Sets and worlds again

Analysis 72 (2):304-309 (2012)
Bringsjord (1985) argues that the definition W of possible worlds as maximal possible sets of propositions is incoherent. Menzel (1986a) notes that Bringsjord’s argument depends on the Powerset axiom and that the axiom can be reasonably denied. Grim (1986) counters that W can be proved to be incoherent without Powerset. Grim was right. However, the argument he provided is deeply flawed. The purpose of this note is to detail the problems with Grim’s argument and to present a sound alternative argument for his conclusion – basically the argument Russell gave to establish a well-known paradox in The Principles of Mathematics
Keywords Possible worlds  Paradox  Maximal consistent sets  Powerset axiom
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DOI 10.1093/analys/ans044
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