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.
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DOI 10.1093/analys/anp010
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References found in this work BETA
Timothy Williamson (1998). Bare Possibilia. Erkenntnis 48 (2/3):257--73.
George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.
Daniel Nolan (1996). Recombination Unbound. Philosophical Studies 84 (2-3):239 - 262.

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Gabriel Uzquiano (2015). Modality and Paradox. Philosophy Compass 10 (4):284-300.

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