- The whole point of fictionalism1 is, of course, to keep open the option of accepting fictionalized versions of quantifications over possible worlds, whilst rejecting the modal realist's ontology, or at least going agnostic about it. For simplicity, let's suppose the fictionalist wants to go atheist - he thinks that PW2 is false. Then the dilemma to which my title alludes may be posed by asking: Does he think it's contingently false, or that it's necessarily false? If the latter, then he runs into trouble immediately - whatever modal statement P is, his replacement for its possible world translation is going to be vacuously true, simply by virtue of the necessary falsehood of its antecedent. If, instead, he opts for the view that PW, though false, is no worse than contingently so, he must hold that PW might be (or might have been) true.
- But how is this modal claim - the claim that possibly PW is true - to be understood? If we apply the usual fictionalist recipe, what we get is: 'According to PW, there is a possible world at which PW is true', which is equivalent to the conditional: 'If PW were true, there would be a world at which PW is true'. Since what the antecedent hypothesizes is PW's truth at the actual world @, this conditional is an immediate consequence of 'If PW were true at @, PW would be true at @'. But this conditional is merely an instance of the schema 'If A were true at @, A would be true at @', which holds whatever proposition A may be - even an impossible one. In particular, 'If PW were true at @, PW would be true at @' - and hence its consequence 'According to PW, there is a possible world at which PW is true' - would be true, even if PW were impossible. Thus the official fictionalist paraphrase certainly cannot adequately capture the content of the claim that possibly PW is true.
Footnote 2: 'PW' denotes some suitable version of possible worlds theory, such as that of David Lewis.
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