Deductive Cardinality Results and Nuisance-Like Principles

Sean C. Ebels-Duggan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
JournalReview of Symbolic Logic
StateAccepted/In press - 2021

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Philosophy
  • Logic


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