle provides a criterion of identity for objects falling under the concept of Number–namely, 1–1 correspondence—the principle fails to deliver a criterion of application. That is, it fails to deliver a criterion that will tell us which objects fall under the concept Number, and so, leaves unanswered the question whether Caesar could be a number. Hale and Wright have recently offered a neo-Fregean solution to this problem. The solution appeals to the notion of a categorical sortal. This paper offers a reconstruction of their solution, which has the advantage over Hale and Wright’s original proposal of making clear what the structure of the background ontology is. In addition, it is shown that the Caesar Problem can be solved in a framework more minimal than that of Hale and Wright, viz . one that dispenses with categorical sortals. The paper ends by discussing an objection to the proposed neo-Fregean solutions, based on the idea that Leibniz’s Law gives a universal criterion of identity. This is an idea that Hale and Wright reject. However, it is shown that a solution very much in keeping with their own proposal is available, even if it is granted that Leibniz’s Law provides a universal criterion of identity.
|Keywords||Philosophy Logic Ethics Ontology Epistemology Philosophy|
|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
Michael R. Ayers (1974). Individuals Without Sortals. Canadian Journal of Philosophy 4 (1):113 - 148.
P. T. Geach (1967). Identity. Review of Metaphysics 21 (1):3 - 12.
P. T. Geach (1962/1968). Reference and Generality. Ithaca, N.Y.,Cornell University Press.
Citations of this work BETA
No citations found.
Similar books and articles
John MacFarlane (2009). Double Vision: Two Questions About the Neo-Fregean Program. Synthese 170 (3):443 - 456.
Sandy Berkovski (2011). Possible Worlds: A Neo-Fregean Alternative. Axiomathes 21 (4):531-551.
Bob Hale (2000). Reals by Abstraction. Philosophia Mathematica 8 (2):100--123.
Richard Heck (2011). The Existence (and Non-Existence) of Abstract Objects. In Frege's Theorem. Oxford University Press.
Peter Sullivan & Michael Potter (1997). Hale on Caesar. Philosophia Mathematica 5 (2):135--52.
Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press.
Bob Hale (1994). Dummett's Critique of Wright's Attempt to Resuscitate Frege. Philosophia Mathematica 2 (2):122-147.
Matthias Schirn (2003). Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic. Erkenntnis 59 (2):203 - 232.
Added to index2009-02-12
Total downloads37 ( #56,407 of 1,692,471 )
Recent downloads (6 months)3 ( #78,120 of 1,692,471 )
How can I increase my downloads?