For a long time I have wondered, with an uneasy feeling that there was something I couldn't see, about the relationship between two-dimensional semantics and my approach to analysing subjunctive necessity de dicto. As I flagged in the previous post, this has become even more urgent in light of my new, relational account involving the notion of a counterfactual invariance (CI) decider.
I think I've finally made a breakthrough here, and found a clear connection. There is more to say, but here it is briefly.
Recall that my account states that a proposition is necessary (i.e. necessarily true or necessarily false) iff it has a true positive counterfactual invariance (CI) decider.
(P is a positive counterfactual invariance decider for Q iff Q does not vary across genuine counterfactual scenario descriptions for which P is held true.)
A close analogue of this account can be stated in terms of two-dimensional semantics: a proposition Q is necessary iff there is a true proposition P such that for every scenario S in which P is true, Q's two-dimensional intension maps, for all W, <S, W> to the same truth-value.
And I think I can maintain, as CI deciderhood is plausibly a priori tractable and arguably a semantic matter, so too is the question whether, given some propositions P and Q, P is such that for every scenario S in which P is true, Q's two-dimensional intension maps, for all W, <S, W> to the same truth-value.
This makes clear one major way in which my analysis goes beyond the normal two-dimensional account of subjunctive necessity in terms of secondary (or C) intension - and this way can then be translated into two-dimensional terms. And looking at necessity this way, as opposed to with just the usual two-dimensional account of subjunctive necessity, gives us a finer grained picture of the role played by what Kripke called 'a priori philosophical analysis' in our knowledge of necessity. You don't have to know which scenario is actual to know that a proposition is necessary - you just need to know that you're in one of some range of scenarios such that, if they were actual, the proposition would be necessary. And such a range can be characterized by a proposition which you can know a priori to be a CI decider for the necessary proposition in question.