David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Frege's main contributions to logic and the philosophy of mathematics are, on the one hand, his introduction of modern relational and quantificational logic and, on the other, his analysis of the concept of number. My focus in this paper will be on the latter, although the two are closely related, of course, in ways that will also play a role. More specifically, I will discuss Frege's logicist reconceptualization of the natural numbers with the goal of clarifying two aspects: the motivations for its core ideas; the step-by-step development of these ideas, from Begriffsschrift through Die Grundlagen der Arithmetik and Grundgesetze der Arithmetik to Frege's very last writings, indeed even beyond those, to a number of recent "neo-Fregean" proposals for how to update them. One main development, or break, in Frege's views occurred after he was informed of Russell's antinomy. His attempt to come to terms with this antinomy has found some attention in the literature already. It has seldom been analyzed in connection with earlier changes in his views, however, partly because those changes themselves have been largely ignored. Nor has it been discussed much in connection with Frege's basic motivations, as formed in reaction to earlier positions. Doing both in this paper will not only shed new light on his response to Russell's antinomy, but also on other aspects of his views. In addition, it will provide us with a framework for comparing recent updates of these views, thus for assessing the remaining attraction of Frege's general approach. I will proceed as follows: In the first part of the paper (§1.1 and §1.2), I will consider the relationship of Frege's conception of the natural numbers to earlier conceptions, in particular to what I will call the "pluralities conception", thus bringing into sharper focus his core ideas and their motivations. In the next part (§2.1 and §2.2), I will trace the order in which these ideas come up in Frege's writings, as well as the ways in which his position gets modified along the way, both before and after Russell's antinomy..
|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
Richard Heck & George Boolos (1998). Die Grundlagen der Arithmetik §§82-83. In M. Schirn (ed.), Philosophy of Mathematics Today. OUP.
Uwe Dathe (1995). Gottlob Frege Und Rudolf Eucken—Gesprächspartner in der Herausbildungsphase der Modernen Logik. History and Philosophy of Logic 16 (2):245-255.
Howard Wettstein (1990). Frege‐Russell Semantics? Dialectica 44 (1‐2):113-135.
Matthias Schirn (1994). Frege Y Los Nombres de Cursos de Valores. Theoria 9 (2):109-133.
William W. Taschek (2008). Truth, Assertion, and the Horizontal: Frege on "the Essence of Logic". Mind 117 (466):375-401.
Matthias Schirn (2003). Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic. Erkenntnis 59 (2):203 - 232.
Erich H. Reck (2005). Frege on Numbers: Beyond the Platonist Picture. The Harvard Review of Philosophy 13 (2):25-40.
Kevin C. Klement (2012). Frege's Changing Conception of Number. Theoria 78 (2):146-167.
Marcus Rossberg & Philip A. Ebert (2010). Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der Arithmetik. History and Philosophy of Logic 30 (4):341-348.
Added to index2009-01-28
Total downloads14 ( #126,305 of 1,413,411 )
Recent downloads (6 months)1 ( #154,345 of 1,413,411 )
How can I increase my downloads?