Sets and supersets

Synthese 193 (6):1875-1907 (2016)
  Copy   BIBTEX

Abstract

It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can talk about the collection of all the sets and many more collections beyond that. A method of articulating this idea is offered through an indefinitely extending hierarchy of set theories. It is argued that this approach provides a natural extension to ordinary set theory and leaves ordinary mathematical practice untouched.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,636

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2015-07-07

Downloads
174 (#137,262)

6 months
20 (#148,289)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Toby Meadows
University of California, Irvine

Citations of this work

Plurals and Mereology.Salvatore Florio & David Nicolas - 2020 - Journal of Philosophical Logic 50 (3):415-445.
Fragmented Truth.Andy Demfree Yu - 2016 - Dissertation, University of Oxford

Add more citations

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
Saving truth from paradox.Hartry Field - 2008 - New York: Oxford University Press.

View all 69 references / Add more references