Stewart Shapiro
Ohio State University
Since virtually every mathematical theory can be interpreted in Zermelo-Fraenkel set theory, it is a foundation for mathematics. There are other foundations, such as alternate set theories, higher-order logic, ramified type theory, and category theory. Whether set theory is the right foundation for mathematics depends on what a foundation is for. One purpose is to provide the ultimate metaphysical basis for mathematics. A second is to assure the basic epistemological coherence of all mathematical knowledge. A third is to serve mathematics, by lending insight into the various fields and suggesting fruitful techniques of research. A fourth purpose of a foundation is to provide an arena for exploring relations and interactions between mathematical fields. While set theory does better with regard to some of these and worse with regard to others, it has become the de facto arena for deciding questions of existence, something one might expect of a foundation. Given the different goals, there is little point to determining a single foundation for all of mathematics
Keywords Conference Proceedings  Contemporary Philosophy  General Interest
Categories (categorize this paper)
ISBN(s) 978-1-889680-19-4
DOI wcp202000638
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,252
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

A Naturalistic Justification of the Generic Multiverse with a Core.Matteo de Ceglie - 2018 - Contributions of the Austrian Ludwig Wittgenstein Society 26:34-36.

Add more citations

Similar books and articles


Added to PP index

Total views
89 ( #122,533 of 64,217 )

Recent downloads (6 months)
1 ( #449,201 of 64,217 )

How can I increase my downloads?


My notes