Second‐Order Logic and Set Theory
Jouko Väänánen · Philosophy Compass · 2015
Abstract 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.