Monday, August 23, 2010

A Reply To Same Objections Made During the Liar Paradox Series

In the series of posts I did over the course of the last couple weeks, I laid out my preferred solution to the Liar Paradox. In Part I, I argued on the basis of disquotationalist considerations about truth that sentences that like the Liar ("this sentence is false") and the Truth-Teller ("this sentence is true"), while they may seem meaningful, are actually meaningless. Attributions of truth to a sentence mean nothing above and beyond the meaning of whatever sentence they attribute truth to, and attributions of falsehood to a sentence mean nothing above and beyond the meaning of the negation of the sentence they attribute falsehood to. Given a string of sentences like:

Sentence 1: Sentence 2 is true.
Sentence 2: Sentence 3 is true.
Sentence 3: Snow is white.

....the rest of the sentences in the series inherit their meaning from Sentence 3. This view can be summed up by saying that meaningful truth talk reduces to truth-free talk. Sentences like the Liar and the Truth-Teller, which lack any 'true'-free sentences from which they can inherit their meanings, are therefore literally meaningless. Although this is a straightforward consequence of an independently-motivated, principled view rather than a desperate attempt to save consistency or retain classical logic, it does have the happy consequence that, if we accept it (as opposed to many standard approaches to the Liar) we are entitled to hold onto full logical orthodoxy.

In Part II, I argued against the view that competent speakers are infallible on questions of meaningfulness. Rather, I argued, it's quite possible for a sentence to be meaningless even if most people's initial intuition is that it is meaningful, or vice versa. I also provided some specific reasons why this might be a case where people are particularly likely to make mistakes about meaningfulness. Part of that error theory, which I should make more explicit now, is that, in certain contexts, the same combination of words does add up to a meaningful sentence. If someone has written "the Normans conquered England in 1066" on a chalkboard and I point to it and say "this sentence is true", I have said something meaningful, since (given my preferred story about truth) what I have said can be accurately translated into "the Normans conquered England in 1066", a meaningful sentence. It's only if the "this" is intended to refer to the sentence being spoken--or some other bit of truth talk that doesn't succeed in inheriting its meaning from a 'true'-free source, or of course some other sort of meaningless sentence, like "colorless green ideas sleep furiously"--that "this sentence is true" is meaningless.

Similarly, "this is true" is surely often a meaningful utterance, as in the following snatch of conversation:

Tom: "The Normans conquered England in 1066."
Jerry: "This is true."

If, on the other hand, Jerry points to a rock and says "this is true," and subsequent questioning shows that he intends for the "this" to refer to the rock, "this is true" is meaningless. Rocks simply aren't the sorts of things to which truth talk meaningfully applies. Neither are bits of irreducible truth talk.

In Part III, I took on various revenge paradoxes like the one posed by "this sentence is either false or meaningless" and in Part IV I argued that the solution I'd been arguing for had the benefit of providing an absolutely unified account of all of the standard semantic paradoxes, and that this was a considerable advantage, given the embarrassingly disunified account of the Liar and Curry you get with the leading non-classical approaches.

There were a couple of interesting objections raised in the comment thread on Part II that I didn't really have time to address earlier, so, rather than going back to a two-week-old comment thread occasional readers are hardly likely to be haunting for further developments, I thought I'd say something about them here:

Jonas asked whether I'd characterize bits of self-referential truth talk that intuitively seemed clearly true or clearly false--one of his examples was "this sentence is obviously false"--as meaningless. (As I understand it, since it's not obvious one way or the other whether "this sentence is obviously false" is false, it is false, but not obviously so, making it unproblematically and unparadoxically false.) I think an even cleaner example of an unproblematically-false looking or unproblematically-true-looking Liar-like sentence would be "this sentence is either true or false." (We can call that the Disjunctive Liar/Truth-Teller.) And my answer would be that yes, it's meaningless. It's possible to engineer bits of irreducible truth talk that seem to be simply true or false (like the examples just given) or that seem to be both true and false (like standard Liars) or that seem to show that everything is true (like Curry) or whose truth-value seems to be totally and permanently mysterious (like the Truth-Teller). In all cases, though, if my arguments in Parts I and II go through, we both have a good, plausible reason to suppose that such sentences are meaningless and we have a good explanation of why they might initially seem meaningful.

