David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Secondly, he was the first to publish a logical analysis of the ancestral R* of a relation R, which yields a definition of R* in second-order logic.1 Only a narrow and arid conception of philosophy would exclude these two achievements. Thirdly and very importantly, the discussion in §§58-60 of the G r u n d l a g e n defends a conception of mathematical existence, to be found in Cantor (1883) and later in the writings of Dedekind and Hilbert, by basing it upon considerations about meaning which have general application, outside mathematics.2..
|Keywords||No keywords specified (fix it)|
|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
No references found.
Citations of this work BETA
Audrey Yap (2009). Logical Structuralism and Benacerraf's Problem. Synthese 171 (1):157 - 173.
Audrey Yap (2009). Predicativity and Structuralism in Dedekind's Construction of the Reals. Erkenntnis 71 (2):157 - 173.
Audrey Yap (2009). Predicativity and Structuralism in Dedekind’s Construction of the Reals. Erkenntnis 71 (2):157-173.
Audrey Yap (2009). Logical Structuralism and Benacerraf’s Problem. Synthese 171 (1):157-173.
Similar books and articles
Mikhail G. Katz & Thomas Mormann, Infinitesimals and Other Idealizing Completions in Neo-Kantian Philosophy of Mathematics.
Eva Picardi (1994). Kerry und Frege über Begriff und Gegenstand. History and Philosophy of Logic 15 (1):9-32.
Edward N. Zalta, Frege's Logic, Theorem, and Foundations for Arithmetic. Stanford Encyclopedia of Philosophy.
Richard Heck (1998). The Finite and the Infinite in Frege's Grundgesetze der Arithmetik. In M. Schirn (ed.), Philosophy of Mathematics Today. OUP
Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
William Boos (1987). Consistency and Konsistenz. Erkenntnis 26 (1):1 - 43.
George Cantor (1899). Letter to Dedekind. In J. Van Heijenoort (ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879--1931. Harvard University Press 113--117.
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 downloads60 ( #60,502 of 1,778,424 )
Recent downloads (6 months)8 ( #86,917 of 1,778,424 )
How can I increase my downloads?