So J.C. Beall devotes a full chapter of "Spandrels of Truth" to dealing with the difficulties that dialetheists' have with making sense of the claim that, while some sentences are both true and false, some sentences are "just true." I've dealt with this question here before, since the claim just made is one that it's very important for the dialetheist to make, so they can differentiate their position from trivialism, and the difficulties involved (given their position) are enormous. And at some point soon, I do want to dissect Beall's discussion of "just true." For now, though, I want to make a much quicker point about a place where Beall (it seems to me) accidentally brushes up against a closely related issue.
In "Spandrels of Truth", Beall argues that all "ttruth-ineliminable sentences" (what, in more familiar Kripkean terms, are called "ungrounded" sentences) should be treated as gluts. Thus, not only Liars, but also variants on the Truth-Teller, like the sentence marked with the dollar sign below....
$ The sentence marked with the dollar sign in Ben's blog post, "Beall and 'Just True' (Part I)" is true.
...are both true and false.
(In section 1.5.2, he discusses these cases explicitly, and says, "For present purposes, I treat all such sentences as gluts."
He also discusses the question of whether being grounded is a pre-condition for being truth-evaluable, in section 1.5.3:
"According to the driving picture, ttruth is a constructed see-through device, one brought in to overcome practical difficulties that we otherwise confront with our (otherwise quite sufficient) base language. Given that the device is constructed to be entirely transparent, one expects a certain supervenience to hold. In particular, one expects ttruth to supervene on base-language facts--the base language ttruths.
"The expectation of such supervenience, I think, is natural. If one were to insist on such supervenience across the board, then one would need to reject that some of the given spandrels are gluts, since such sentences are ttrue without their ttruth 'depending' on base-language ttruths. But I see no reason to so insist.... Why insist as much when the constructed device that might yield spandrels that buck supervenience?"
The combination of his stance on Truth-Tellers and his stance on the supervenience requirement, I think, yields an embarassment that (while slightly different than the "just truth" issue) constitutes a fairly good introduction to our eventual discussion of his take on "just truth."
In his discussion on supervience, Beall, it seems to me, is making a distinction between two types of true sentences, true sentences of the kind whose truth Ultimately Depends on the truth of some base language sentence (let's call them udtruths, a category that would include all true base language sentences as well as true sentences that are "ttruth-eliminable"), and true sentences whose truth ultimately Fails to Depend on the truth of some base language sentence (let's call them fdtruths, a category that would include all "ttruth-ineliminable" sentences). Now that we've introduced this terminology (which Beall can hardly object to, since it's a conceptual distinction that he himself makes), we can see that it gives rise to the following "spandrel":
# The sentence marked with the number sign in Ben's blog post "Beall And 'Just True' (Part I)" is udtrue.
If Truth-Tellers are gluts, as Beall wants them to be, and # is a recognizable Truth-Teller (albeit one that attributes a particular sort of truth to itself rather than truth simpliciter), then it seems like we have no choice but to say that it's true (because it's both true and false) that # is true in a way that ultimately depends on the truth of some base-language sentnece, which it certainly doesn't seem to be.
I'm not sure how much to conclude from this, but at the very least, if he is in fact forced to this conclusion, this looks like an embarassment for Beall's position. More so because he says elsewhere in "Spandrels..." that he doesn't think there are any gluts in the base language, and that this seems difficult to square with there being a glut whose truth ultimately depends on the truth of a base-language sentence. At the very least, to reconcile those two claims, we have to say about # that (somehow) it's truth relies on the truth of some base-language sentence, but it's falsity comes from a different source, which is...at the very least...strange.