(On a somewhat related point, in the comments on Part IV, Emil asked me what view of truth and meaning I was working from. On truth, my view is radically disquotationalist--the meaning of a sentence that attributes truth simply is the meaning of the sentence it attributes truth to--and I think the best argument for that is that it's the simplest, cleanest theory of truth talk that there is. Talking about elaborate structural correspondence or coherence with other sentences in an overall framework adopted at the end of inquiry or whatever--or even, as in more 'substantive' versions of disquotationalism like JC Beall's, talking about obeying certain inference rules--strikes me as introducing complications that are unnecessary to an explanation of the phenomenon at hand. In terms of meaning, I think it's a virtue of this view is that it doesn't require any controversial assumptions about meaning, above and beyond the view--which, as I argued in Part II, we have plenty of independent reasons to accept--that competent speakers are fallible on questions of meaningfulness. To make a synonymy claim, or even to simultaneously assert a whole type of synonymy claims--e.g. "a simple, literally-intended German sentence that does nothing more than refer to some stuff on the ground and say that it 'est schnee' doesn't mean anything different than a simple, literally-intended English sentence that does nothing more than to refer to the same stuff and say that it 'is snow'--isn't to commit yourself to any particular theory of meaning.)

Also in the comment thread on Part II, Jason Streitfeld made a comment that's interesting enough to be worth breaking down in detail:

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I'm not sure why "This sentence is false" (P) is meaningless when said of "colorless green ideas sleep furiously." What if somebody really believed that idea made sense and was false? They might be wrong, but that doesn't make their assertion meaningless.

I think you are making a mistake in your argument. You over-generalize from Quine's disquotationalism. Quine's point is about adding "is true" to sentence. That does not mean that the meaning of all "X is true" sentences mean the same as X. For example, "What she says is true" does not simply mean "What she says." "What she says" is not a well-constructed sentence. Similarly, "This sentence is true" does not mean "This sentence," which also is not a well-constructed sentence.

As you agreed earlier, we can use "this sentence is true" in clearly meaningful ways. I think you want to distinguish these meaningful cases with the Liar Paradox by claiming that "this" in P lacks content (in the relevant contexts). But I don't see how you are establishing that.

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Let's take this one piece at a time.

"I'm not sure why 'This sentence is false' (P) is meaningless when said of 'colorless green ideas sleep furiously.' What if somebody really believed that idea made sense and was false? They might be wrong, but that doesn't make their assertion meaningless."


Well, someone might be wrong about whether it was meaningful, and thus falsely say "'colorless green ideas sleep furiously' is a meaningful utterance", and in that instance, the fact that they were wrong certainly wouldn't make their assertion meaningless. (Their statement would be false, not meaningless.) If, on the other hand, they thought thought it was meaningful and true, and thus they asserted it (that being a natural thing to do when one takes a statement to be true), simply saying "colorless green ideas sleep furiously", then, of course, given that our starting point was that this is a meaningless combination of words, their statement would be meaningless. If they expressed their belief that it was true in a different way, by saying "'colorless green ideas sleep furiously' is true", would that be any more meaningful? How about it if they pointed at "colorless green ideas", written on a chalkboard, and said, "this sentence is true"? From my point of view, all three sentences--the raw assertion of the original sentence, the quotation of the original sentence with 'is true' appended to the quotation, and the reference to it as true, necessarily mean the same thing...which is to say that none of them mean anything at all.

If you, dear reader, do take this series of utterances--going from "colorless green ideas sleep furiously" to "'colorless green ideas sleep furiously' is true" to "this sentence is true"--where the "this sentence" is meant to refer to "colorless green ideas sleep furiously"--at some point becomes meaningful, I'd be interested in hearing in the comments section about where the cutoff point is. Which of these formulations is meaningful, and what's the difference between it and the meaningless formulation(s)?

Similarly, if someone believes--correctly!--that "snow is white" is meaningful and in fact true, and expresses this belief by simply saying "snow is white", or they express it in a slightly more elaborate way by saying "'snow is white' is true", or they express it a slightly more indirect way by pointing at "snow is white" written on a chalkboard and saying "this sentence is true", it seems to me that all three sentences have precisely the same meaning. None of them do anything but ascribe whiteness to snow. Again, if anyone has a different take on this, I'd be interested to hear it--if one of these sentences means something else, exactly what does it mean?

