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FREGE’S THEORY OF REAL NUMBERS: A CONSISTENT RENDERING
Part of
FRANCESCA BOCCUNI, MARCO PANZA
Journal: The Review of Symbolic Logic / Volume 15 / Issue 3 / September 2022
Published online by Cambridge University Press: 22 February 2021, pp. 624-667
Print publication: September 2022
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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.