Second-Order Logic and Set Theory

被引：2
|
作者：
Vaananen, Jouko [1 ,2 ]
机构：
[1] Univ Helsinki, Dept Math & Stat, Helsinki, Finland
[2] Univ Amsterdam, Inst Log Language & Computat, Amsterdam, Netherlands
来源：
PHILOSOPHY COMPASS | 2015年 / 10卷 / 07期
关键词：
FOUNDATIONS;
D O I：
10.1111/phc3.12229
中图分类号：
B [哲学、宗教];
学科分类号：
01 ; 0101 ;
摘要：
Both second-order logic and set theory can be used as a foundation for mathematics, that is, as a formal language in which propositions of mathematics can be expressed and proved. We take it upon ourselves in this paper to compare the two approaches, second-order logic on one hand and set theory on the other hand, evaluating their merits and weaknesses. We argue that we should think of first-order set theory as a very high-order logic.
引用
收藏
页码：463 / 478
页数：16
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