Too hard trying to find where he made the claim about LNC. That's okay, I guess it doesn't bear on this discussion.

It's here:

And that also means that......the law of non-contradiction is contingently true (look - 'true'....it's 'true', not false), not necessarily true. It's 'true'. But it is not 'necessarily' true. True, but not necessarily true. — Bartricks

(My bolding)

But it'd be maltreating a deceased equine to continue. Once LNC is rejected, reasoned discussion follows. Lesson is, don't pay any nevermind to Bart.

Maybe there's a paraconsistent modal logic system, and semantics for it that provide that LNC is true in some models but not in other models?

What are your thoughts on this?:

https://thephilosophyforum.com/discussion/comment/565970

Once LNC is rejected, reasoned discussion follows. Lesson is, don't pay any nevermind to Bart. — Banno

There's a particular subject in history of ideas that has bearing on this. It has to do with the advent of nominalism and voluntarism in medieval philosophy. The idea is that the scholastics, such as Aquinas, believed that the principles of logic were inviolable. This is not actually to claim, as I understand it, that God was bound by logic, but was in some sense rational, even if in other senses could be supra-rational. However the voluntarists, lead by the Franciscans, regarded this as an artificial limitation on divine omnipotence. This is explored in some depth in Michael Allen Gillespie's excellent 2009 book The Theological Origins of Modernity.

Gillespie turns the conventional reading of the Enlightenment (as reason overcoming religion) on its head by explaining how the humanism of Petrarch, the free-will debate between Luther and Erasmus, the scientific forays of Francis Bacon, the epistemological debate between Descarte and Hobbes, were all motivated by an underlying wrestling with the questions posed by nominalism, which according to Gillespie dismantled the rational God / universe of medieval scholasticism and introduced (by way of the Franciscans) a fideistic God-of-pure-will, born of a concern that anything less than such would jeopardize His divine omnipotence. — Christopher Blosser

Apparently.

So what remains is for an account to be given of how to talk about a god without such limitation on divine omnipotence.

Can you do that?

The problem is that (p & ~p)⊃q; the account becomes anything.

Can you do that? — Banno

Probably not without a 5,000 word essay which nobody would read anyway.

It's just something which I think is a background factor behind what you've been discussing.

Well, if it were written I might scan it.

One potential problem in my way of thinking about logic is that it ought not be possible to give an account of god in the way proposed. If logic is just grammar, then god not being able to perform contradictions is outlawed simply because if god did do something that was apparently a contradiction, then the response would be to re-formulate the apparent contradiction so that it no longer was a contradiction.

Now exactly what that might look like remains hidden.

One way for me to knut through it would be to give consideration to claimed paradoxes - the Trinity, for example, and to ask what it would really be like for an individual to have three essences, or whatever the explanation is.

Sorry if I am stepping on some sore toes here, but is S4 adressing to a problem regarding infinite regress -- which, certainly, must be very hard to claim to be possible given that individuals may exist in different (actual) possible worlds -- and as such it does its job flawless as it lays the ground for the coming S5.

I believe that what you are looking for is found in the theorems reflexiveness, which according to https://plato.stanford.edu/entries/logic-modal-origins/#LewiSyst is given as the first axiom in S1.

Its been a long while since I did formal modal logic, and I now just glanced at it, so maybe this is an answer in full unsuited for answering your question. If so, I beg your pardon.

Also, I think your question really is about the metaphysics of modal realism. Maybe it may be worth your while to take a stroll down that street.