Update on my Necessity and Propositions account (and my haste to declare it false)

In some recent posts here I have discussed propositions like 'Air is airy' (due to Jens Kipper) which we know to be necessarily true, but only because we know empirically that air is not a natural kind, and hence that all there is to being air is being airy, and 'Eminem is not taller than Marshall Mathers' (due to Strohminger and Yli-Vakkuri), which we know to be necessarily true, but only because we know empirically that Eminem is Marshall Mathers, in relation to the account of necessity defended in my thesis. That account says that a proposition is necessarily true iff it is in the deductive closure of the set of true inherently counterfactually invariant propositions. (Roughly, a proposition is ICI if it does not vary across counterfactual scenarios when held true. For more detail see Chapter 5 of my thesis.)

At first, I reacted by thinking that such propositions show that account to be false. I then came up with another account, based on the idea of a counterfactual invariance decider. I still find this new account more elegant, but I soon came to have doubts about just how threatening they are to the ICI-based account in my thesis.

I have recently realised that the ICI-account fares even better in the face of these examples than suggested in the post mentioned above. There, I suggested in effect that 'All there is to being air is being airy' could be argued to imply 'Air is airy' on a suitably rich notion of implication, thus saving the ICI-account, and similarly that 'Eminem is Marshall Mathers' could be argued to imply 'Eminem is not taller than Marshall Mathers' on a suitably rich notion of implication.

But, I have realised, no such rich notion of implication is required! We just need to conjoin the empirical proposition which decides the modal matter with the proposition whose modal status is in question. 'Air is not a natural kind and air is airy', or 'All there is to being air is being airy and air is airy', are both true and ICI, and they both - very straightforwardly, by conjunction elimination - imply the desired proposition. For the Eminem case we have 'Eminem is Marshall Mathers and Eminem is not taller than Marshall Mathers'. So there was never a serious problem for the ICI-account after all! 

Admittedly, these impliers do perhaps seem a bit "clever", a bit artificial in some way, and this - together with not requiring any appeal to implication at all - is why I still think the CI decider account is more elegant. 

One thing that I think went wrong in my thought process around this is that I got a kind of kick out of concluding that my original account was false. Doing so made me feel like a virtuous philosopher, open to changing their views. But I am glad that I now have a more elegant account, and the notion of a CI decider. (I wonder: Would the CI decider account still have come to me if I had not overreacted and thought my original account falsified? Or did my foolishness here cause me to come up with the CI decider account?)

Two-Dimensional Semantics and Counterfactual Invariance Deciders

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.