Mind 116 (463):677 - 716 (2007)
|Abstract||Frege wanted to define the number 1 and the concept of number. What is required of a satisfactory definition? A truly arbitrary definition will not do: to stipulate that the number one is Julius Caesar is to change the subject. One might expect Frege to define the number 1 by giving a description that picks out the object that the numeral '1' already names; to define the concept of number by giving a description that picks out precisely those objects that are numbers. Yet Frege appears to do no such thing. Indeed, when he defends his definitions, he does not argue that they pick out objects that we have been talking about all along-the issue never comes up. The aim of this paper is to explain why. I argue that, on Frege's view, our numerals do not, antecedent to his work, name particular objects. This raises an obvious question: If (like 'Odysseus') the numerals do not name particular objects, how can Frege write (as he does) as if sentences in which numerals appear state truths? One central concern of this paper is exegetical-to answer these questions. But my aim is not solely exegetical. For these questions direct us to something that, I believe, creates only an apparent problem for Frege but an actual problem for many contemporary philosophers: the assumption that singular terms appearing in statements about the world must actually have referents. Another aim of this paper is to suggest that the problem-as well as a solution that can be found in Frege's writings-should be of import to contemporary philosophers|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Mark Textor (2009). Unsaturatedness: Wittgenstein's Challenge, Frege's Answer. Proceedings of the Aristotelian Society 109 (1pt1):61-82.
Edward N. Zalta (1999). Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege"s Grundgesetze in Object Theory. Journal of Philosophical Logic 28 (6):619-660.
Marco Ruffino (2003). Why Frege Would Not Be a Neo-Fregean. Mind 112 (445):51-78.
Joan Weiner (1995). Realismbei Frege: Reply to Burge. Synthese 102 (3):363 - 382.
J. L. Shaw (1982). Number: From the Nyāya to Frege-Russell. Studia Logica 41 (2-3):283 - 291.
Gregory Landini (2006). Frege's Cardinals as Concept-Correlates. Erkenntnis 65 (2):207 - 243.
Matthias Schirn (2006). Concepts, Extensions, and Frege's Logicist Project. Mind 115 (460):983-1006.
Matthias Schirn (2003). Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic. Erkenntnis 59 (2):203 - 232.
Marco Ruffino (2000). Extensions as Representative Objects in Frege's Logic. Erkenntnis 52 (2):239-252.
Friederike Moltmann (forthcoming). The Number of Planets, a Number-Referring Term? In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford University Press.
Added to index2009-01-28
Total downloads24 ( #51,605 of 549,069 )
Recent downloads (6 months)2 ( #37,252 of 549,069 )
How can I increase my downloads?