Williamson's many necessary existents

Analysis 69 (2):250-258 (2009)
This note is to show that a well-known point about David Lewis’s (1986) modal realism applies to Timothy Williamson’s (1998; 2002) theory of necessary existents as well.1 Each theory, together with certain “recombination” principles, generates individuals too numerous to form a set. The simplest version of the argument comes from Daniel Nolan (1996).2 Assume the following recombination principle: for each cardinal number, ν, it’s possible that there exist ν nonsets. Then given Lewis’s modal realism it follows that there can be no set of all (that is, Absolutely All) the nonsets. For suppose for reductio that there were such a set, A; let ν be A’s cardinality; and let µ be any cardinal number larger than ν. By the recombination principle, it’s possible that there exist µ nonsets; by modal realism, there exists a possible world containing, as parts, µ nonsets; each of these nonsets is a member of A
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/analys/anp010
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,798
Through your library
References found in this work BETA
Bare Possibilia.Timothy Williamson - 1998 - Erkenntnis 48 (2/3):257--73.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
In Defense of the Contingently Nonconcrete.Bernard Linsky & Edward N. Zalta - 1996 - Philosophical Studies 84 (2-3):283-294.
Recombination Unbound.Daniel Nolan - 1996 - Philosophical Studies 84 (2-3):239-262.
An Argument Against David Lewis' Theory of Possible Worlds.Peter Forrest & D. M. Armstrong - 1984 - Australasian Journal of Philosophy 62 (2):164 – 168.

View all 6 references / Add more references

Citations of this work BETA
Modality and Paradox.Gabriel Uzquiano - 2015 - Philosophy Compass 10 (4):284-300.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

129 ( #37,748 of 2,177,962 )

Recent downloads (6 months)

2 ( #166,489 of 2,177,962 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums