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DEDUCTIVE CARDINALITY RESULTS AND NUISANCE-LIKE PRINCIPLES

Part of: General and miscellaneous specific topics Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  20 April 2021

SEAN C. EBELS-DUGGAN
SEAN C. EBELS-DUGGAN*
Affiliation:
DEPARTMENT OF PHILOSOPHY NORTHWESTERN UNIVERSITYEVANSTON, IL60208, USAE-mail:s-ebelsduggan@northwestern.edu
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Abstract

The injective version of Cantor’s theorem appears in full second-order logic as the inconsistency of the abstraction principle, Frege’s Basic Law V (BLV), an inconsistency easily shown using Russell’s paradox. This incompatibility is akin to others—most notably that of a (Dedekind) infinite universe with the Nuisance Principle (NP) discussed by neo-Fregean philosophers of mathematics. This paper uses the Burali–Forti paradox to demonstrate this incompatibility, and another closely related, without appeal to principles related to the axiom of choice—a result hitherto unestablished. It discusses both the general interest of this result, its interest to neo-Fregean philosophy of mathematics, and the potential significance of the Burali–Fortian method of proof.

Keywords

neo-logicismabstraction principlesCantor’s theoremcardinalitysecond-order logic

MSC classification

Primary: 00A30: Philosophy of mathematics
Secondary: 03A05: Philosophical and critical
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 3 , September 2021 , pp. 592 - 623
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Copyright
© Association for Symbolic Logic, 2021

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