FREGE’S THEORY OF REAL NUMBERS: A CONSISTENT RENDERING

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 foundati...

Full description

Saved in:
Bibliographic Details
Published inThe review of symbolic logic Vol. 15; no. 3; pp. 624 - 667
Main Authors BOCCUNI, FRANCESCA, PANZA, MARCO
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.09.2022
Subjects
03B30
foundation of real analysis
03-03
Logicism
Frege’s theory of real numbers
00A30
Frege
03F35
Euclid’s Principle
03A05
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1755-0203
1755-0211
DOI:10.1017/S175502032000026X