Second-Order Logic and Set Theory
Bibliographic Data
| ID | 4079676 |
|---|---|
| Authors | Jouko Väänänen (0000-0003-4356-7974, Statistics Finland, corresponding author) |
| Year | 2015 |
| Volume | 10 |
| Issue | 7 |
| Pages | 463-478 |
| Publication date | 2015-07-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Philosophy Compass (JOURNAL) |
| Journal identifiers | ISSN: 1747-9991 • E-ISSN: 1747-9991 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1111/phc3.12229 |
| OpenAlex | W1533359299 |
| Language | EN |
| References cited | 15 |
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
Abstract model theory · Algorithm · Description logic · First-order logic · Foundations of mathematics · Higher-order logic · Mathematical logic · Mathematics education · Programming language · Second-order logic · Set theory · Theory · Universal set · Computability, Logic, AI Algorithms · Computer Science · Mathematical and Theoretical Analysis · Mathematics · Philosophy and Theoretical Science · Theoretical Computer Science
| Highly cited | No |
|---|