DEDUCTIVE CARDINALITY RESULTS AND NUISANCE-LIKE PRINCIPLES

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...

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Bibliographic Details
Published inThe review of symbolic logic Vol. 14; no. 3; pp. 592 - 623
Main Author EBELS-DUGGAN, SEAN C.
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.09.2021
Subjects
Incompatibility
Logic
Mathematical analysis
Nuisance
Paradoxes
Principles
Russell, Bertrand Arthur William (1872-1970)
Semantics
neo-logicism
00A30
Cantor’s theorem
second-order logic
abstraction principles
cardinality
03A05
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Summary: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.
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content type line 14
ISSN:1755-0203
1755-0211
DOI:10.1017/S1755020318000230