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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.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in The Review of Symbolic Logic, volume 15, issue 3, in 2022 following peer review. This article may not exactly replicate the final published version. The definitive publisher-authenticated version is available online at

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