Frege’s Theory of Real Numbers: A Consistent Rendering

Authors

Francesca Boccuni, Vita-Salute San Raffaele UniversityFollow
Marco Panza, Chapman UniversityFollow

Document Type

Article

Publication Date

2-22-2021

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.

Comments

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 https://doi.org/10.1017/S175502032000026X.

Recommended Citation

Biccuni, F., & Panza, M. (2022). Frege’s Theory of Real Numbers: A Consistent Rendering. The Review of Symbolic Logic, 15(3), 624-667. https://doi.org/10.1017/S175502032000026X

Peer Reviewed

1

Copyright

The authors