English

Frege's Theory of Real Numbers: A consistent Rendering

Logic 2021-01-06 v1

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.

Keywords

Cite

@article{arxiv.2101.01643,
  title  = {Frege's Theory of Real Numbers: A consistent Rendering},
  author = {Francesca Boccuni and Marco Panza},
  journal= {arXiv preprint arXiv:2101.01643},
  year   = {2021}
}
R2 v1 2026-06-23T21:48:23.901Z