Article ID: CBB001212887

Frege's Approach to the Foundations of Analysis (1874--1903) (2013)

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Schirn, Matthias (Author)


History and Philosophy of Logic
Volume: 34, no. 3
Issue: 3
Pages: 266-292


Publication Date: 2013
Edition Details: Part of a special issue, “Frege's Philosophy of Mathematics and Logic”
Language: English

The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as `theory of quantity' (`Größenlehre') in the second volume of his opus magnum Grundgesetze der Arithmetik (Frege 1903). In this essay, I deal, in a critical way, with Frege's treatment of the concept of quantity and his approach to analysis from the beginning of his academic career until Frege 1903. I begin with a few introductory remarks. In Section 2, I first analyze Frege's use of the term `source of knowledge' (`Erkenntnisquelle') with particular emphasis on the logical source of knowledge. The analysis includes a brief comparison between Frege and Kant's conceptions of logic and the logical source of knowledge. In a second step, I examine Frege's theory of quantity in Rechnungsmethoden, die sich auf eine Erweiterung des Größenbegriffes gründen (Frege 1874). Section 3 contains a couple of critical observations on Frege's comments on Hankel's theory of real numbers in Die Grundlagen der Arithmetik (Frege 1884). In Section 4, I consider Frege's discussion of the concept of quantity in Frege 1903. Section 5 is devoted to Cantor's theory of irrational numbers and the critique deployed by Frege. In Section 6, I return to Frege's own constructive treatment of analysis in Frege 1903 and succinctly describe what I take to be the quintessence of his account.

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Article Lavers, Gregory (2013) Frege, Carnap, and Explication: “Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science”. History and Philosophy of Logic (pp. 225-241). unapi

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Authors & Contributors
Belna, Jean-Pierre
Wright, Crispin
Wagner, Steven
Schirn, Matthias
Simons, Peter M.
Hill, Claire Ortiz
Journals
History and Philosophy of Logic
Notre Dame Journal of Formal Logic
Monist: An International Quarterly Journal of General Philosophical Inquiry
Revue d'Histoire des Sciences
Logica Universalis
British Journal for the History of Philosophy
Publishers
Aberdeen Univ. Press
Vrin
Farrar, Straus & Giroux
Springer
Cambridge University Press
Oxford University Press
Concepts
Number theory; number concept
Logic
Philosophy
Mathematical analysis
Mathematics
Philosophy of mathematics
People
Frege, Gottlob
Husserl, Edmund
Cantor, Georg Ferdinand Ludwig
Dedekind, Richard
Riemann, Georg Friedrich Bernhard
Peirce, Charles Sanders
Time Periods
19th century
20th century, early
Places
Central Europe: Germany, Austria, Switzerland
North America
Europe
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