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Article ID: CBB001212887

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

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

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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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