Journal Article

The Ins and Outs of Frege's Way Out†

Gregory Landini

in Philosophia Mathematica

Volume 14, issue 1, pages 1-25
Published in print February 2006 | ISSN: 0031-8019
Published online January 2006 | e-ISSN: 1744-6406 | DOI: https://dx.doi.org/10.1093/philmat/nkj001
The Ins and Outs of Frege's Way Out†

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Confronted with Russell's Paradox, Frege wrote an appendix to volume II of his Grundgesetze der Arithmetik. In it he offered a revision to Basic Law V, and proclaimed with confidence that the major theorems for arithmetic are recoverable. This paper shows that Frege's revised system has been seriously undermined by interpretations that transcribe his system into a predicate logic that is inattentive to important details of his concept-script. By examining the revised system as a concept-script, we see how Frege imagined that minor modifications of his former proofs would recover arithmetic.

Journal Article.  8084 words.  Illustrated.

Subjects: Philosophy of Mathematics and Logic ; Mathematics

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