Wednesday, February 10, 2010

Beall And "Just True" (Part I)

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.

9 comments:

Colin Caret said...

Hey Ben, I suppose you had to expect to see me on this one :) I don't see the problem here at all. First of all, at the end of the day there is just one truth predicate for Beall, the ttruth predicate. I propose that we should translate your predicate 'is udtrue' into Beall's preferred terminology. What we might call 'udtruth-aptness' is really just a grammatical fact about whether or not a sentence is constructed in such a way that instances of the ttruth predicate are eliminable. In that case, 'is udtrue' just translates into the conjunctive predicate 'is ttrue and is a ttruth-eliminable sentence'. But since your sentence # is not a ttruth-eliminable sentence, one of these conjuncts is false of it (even though the other may be true of it) making the whole sentence false. It is like a sentence that says "This sentence is true and is three hundred words long."

Ben said...

Colin,

Yeah, I was definitely expecting you'd get in on this one. I think you might be right about the key point. (In fact, about ten minutes after I finished banging out Wednesday's post and caught up to friends heading out to the bar, I started worrying on and off that there might be a plausible reply to this where it's seen as a disguised conjunction and hence just false. I had a twinge of uneasiness about that, but I decided to keep it up to see how people who know the ins and outs of Beall's flavor of dialetheism better than I do--like you--reacted to the case. It's still not 100% clear to me that the disguised conjunction reply makes the problem go away, but I'm certainly not confident that it doesn't.) A few quick thoughts about it, though:

(1) I'm not sure the distinction is a merely grammatical one, or that the picture Beall ends up with is really one with just one kind of truth (although clearly that's what most of his rhetoric about truth suggests). He starts out "Spandrels..." by saying that (although we couldn't) God could compeltely specify our world without using the word "true." The truth predicate is then addressed, not to talk about any fact about the way the world is not already picked out by other predicates, but simply as an expressive device for allowing us to make certain sorts of generalizations. Once, introduced, though, there are these spandrels, which don't derive their truth or falsity from the way the world is--all the stuff God could be omniscient about without His personal language requiring a truth predicate. Rather, these spandrels are made true in a different way:

"If anything is to determine the ttruth or tfalsity of such sentences, it's at most the overall logic (or rules) of the language." (p. 16)

This comes at the very end of the discussion about supervenience in 1.5.3, and in context it looks like his conceptual justification of the breakdown of supervenience for spandrels.

Now, at this point in the story, it looks suspiciously like we have two very different flavors of truth, not just one, and in fact that the conceptual distinction between the two varieties of truth seem to more or less mirror a very traditional (truth-making) version of the analytic/synthetic distinction....some sentences are made true by the way the world is, while other sentences are made true by logical rules inherent in language or some such.

(2) That said, even if I'm right here and Beall's distinction (which I'm trying to capture as udtruth vs. fdtruth) is a conceptual one about truth-making rather than an appeal to a merely grammatical fact analogous to "is three hundred words long," I'm not sure how much it matters. After all, even a sentence that says that it "is true in the sense of 'true' that depends on the way the world is" can still be glossed as a disguised conjunction, where the first conjunct is true and false (like all othe truth-tellers) and the second conjunct is (just) false, and hence the whole conjunction is (just) false.

Ben said...

(3) Then again, maybe not. When we read "udtrue"/"fdtrue" as tracking Beall's analytic/synthetic-like distinction about the different ways in which sentences become true, then "this sentence is udtrue," read as a disguised conjunction, is something like:

"This sentence is true and its truth-value is determined by the way the world is, rather than the overall logic of our language."

(I know you don't like talk of truth-values, but I'm just using it here as a short-hand for "whether its true, false or both or whatever." I don't want to have the second conjunct be "the fact that its true is a result of the way the world is," because that makes it much less plausible that it is a disguised conjunction, given that all the information in 'the first conjunct' would not be contained in 'the second conjunct.')

So, given that the "this sentence," in both iterations of the phrase, refers to the entire sentence, not just one conjunct or the other, and we need one of the conjuncts to be (just) false in order for the whole conjunction to be (just) false, which conjunct is wrong?

If the right conjunct is (just) false, then the whole sentence *is* ttruth-ineliminable, and hence (since Beall wants all ttruth-ineliminable sentences to be gluts), the whole sentence is both true and false. So that just lands us right back where we started.

If the left conjunct is (just) false, though, we have a different sort of problem. If it's (just) false to say that the sentence is true, it must be ttruth-eliminable, since, if it were ttruth-ineliminable, that left conjunct wouldn't be (just) false, it would be both true and false. But, if the sentence is ttruth-ineliminable, then we have to come up with a paraphrase that doesn't include a truth-ascription, and that seems impossible. After all, since the "this" clearly refers to the whole sentence, it's not *just* attributing truth to the claim that it's truth-value is determined by the way the world is, it's *also* attributing truth to the claim that it is true, and that second truth-attribution seems as ineliminable as the day is long.

