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arXiv · 2101.01643

Frege's Theory of Real Numbers: A consistent Rendering

Francesca Boccuni·Marco Panza
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Abstract

Frege's definition of the real numbers, as envisaged in the second volume of \textit{Grundgesetze der Arithmetik}, is fatally flawed by the inconsistency of Frege's ill-fated \textit{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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Francesca Boccuni, Marco Panza. 2021-01-05. Frege's Theory of Real Numbers: A consistent Rendering. https://arxiv.org/abs/2101.01643

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