Trivialism "inside" a paraconsistent logic?

Question

Trivialism is the view that every contradiction is true and accepts the principle of explosion of inconsistencies

Paraconsistency in turn is an attempt to study contradictions in a controlled way. Paraconsistency accepts some contradictions (but not all contradictions) and takes the principle of non-explosion (similarly to the principle of non contradiction of classical logics) to avoid trivialism

However, if paraconsistent logics "isolate" contradictions to avoid the principle of explosion to study them in a controlled manner, couldn't a paraconsistent system "isolate" a trivialist system to study it with control?

We might be generalizing over "how pcL deals with contradictions" to "how xL deals with trivializations," with x ranging over logics in general. That is, yes, some pcL could be designed with such concerns in mind, but so could non-pcL's. — Kristian Berry, Commented Aug 25 at 9:20
Contradictions can be "isolated" because they are individual statements, trivialism only applies to all statements at once. What exactly are you proposing to "isolate"? If not all statements are both true and false then the system is not trivial. And if they are what is there to study? — Conifold, Commented Aug 25 at 9:20
Under trivialism, all propositions are true, so there is nothing for logic to do and nothing to study. — Bumble, Commented Aug 25 at 12:21

Kristian Berry · Accepted Answer · 2024-08-29 10:56:57Z

2

Zalta (AKA one of those who heads up the entire SEP project) has a recent paper in which he discusses such a question:

I've decided to include screenshots of the part of the paper where Zalta develops the above. The paper is open-access anyway so I don't think I'm pulling a micro-SciHub kinda move, here.