Analysis 69 (2):250-258 (2009)
|Abstract||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)|
Similar books and articles
Neil Tennant (2010). Williamson's Woes. Synthese 173 (1):9 - 23.
Andrea Sauchelli (2010). Concrete Possible Worlds and Counterfactual Conditionals: Lewis Versus Williamson on Modal Knowledge. Synthese 176 (3):345-359.
Alexander R. Pruss (2001). The Cardinality Objection to David Lewis's Modal Realism. Philosophical Studies 104 (2):169-178.
Ian Rumfitt (2003). Contingent Existents. Philosophy 78 (4):461-481.
J. Hawthorne & G. Uzquiano (2011). How Many Angels Can Dance on the Point of a Needle? Transcendental Theology Meets Modal Metaphysics. Mind 120 (477):53-81.
Daniel Nolan (1996). Recombination Unbound. Philosophical Studies 84 (2-3):239 - 262.
George Darby & Duncan Watson (2010). Lewis's Principle of Recombination: Reply to Efird and Stoneham. Dialectica 64 (3):435-445.
Added to index2009-04-11
Total downloads43 ( #30,732 of 722,853 )
Recent downloads (6 months)2 ( #36,757 of 722,853 )
How can I increase my downloads?