Are there known ways of formalizing the notion of propositions that can't be targeted by counterfactuals in a coherent way? Or of propositions that are outside the scope of the framework in question?
As a quick example of what I mean, here's an example of extending a modal logic (let's say S5 for concreteness) with a non-primitive modal operator Y that attempts to capture some of the intuition I'm going for.
Let's take a proposition like The number 4 exists.. There are many, many ways of analyzing that proposition including denying that it has a meaning or denying that it has a truth value. Let's suppose we're working in a framework that accepts that The number 4 exists. has a truth value, but doesn't commit to a particular truth value. Let's further suppose that our framework imposes the additional constraint that all possible worlds in our framework have the same truth value for The number 4 exists..
In a certain sense, we've said something rather interesting about our notion of possibility/necessity, namely that it isn't powerful enough to consider questions like the existence of numbers but doesn't make a commitment either. Another way of looking at it is this is the "inside view" of questions outside the scope of the framework we're working in.
I can think of one sort of silly way to formalize this with a derived modal operator Y which means
Yx = ALxLNx either x is necessarily true or x is necessarily false
Y has some nice properties like closure under negation.
Yx if and only if YNx
Y is also closed under conjunction.
Ya and Yb implies YKab
And {N,K} is functionally complete, which is good but hardly definitive.
