Analysis 69 (2):250-258 (2009)

Theodore Sider
Rutgers University - New Brunswick
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
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DOI 10.1093/analys/anp010
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References found in this work BETA

On the Plurality of Worlds.David Lewis - 1986 - Wiley-Blackwell.
What is a Law of Nature?D. M. Armstrong - 1983 - Cambridge University Press.
Nature’s Metaphysics.Alexander Bird - 2007 - Oxford University Press.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
A World of States of Affairs.D. Armstrong - 1993 - Philosophical Perspectives 7:429-440.

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Citations of this work BETA

Modality and Paradox.Gabriel Uzquiano - 2015 - Philosophy Compass 10 (4):284-300.
Possible Patterns.Jeffrey Sanford Russell & John Hawthorne - 2018 - Oxford Studies in Metaphysics 11.
In Defence of No Best World.Daniel Rubio - 2020 - Australasian Journal of Philosophy (4):811-825.
A Purely Recombinatorial Puzzle.Fritz Peter - 2017 - Noûs 51 (3):547-564.
Ontology and Arbitrariness.David Builes - forthcoming - Australasian Journal of Philosophy.

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