Frege’s Theory of Real Numbers: A Consistent Rendering

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Review of Symbolic Logic:1-44 (forthcoming)
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Abstract

Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.

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10.1017/s175502032000026x

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Author Profiles

Francesca Boccuni
University Vita-Salute San Raffaele
Marco Panza
Centre National de la Recherche Scientifique

Citations of this work

Plural Frege Arithmetic.Francesca Boccuni - 2022 - Philosophia Scientiae 26:189-206.
Plural Frege Arithmetic.Francesca Boccuni - 2022 - Philosophia Scientiae:189-206.

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References found in this work

Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
Logic, Logic and Logic.George Boolos & Richard C. Jeffrey - 1998 - Studia Logica 66 (3):428-432.
Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
Basic laws of arithmetic.Gottlob Frege - 1893 - In Basic Laws of Arithmetic. Oxford, U.K.: Oxford University Press.

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