(4) Caveat: I'm going to stop typing now, since this response has gone on for entirely too long, but I'll just quickly note that I'm not sure how much of the analysis from (3) would transfer over to "This sentence is true and is three hundred words long." I'm also not sure whether, if a lot of it did transfer over, that would show an even deeper problem with the package of Bellean views I'm criticizing (truth-tellers are gluts, no gluts in the base language, etc.), or if it would just show that I've missed something about the case at hand.

Emil said...

I didn't understand much of the post. Probably due to I not having read the relevant Beall papers/books (I've read Priest).

Anyway, I simply noted that this paragraph seems to be ill-formated. There are seven quotation marks and a comma inside the first one that shouldn't be there, I think.

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....

Colin Caret said...

Okay saying that 'groundedness' is a grammatical fact is contentious, but it only assumes this much:

1) That we've got some kind of Godel coding from the syntax into arithmetic.

2) That we've got some syntactic criterion of 'standard names' of numbers and so, via our coding, a syntactic criterion of the-name-of-A for any given sentence A.

3) That it is decidable whether any given sentence A contains as a sub-sentence something of the form True(A).

But grant me these assumptions, and then it just becomes a question of grammar whether or not a sentence is grounded, ttruth-eliminable, or what have you (a sentence is grounded if it does not satisfy (3) above). Of course, I think this issue is not really central to the bigger issue we are debating, so we can maybe forget about it for the time being.

To the bigger issue, I'm afraid I don't have a lot to say other than to cite anecdotal evidence. My hunch is that, if pushed, Beall wants to admit just one notion of truth, namely the deflationary notion, the expressive device 'is ttrue'. What that means for his claims about God's description of the world and the non-supervenience stuff could go one of two ways.

One way: these dependency claims, which appear to invoke some second (more robust? realist?) notion of truth, can in fact be cashed out in other, deflationary-friendly terms. Doing so explains away the apparent appeal to a second notion of truth and demonstrates how these claims are compatible with the deflationary project.

Other way: these dependency claims entail an ineliminable commitment to a second (more robust? realist?) notion of truth, in which case Beall is not entitled to make them at all. Worse yet, according to you this commitment also generates paradoxes that his theory cannot handle. Now we are stuck with figuring out how important this notion of truth and these dependency claims are to the bigger project, and which parts of the project stand or fall with them.

In the end, I think that Beall makes these claims about dependence or determination of truth in the most 'light-handed' spirit possible (note the scare quotes around 'depending' in the section that you quoted about supervenience). I suspect that he doesn't want a theory of truth-making to follow from these claims, especially not one that involves a commitment to any kind of non-deflationary truth property. Beyond that I don't think I have anything very illuminating to say.

What would be interesting is to figure out which, if any, of his 'important' theses ride on this issue. Here is one way I can imagine the dialectic going that I think you would not find very satisfying. Maybe it turns out that Beall is not entitled to make any kind of claims about the dependence or determination of truth, because any such claims entail commitment to a non-deflationary truth property that he explicitly rejects. But then, if such claims cannot be expressed one way or the other on his view, than it is question-begging to accuse his view of commitment to some problematic form of failure of supervenience. The view ends up being a sort of 'quietism' about the supervenience issue and circumvents the sort of revenge problems you raise by making no claims one way or the other about supervenience/dependence.

Ben said...

Colin,

Thanks for that...I'm still not 100% sure about what to make of all of this, but that was definitely useful.

A related worry is this:

Let's accept that nothing deep or conceptual is riding on the supervenience/dependence stuff, and that as such # really is no more of a problem than "this sentence is true and 300 words long."

I'm starting to wonder if there isn't a serious concern about what to make of "this sentence is true and 300 words long" on Beall's account. Given that he wants all ttruth-ineliminable sentences to be gluts, what do you do with conjunctions where one of the conjuncts is ttruth-ineliminable, and refers to the truth (or falsity) of the whole conjunction? On the face of it, for any sentence L such that L is the conjunction T(L) & P, and P can be any random base-language claim, what do we say about the truth or falsity of L?

After all, we *can't* paraphrase away the use of the truth predicate here, since the first conjunct doesn't just attribute truth to the second conjunct, but also attributes it to itself. So if P is "this sentence is 300 words long" or "the moon is made of green cheese" or whatever, and we want to say that the whole conjunction is therefore just false (and not also true), then that means that at least one ttruth-ineliminable statement isn't glutty. OTOH, if we stick with the principle that all ttruth ineliminable claims are glutty, that means that the first conjunct is true, hence the whole thing is true, and triviality follows.

