David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
For both Gottlob Frege and Bertrand Russell, providing a philosophical account of the concept of number was a central goal, pursued along similar logicist lines. In the present paper, I want to focus on a particular aspect of their accounts: their definitions, or reconstructions, of the natural numbers as equivalence classes of equinumerous classes. In other words, I want to examine what is often called the "Frege-Russell conception of the natural numbers" or, more briefly, the Frege-Russell numbers. My main concern will be to determine the precise sense in which this conception was, or could be, meant to constitute an analysis.1 I will be mostly concerned with Frege’s views on the matter; but Russell will come up along the way, for illustration and comparison, as will some recent neo-Fregean proposals and results. The structure of the paper is as follows: In the first section, I sketch Frege's general approach. Next, I differentiate several kinds, or modes, of analysis, as further background. In the third section, I zero in on the equivalence class construction, raising the question of why it might, from a Fregean point of view, be seen as 'the right' construction, thus as an analysis in a strong sense. In the fourth section, I provide a contrasting, more conventionalist view of the matter, often associated with the Carnapian notion of explication, and expressed in some remarks by Russell. I then discuss the motivation for the Frege-Russell numbers in more depth. In the sixth section, I introduce a neo-Fregean alternative, to be examined along similar lines. Finally, I reflect further on the significance of the kinds of arguments available in this connection.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Kevin C. Klement (2009). A Cantorian Argument Against Frege's and Early Russell's Theories of Descriptions. In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of "on Denoting". Routledge.
Gideon Makin (2000). The Metaphysicians of Meaning: Russell and Frege on Sense and Denotation. Routledge.
James Levine (2002). Analysis and Decomposition in Frege and Russell. Philosophical Quarterly 52 (207):195-216.
Gregory Landini (2006). Frege's Cardinals as Concept-Correlates. Erkenntnis 65 (2):207 - 243.
Kevin C. Klement (2012). Frege's Changing Conception of Number. Theoria 78 (2):146-167.
Richard L. Mendelsohn (2005). The Philosophy of Gottlob Frege. Cambridge University Press.
Graham Stevens (2003). The Truth and Nothing but the Truth, yet Never the Whole Truth: Frege, Russell and the Analysis of Unities. History and Philosophy of Logic 24 (3):221-240.
Howard Wettstein (1990). Frege‐Russell Semantics? Dialectica 44 (1‐2):113-135.
Added to index2009-01-28
Total downloads27 ( #53,420 of 1,011,713 )
Recent downloads (6 months)1 ( #64,700 of 1,011,713 )
How can I increase my downloads?