Foundations of Mathematics
Metaphysics, Epistemology, Structure
Bibliographic Data
| ID | 4352023 |
|---|---|
| Authors | Stewart Shapiro (0000-0002-4895-0772, Andrews University, corresponding author) |
| Year | 2004 |
| Volume | 54 |
| Issue | 214 |
| Pages | 16-37 |
| Publication date | 2004-01-01 |
| Open Access | No |
| Type | ARTICLE |
| Venue | The Philosophical Quarterly (JOURNAL) |
| Journal identifiers | ISSN: 0031-8094 • E-ISSN: 1467-9213 |
| Publisher | Oxford University Press (OUP) (PUBLISHER) |
| DOI | 10.1111/j.0031-8094.2004.00340.x |
| OpenAlex | W2137732828 |
| Language | EN |
| Citations received | 3 |
| References cited | 12 |
Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics
Epistemology · Metaphysics · Philosophy · Philosophy and Theoretical Science
| Citations per year | 0.17 |
|---|---|
| Citation span | 2008 - 2026 (19) |
| Highly cited | No |