David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Erkenntnis 59 (2):203 - 232 (2003)
In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle'' (HP): The number of Fsis identical with the number of Gs if and only if F and G are equinumerous.The attempt miscarried, because in its role as a contextual definition HP fails tofix uniquely the reference of the cardinality operator ``the number of Fs''. Thisproblem of referential indeterminacy is usually called ``the Julius Caesar problem''.In this paper, Frege's treatment of the problem in Grundlagen is critically assessed. In particular, I try to shed new light on it by paying special attention to the framework of his logicism in which it appears embedded. I argue, among other things, that the Caesar problem, which is supposed to stem from Frege's tentative inductive definition of the natural numbers, is only spurious, not genuine; that the genuine Caesar problem deriving from HP is a purely semantic one and that the prospects of removing it by explicitly defining cardinal numbers as objects which are not classes are presumably poor for Frege. I conclude by rejecting two closely connected theses concerning Caesar put forward by Richard Heck: (i) that Frege could not abandon Axiom V because he could not solve the Julius Caesar problem without it; (ii) that (by his own lights) his logicist programme in Grundgesetze der Arithmetik failed because he could not overcome that problem.
|Keywords||No keywords specified (fix it)|
No categories specified
(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
No citations found.
Similar books and articles
Joan Weiner (2007). What's in a Numeral? Frege's Answer. Mind 116 (463):677 - 716.
Nikolaj Jang Lee Linding Pedersen (2009). Solving the Caesar Problem Without Categorical Sortals. Erkenntnis 71 (2):141 - 155.
Richard Heck (1997). The Julius Caesar Objection. In R. Heck (ed.), Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford University Press. 273--308.
Richard Heck (2005). Julius Caesar and Basic Law V. Dialectica 59 (2):161–178.
Richard Heck (1993). The Development of Arithmetic in Frege's Grundgesetze der Arithmetik. Journal of Symbolic Logic 58 (2):579-601.
Matthias Schirn (1994). Frege Y Los Nombres de Cursos de Valores. Theoria 9 (2):109-133.
Matthias Schirn (2011). On Translating Frege's Die Grundlagen der Arithmetik. History and Philosophy of Logic 31 (1):47-72.
Gregory Landini (2006). Frege's Cardinals as Concept-Correlates. Erkenntnis 65 (2):207 - 243.
Added to index2009-01-28
Total downloads27 ( #68,876 of 1,101,958 )
Recent downloads (6 months)5 ( #68,246 of 1,101,958 )
How can I increase my downloads?