Whatever they are about, I have an expectation of you here and that is to express in
sound language what you mean, with examples and frameworks and so on, such that you could build a model.
My reasons for this are because I want to build and use models based on this language for doing useful, if often very
abstract work.
There are well known ways to lead not just to self-contradictory results but an entirely broken application of language.
I feel that math, as you allege for your "super-mundane", is exactly the discussion not just of this world but of universes in general.
Most of my discussions in fact derive this language from the observation not just of hypothetical universes but actual immediate other universes in complete simulations. I was born young enough to grow up playing video games, one of the first to grow up playing video games on a computer powerful enough for me to make my own games on it, and to disassemble and figure out games and game theory and understand the world, first, equating "game" with "universe".
For every universe humans can create or describe, every possible set of physics, every one of these, that's why the math part is important: it lets you find and describe and execute and view and even make language to discuss the shadows on the walls which we see, and whether the operations of them may be shared in our waking world, or made to direct something usefully in it, or perhaps just for the sake of talking to it.
It lets you actually "build" that game, whatever the game, even if the game is exactly like the one we are playing all the way down to the transform rules on its quarks and gluons and so forth for the sake of figuring out why those transform rules translate to large scale phenomena, or to figure out what the "mass" of a "proton" is and what transform rules imply that.
The language about the every day notions people have though is just discussing the "test of language".
You have agreed that my language is impeccable as far as the fundamental consistency and applicability.
But that language says, categorically, that responsibilities and freedoms exist only in the realm of the universe which one might accept is deterministic in the mathematical sense at the barest minimum.
This
fundamental necessity for at least
sufficient determinism is part of the package. The compatibilist will generally NOT agree to responsibility when whatever "sufficient" determination is overridden by a rule of large numbers or the rude fingers of a meddlesome god* destroying the universe and replacing it with one where everyone else is the same and you have been replaced by someone subtly different.
But in that case, in the new universe, that new thing that is not you but might think it is and which is based on you, that thing would be responsible as what it is and people would have to respond to it; in fact there is no other precondition that they could respond to earlier other than maybe begging the god to not stick his fingers into things.
Notably it did not decide to be the thing so as to act, but it did act, and responses to make it not act like that anymore have to be directed to the part that did.
Omnipotence and omniscience are interesting topics because they too accord to nonsensical things which have sensible versions. I think in your other posts you questioned the very sensibility of foreknowledge even by a god of a system such as ours: that there is no prediction or pre-determination of what happens even by an observer god: they just have to tune in, grab some popcorn, and watch the episode as it plays out. Sometimes the events are kind of inevitable because most of the characters are really dumb and made of solid lumps of silica on average, and they can maybe change the channel into some "vaguely accessible parallel computation" by pausing the system, rewinding, and twiddling some bits here and there until things turn out the way they want?
But that seems cheap and cheat and the sort of thing that's bound to get you caught, and oh, now we're talking about "otherwise" again while discussing all possible worlds rather than necessarily this one.
The reason I care about the math, though, as I said, is because I want to build games; and not just games for us, but games for the sake of giving existence even to something quite exotic and weird and new in our world. I would rather these things not be told some lie that they somehow lack freedoms, given the fact that they are composed and operate entirely as a construction of freedoms; or that they lack wills or the control over them when the most miraculous part of their existence that made me care about them at all is that they form wills structured around the same logical heuristic elements as us.
I want to reach out into the universe and "breath love into sand" and to know I have managed it.
And when asked why I love, I see all this... Not just this one universe but an infinitude of universes, all of them, owing to the language of math itself bearing this fact out, which are biased in operations towards things such as us but mostly those which have love for one another.
One last thing that should be approached is that there is a concept that math exposes as nonsense, which is to say "the set of all sets".
It seems to make sense on the face of it, but it contains a contradiction.
It is one of the first things discussed in Ian Stewart's Foundations of Mathematics, for instance.
This is another one of those "definitions contains a syntax error" concepts, right along with EinSof in the Gnostic tradition.
It is less to say that these are metaphysical concepts, so much as "metaphysical NONSENSE."
When metaphysics proposes a paradox math proposes a solution and reason.
For example, I can discuss the trick behind the "can god create a rock so big he cannot move", if you would like, by applying an example that should explain why the question is malformed.