The Logic of What Might Have Been
Salmon (Nathan)
Source: Salmon (Nathan) - Metaphysics, Mathematics, and Meaning, 2005
Paper - Abstract

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    The author's view that s4 modal logic1 is fallacious is defended. It is argued further that even b modal logic2 has not been adequately justified. Equivocation between two senses of the phrase 'possible world' is seen as the likely source of the myth that necessity is properly analyzed as truth in every world. A natural definition of accessibility is proposed. Acceptance of s5 is seen as entailing the unjustified claim that, by logic alone, it is an essential property of any possible world that it be possible. Whether a given world is possible can be a question of contingent fact. (OSO): It is argued that some possible worlds are only contingently possible, and likewise that some impossible worlds are only contingently impossible. There are counterexamples to S5 modal logic3 and even to S4. What about B? Although there are no convincing grounds for supposing that even the actual world is only contingently possible, as far as the logic of modality4 is concerned (as opposed to the metaphysical reality), the actual world might instead have been impossible. The correct modal5 propositional logic is the simple system T.

    (PI): The author's view that s4 modal logic6 is fallacious is defended. It is argued further that even b modal logic7 has not been adequately justified. Equivocation between two senses of the phrase 'possible world' is seen as the likely source of the myth that necessity is properly analyzed as truth in every world. A natural definition of accessibility is proposed. Acceptance of s5 is seen as entailing the unjustified claim that, by logic alone, it is an essential property of any possible world that it be possible. Whether a given world is possible can be a question of contingent fact.

Comment:

Philosophical Review, Vol. 98, No. 1, Jan., 1989, pp. 3-34

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