If there are set-theoretic "possible worlds," are there set-theoretic "possible situations"?

Question

The SEP entry on situations in natural-language semantics reads:

Situation semantics was developed as an alternative to possible worlds semantics. In situation semantics, linguistic expressions are evaluated with respect to partial, rather than complete, worlds.

Yet elsewhere in the SEP we read,

On the face of it, anyway, it seems quite reasonable to believe that this series [of more and more detailed situations] has a limit, that is, that there is a maximally inclusive situation encompassing all others: things, as a whole or, more succinctly, the actual world.

At any rate, if we can adapt modal metaphysics as such to set theory, as in the work of Hamkins, should we be able to talk of "set-theoretic situations" as well? Hamkins does use this very phrase in another paper of his (about V = L), but I don't know that he's using it in the sense I'm asking about. (Yet he might well be, what with his well-developed modal knowledge.)

• Motivation: my reason for asking this question is that I want the opening to an abstract for a possible essay about a set-theory topic I'm working on to be:

We start in a situation with “relativized” choice (the term “RC” would cover all variations on compromised AC such as countable or dependent choice; here it particularly covers an otherwise unspecified such alternative to (possibly global) AC).

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REASON FOR CONFUSION: why is situation semantics an alternative to PWS rather than just a weaker version of the same kind of thing? Maybe I'm confused by my own confusion...

Answer 1

In the comments, there is confusion about what possible situations are supposed to be. The idea is that they are supposed to be like incompletely specified possible worlds.

One traditional understanding of possible worlds in modal logic is that they are fully specified ways that things could be, i.e., maximal consistent sets of propositions. Fine, but one of the motivations for modal logic is that it ought to regiment commonplace, natural-language counterfactual reasoning. The trouble is that, when I say something like "if you hadn't gone to work today, you wouldn't have gotten fired," I don't have in mind a fully specified way that things could be. For example, I don't have in mind what you did today instead of going to work. What I have in mind, in this example of natural-language counterfactual reasoning, isn't a possible world; it's only a possible situation.

That is one of the major motivations for possible situation semantics, and it helps make it clear what possible situations are supposed to be, and how they are different from possible worlds.

Now to answer the original question, "should we be able to talk of 'set-theoretic situations'": sure, if you want, but I seriously doubt that any theory has been developed in that direction. I haven't read the original book on situation semantics by Barwise and Perry, but from reading Lindstrom's review of it, my understanding that in Barwise-Perry's semantics, in every model, every object is marked with a space-time location. Already you can see that it is not designed for reasoning about abstract objects like sets! My understanding is that later versions of situation semantics (e.g. by Kratzer) cleaved even more closely to linguistic applications and natural-language utterances, rather than transparent applications to mathematics or metaphysics. To the best of my knowledge, nobody has attempted to take the Hamkins-Loewe approach to modal logic and forcing and then do something similar using situation semantics rather than possible worlds semantics.