Sets and worlds again

Analysis 72 (2):304-309 (2012)
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Abstract

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

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Christopher Menzel
Texas A&M University

Citations of this work

In Defense of the Possibilism–Actualism Distinction.Christopher Menzel - 2020 - Philosophical Studies 177 (7):1971-1997.
Possible Worlds.Christopher Menzel - 2013 - Stanford Encyclopedia of Philosophy.
The Paradox of Sufficient Reason.Samuel Levey - 2016 - Philosophical Review Recent Issues 125 (3):397-430.

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References found in this work

The Logic of What Might Have Been.Nathan Salmon - 1989 - Philosophical Review 98 (1):3-34.
There is No Set of All Truths.Patrick Grim - 1984 - Analysis 44 (4):206-208.
On Sets and Worlds: A Reply to Menzel.Patrick Grim - 1986 - Analysis 46 (4):186 - 191.
On Set Theoretic Possible Worlds.Christopher Menzel - 1986 - Analysis 46 (2):68 - 72.

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