Truth value gluts

As I have discussed here before (notably in connection with the Vienna Circle), I believe there are limits to the applicability of the law of the excluded middle.

One example: one can say with some plausibility that as recently as 1990 the validity of Fermat's last theorem was outside the scope of the law. The answer was not only not known, there was no clear procedure for solving it. So ... it was neither true nor false until such a proof had been created (not discovered, if one is going to take this view: created).

Likewise with the Riemann Hypothesis, still unsolved to this day, though it helpfully provides us with a striking image above. A gentlemen who regularly comments on math issues in Quora wrote recently, "There are several fields of mathematics which only make sense on the premise that the Riemann Hypothesis is true, and a handful of others which only make sense on the premise that it is false."

My point though is that no such situation gets us to a truth value glut. In the lingo of contemporary epistemology, such a contention gets us to a truth value gap. A situation in which we want to say that the Riemann Hypothesis is neither true nor false. If we want to say it is both true AND false, we have a truth value glut.

Bu why would we want to have a truth value glut? One view, advocated by Graham Priest, if I understand him, is that classical paradoxes are best dissolved by simply treating the key sentence as both true and false. "This sentence is false." Well ...is it? Yes. Well, then, it has to be true! Yes, it is that as well.

There is an asymmetry between truth-value gaps and gluts. Gaps are proposed pending a solution -- they are proposed in order to be filled in. Gluts are proposed AS solutions -- they are proposed in order to remain in place.

Also, truth glut logic helps make metaphysical mysteries respectable. There is a new work on Christian theology, Divine Contradiction, Oxford University Press, 2023, in which the author, Jc Beale, says that both of these propositions are true:

1) The Father is God,

2) It is not the case that the Father is God.

BTW, I don't get the notion that Beale calls himself "Jc Beale". Shouldn't it be "J.C. Beale"? I don't know, but apparently it isn't. Is it pronounced "Jack Beale"? Or is it akin to the symbol that Prince adopted for himself, where unpronounceability was the point?

Anyway, Beale thinks, sensibly enough, that these propositions cannot both be affirmed if one is eager to embrace the "law of the excluded middle." But rejecting that law is not enough to make these pair of affirmations work, either. A truth-value gap wouldn't help us with Trinitarianism. We need a truth-value glut.

A believer presumably wants the first of those propositions to be true without further fuss, and the second of them to be both true and false.

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