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FREGE’S THEORY OF REAL NUMBERS: A CONSISTENT RENDERING

Published online by Cambridge University Press:  22 February 2021

FRANCESCA BOCCUNI
Affiliation:
VITA-SALUTE SAN RAFFAELE UNIVERSITY MILAN, ITALY E-mail: boccuni.francesca@unisr.it
MARCO PANZA
Affiliation:
IHPST (CNRS AND UNIVERSITÉ DE PARIS 1, PANTHÉONE SORBONNE) PARIS, FRANCE E-mail: marco.panza@univ-paris1.fr CHAPMAN UNIVERSITY ORANGE, CA, USA E-mail: panza@chapman.edu

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.

Type
Research Article
Copyright
© Association for Symbolic Logic, 2021

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