Topics: History of Analytic Philosophy, Philosophical logic
Keywords: ‘not’, contradiction, impossible worlds, Intensional ‘and’, Lewis
In this paper I show that the ‘and’ in an argument like Lewis’ against concrete impossible worlds cannot be simply assumed to be extensional. An allegedly ‘and’-free argument against impossible worlds employing an alternative definition of ‘contradiction’ can be presented, but besides falling prey of the usual objections to the negation involved in it, such ‘and’-free argument is not quite so since it still needs some sort of premise-binding, thus intensional ‘and’ is needed and that suffices to block the argument at a stage prior to the steps about negation.
Lewis’ argument against impossible worlds (Lewis 1986: 7) goes as follows. If worlds are concrete entities and the expression ‘at world w’ works as a restricting modifier—that is, if it restricts the quantifiers within its scope to parts of w—, then it should distribute through the extensional connectives. Let us say that a modifier M distributes over an n-ary connective © if and only if, if M(©(φ1,…, φn), then ©(M(φ1),…, M(φn)).
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