Journal article
The "Definability" of the Set of Natural Numbers in the 1925 "Principia Mathematica"
Journal of philosophical logic, Vol.25(6), pp.597-615
12/01/1996
DOI: 10.1007/BF00265255
Abstract
In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Godel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionality principles and without reducibility cannot recover mathematical induction. The finite cardinals are indefinable in it. This paper shows that while Gödel and Myhill are correct, Russell was not wrong. The 1925 system employs a different grammar than the original Principia. A new proof for *89.16 is given and induction is recovered.
Details
- Title: Subtitle
- The "Definability" of the Set of Natural Numbers in the 1925 "Principia Mathematica"
- Creators
- Gregory Landini - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of philosophical logic, Vol.25(6), pp.597-615
- Publisher
- Kluwer Academic Publishers
- DOI
- 10.1007/BF00265255
- ISSN
- 0022-3611
- eISSN
- 1573-0433
- Language
- English
- Date published
- 12/01/1996
- Academic Unit
- Philosophy
- Record Identifier
- 9984397180702771
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