I'm not at all sure about this--my feeling is that I've taken a wrong turn here somewhere--but hell if I can figure out where.

Colin Caret said...

I think the answer to all of this is simply that it is not the case that Beall wants all ttruth-ineliminable sentences to be gluts. The sentences we've been discussing are examples of this. For a more telling example, simple Curry paradoxical sentences are obviously ttruth-ineliminable and yet on Beall's account they are false (and not true).

Ben said...

Colin,

"I think the answer to all of this is simply that it is not the case that Beall wants all ttruth-ineliminable sentences to be gluts. The sentences we've been discussing are examples of this. For a more telling example, simple Curry paradoxical sentences are obviously ttruth-ineliminable and yet on Beall's account they are false (and not true)."

Hmm....looking back at the text, it looks like both of us are sort of right and sort of wrong, at least about Beall's position as of the time he wrote "Spandrels..." (I'm sure you're better informed than I am about ways that his views may have changed since then.) In his discussion of Truth-Tellers in Chapter One, he does say that he's taking all ttruth-inelimable sentences as glutty (though he's not married to symmetry considerations, he's open to alternative approaches on this question, etc.).

In his discussion of Curry in Chapter Three, he does qualify this in a significant way, as you say. Unfortunately, though, he doesn't qualify it enough to get around this particular problem. Here's what he says in 2.3.2:

"In Chapter 1, I noted my openness to an asymmetric treatment of such sentences (e.g. treating some ttruth-ineliminable sentences as gluts, some classically), but officially embraced the simple approach whereby all such sentences are gluts--transparently true with transparently true negations. This position remains, but only for the conditional-free fragment."

In light of the issue I'm worried about here--conjunctive truth-tellers (or conjunctive liars) generating triviality--it looks like he needs to make another qualification.

An obvious thought here would be that Beall could just keep his position for the conditional-free and conjunction-free fragment of his language, but this would lead to some weird counter-intuitive results. If one takes Liars to be meaningful, truth-evaluable, etc., then, e.g.

"This sentence is false and not true."

...should come out as glutty (and, indeed, Beall explicitly says that that conjunctive liar is glutty in his discussion of "just true.") In fact, familiar liar reasoning forces us to that result, since regarding it as (just) false, like Beall wants to do with Curry sentences, and I'm suggesting he's going to have to do with some conjunctive liars and conjunctive truth-tellers (since the cost of not doing it is triviality), gets us the result that it's also true.

Fishing around for principles that, consistently applied, would get us the results that Beall wants, one could simply say that all ttruth-ineliminable sentences are gluts except for sentences with ttruth-ineliminable elements--this would let us treat both Curry and the sorts of conjunctive truth-tellers and conjunctive liars I'm worried about--e.g. "this sentence is true and three hundred words long"--as (just) false.

The problem with that is that it would cut out too much. After all, presumably any dialetheist is going to want traditional revenge liars like:

"This sentence is false or meaningless."

...as glutty, and it includes a ttruth-eliminable disjunct.

Ben said...

Colin,

I should add that I do think there's a solution for Beall here that fits plausibly into the overall shape of his account, which would be to start with the opposite default assumption. As is, he starts by taking ttruth-ineliminable sentences in general to be glutty--while being open to being shown that he's wrong about some of them--and then adds a huge qualification, restricting this to only the conditional-free fragment of his language. If I'm right about the conjunctive cases, he might want to restrict it further...the problem being that it starts to look like the general principle is being pock-marked with all sorts of strange ad hoc exceptions. I think a cleaner and more plausible way for him to go might be to *start* with the default assumption that all ttruth-ineliminable sentences are false, and only admit gluts in cases where he's forced to by traditional Liar reasoning--i.e. he could say that all ttruth-ineliminable sentences are false, that some of them are also true (because its a result of their falsehood, plus the overall logic of the language, because statements that attribute falsehood or untruth or whatever to themselves can't be false without also being true), but that the ones we aren't forced to say are gluts are just false.

One advantage of this is that it gives him a more intuitively well-unified account of all of the spandrels--they're all false (although some are true). Another advantage is that it squares nicely with his basic metaphor of spanrels. If ttruth-ineliminable sentences are generally true, that sounds like there's some special feature of these sentences such that they generally end up that way. If their default position is false (because, the truth predicate not being introduced to talk about some new fact, there's nothing to make them true), then the fact that some of them are also true is much more obviously an inevitable and vaguely interesting byproduct of their falsehood + the overall logic of the language.

There might still be some awkward issues here--see tomorrow's post on "Lying Curries"--but it seems like a more promising approach for a Beall-style dialetheist to take than what he says in "Spandrels..."