DEDUCTIVE CARDINALITY RESULTS AND NUISANCE-LIKE PRINCIPLES

被引：1
作者：
Ebels-Duggan, Sean C. [1 ]
机构：
[1] Northwestern Univ, Dept Philosophy, Evanston, IL 60208 USA
来源：
REVIEW OF SYMBOLIC LOGIC | 2021年 / 14卷 / 03期
关键词：
neo-logicism; abstraction principles; Cantor's theorem; cardinality; second-order logic;
D O I：
10.1017/S1755020318000230
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：592 / 623
页数：32
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