Deductive Cardinality Results and Nuisance-Like Principles

Sean C. Ebels-Duggan

doi:10.1017/S1755020318000230

Deductive Cardinality Results and Nuisance-Like Principles

Sean C. Ebels-Duggan^*

^*Corresponding author for this work

Philosophy

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 inconsis-tency 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 princi-ples 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.

Original language	English (US)
Journal	Review of Symbolic Logic
DOIs	https://doi.org/10.1017/S1755020318000230
State	Accepted/In press - 2021

ASJC Scopus subject areas

Mathematics (miscellaneous)
Philosophy
Logic

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Deductive Cardinality Results and Nuisance-Like Principles

Abstract

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