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}
}