In my view that explanation is just compounding problems (note that my comments below are in the context of what's functionally going on, with respect to what's coherent or not, re conventional uses if terms):
* "Possible worlds" talk doesn't make sense except as talk about what is metaphysically possible in the actual world (which for a determinist is only one thing for each "branching point" so to speak . . . also, I see logical possibility as a subset of what's metaphysically possible, although determinists would have to say that it's the subset of things that are possible to non-contradictorily imagine; that, however, is still a subset of metaphysical possibility.) — Terrapin Station
What's logically possible is whatever isn't ruled out by the laws of formal logic alone. Whatever isn't self-contradictory is thus logically possible. Metaphysical possibilities, however you construe them, seem also to exclude propositions that are false because they are ruled out by
a priori conceptual truths or by the laws of nature. (But see also Kripke on the metaphysical necessity of identity or of origin). It is very strange to say that logical possibility "is a subset of what's metaphysically possible", rather than the other way around.
* I don't know if you intended them to, but alethic or temporal possibility wouldn't refer to anything other than metaphysical possibility (they'd just be limiting the consideration to metaphysical possibility re truth-value judgments or changes that obtain relative to something)
Something is an alethic possibility ('a-possibility') if there is a true subjunctive conditional (e.g. a causal conditional) in which it figures as the consequent.
e.g. I arrived at work late because I forgot to set my alarm clock but it is
a-possible that I would have arrived to work in time since if I had (counterfactually) not forgotten to set it then I would have arrived to work in time.
What is the allowed range of counterfactual antecedents that make alethic possibility statements either true or false is of course a pragmatic contextual matter that a semantic model must be sensitive to. (There seems to me to be a flaw with David Lewis's 'counterpart' models and their seemingly context insensitive similarity relations between possible worlds. Saul Kripke seems to me to provide a better informal account in
Naming and Necessity.)
A temporal possibility is a possibility for the future that may become actual after the time has come. When the time has come, and the proposition now represents the past, it becomes (temporally) necessarily true or necessarily false. The range of possible worlds under consideration, in this case, is the set of possible worlds that share the same past with the actual world, at a time, and are branching out in the future consistently with the laws of nature. Just in case determinism is true, of course, then there is no branching out. There only is one actual future.
My point only was that epistemic possibilities depend on neither of those two modalities since they are premised on my ignorance regarding the actual world and don't always depend either on whatever is as of yet unsettled (for the future) or on what would have happened in counterfactual circumstances.
* "Possible worlds as semantic models" -- we can note that the semantic models that individuals happen to possess (meaning is subjective and only obtains insofar as individuals actually think it) are actualized possibilities, but this is still metaphysical possibility (and rob a deterministic actualized (or to-be-actualized possibilities) are the only possibilities there are)
No. Semantic models aren't "actualized possibilities". This is nonsense. They are sets of characterizations of possible worlds with only one among them being labelled as the actual world. When something is actual, then it is possible but only one possible world is actual.
* The idea of "subjective probabilities" is just nonsense--if there are probabilities and that's not just an illusion, that's going to be a name that picks out some objective relational feature(s) of the world
If you throw a die that you know to be fair and balanced, then, regardless on the laws of nature being deterministic or indeterministic,
after the die has been thrown, but before you are informed of the result, the subjective probability for each one of the six conceivable results, from your own epistemic perspective, is p = 1/6. I am unsure why you would think this is nonsense. It is just part of the normal course of practical deliberation for people to make use of their own subjective probability estimates of the consequences of various possible actions, even when the consequences already are settled conditionally to their choices.
* It's fine to note that we can be ignorant about which possibility obtains, where we believe that prior to something obtaining, there is more than one possibility, but if we're determinists we do not believe this; we believe that there is only one thing that's a possibility prior to each "branching point,' and our ignorance is about which thing was possible. Thus (a) ignorance isn't the same thing as some sense of possibility, and (b) this is not a different sense of possibility than metaphysical possibility; we're merely talking about our ignorance and beliefs re metaphysical possibility.
Those are just dogmatic assertions that you are making. Determinists and indeterminists alike usually agree about the fixity of the past. Yet, it makes sense to speak about epistemic possibilities regarding
past events.
* Mathematics (and logic) are simply languages that report our subjective understanding of contingent relations, as they are thought about on the most abstract level, and
* Truth-value is a judgement about the relation of a proposition to something else (the exact something else being whatever the individual believes to be the pertinent relational consideration (for the context at hand). That could be their perception of the external world, or consistency with their stock of previously adjudged propositions, or usefulness per their judgment, etc.)
Well, yes, sure. That's exactly what epistemic modalities are about.