I suspect that the real work is being done in this paragraph by the phrase "really believed," which seems to sneak back in the idea that competent speakers are infallible about at least the meaningfulness or meaninglessness of their own utterances. This seems to me to be falsified by the "bored dinner companion" example I gave in Part II, and also by the simpler case where someone really believed that "colorless green ideas sleep furiously" was meaning, and who really believed that it was true, and therefore asserted it.

Similarly, I think that to assert that a sentence is false is simply to assert its negation--it has no additional content above and beyond this--so "this sentence is false" (where "this sentence" refers to the sentence "snow is white") means the same thing as "snow is not white." Similarly, "this sentence is false", where "this sentence" is supposed to refer to "colorless green ideas sleep furiously", means the same thing as "colorless green ideas don't sleep furiously", which is to say that it means nothing at all.


Moving on to the next paragraph:

"I think you are making a mistake in your argument. You over-generalize from Quine's disquotationalism. Quine's point is about adding 'is true' to sentence. That does not mean that the meaning of all 'X is true' sentences mean the same as X. For example, 'What she says is true' does not simply mean 'What she says.' 'What she says' is not a well-constructed sentence. Similarly, 'This sentence is true' does not mean "This sentence," which also is not a well-constructed sentence."

I want to start with a slightly nit-picky but I think potentially important point, which is that, as I've argued here on multiple occasions before, being "well-constructed" or not has nothing whatever to do with being meaningful or not. Or, to be more precise, "well-constructedness" is neither necessary nor sufficient for meaningfulness. It is, at best, a very weak and defeasible indicator. The usual linguist's and philosopher's stock example of a meaningless sentence--"colorless green ideas sleep furiously" is grammatically "well-constructed." A great many meaningful statements in ordinary conversations, blog posts, quick exchanges with cashiers at coffee shops, objections raised at philosophy talks and so on, are not. The widespread idea that "well-constructedness" (or, more typically, "well-formedness") has its roots, I suspect, in an exaggerated and idealized analogy between the grammatical rules of real languages and the formation rules of formal logical systems.

A perfect example of the obvious possibility of meaningless but not "well-formed" utterances comes from the paragraph I just quoted! "What she said" isn't in itself a well-constructed sentence, but in many contexts is a perfectly meaningful and instantly understood utterance. In fact, in ordinary conversational English as practiced by people of a certain age range, it's a fairly common one, e.g. this snatch of conversation people might have after putting up a roof.

Jack: "What do you think, Jill? Is that good enough."
Jill: "No way. It's going to collapse within a day, two days max."
Jack: "Huh. How 'bout you, John, what do you think?"
John: "What she said."

(In my view, actually, conversational short-cuts like "what she said" actually function quite a bit like truth-attributions.)

Moving on to more substantive issues with the quoted paragraph, to re-cap some of the discussion above, I'm curious about what the difference is supposed to be in content between, say, Sentences 2 and 3 in this series:

Sentence 1: Snow is white.
Sentence 2: 'Snow is white' is true.
Sentence 3: Sentence 1 is true.

My view is that all three sentences mean precisely the same thing. Of course, one could hold an odd sort of combined view where one analyzed Sentence 2 disquotationally and thus argued that it meant the same thing as Sentence 1, but switched to a substantive view of truth when analyzing Sentence 3, thus arguing that it meant, say, "there is a complicated structural correspondence relationship between Sentence 1 and Sentence 3." This hybrid view--that 'truth' means one thing in cases where one bothers to quote the sentence and another thing when one uses short hands like 'Sentence 1' or 'this sentence'--seems like an odd and implausibly complicated position, and I certainly see no reason to attribute it to Quine.

To be clear, my position is not that we accurately capture the meaning of every sentence with the words "is true" in it by chopping off those words from the end of the sentence. It's that all meaningful attributions of truth inherit their meanings from the sentences to which truth is being attributed. So, for example, in the following exchange:

Jill: "The Normans conquered England in 1066."
John: "What she says is true."

....I'd argue that John's statement simply means "the Normans conquered England in 1066."

Similarly, in a more complicated (and, granted, fairly artificial case) like this one:

Jill: "The Normans conquered England in 1066."
John: "What she says is true."
Jack: "The sentence just uttered by John is true."
Jake: "What Jack says is true."
Jose: "What Jake said? Yeah, that's true."
Juan: "My brother Jose just said a true thing."

....the content of every sentence in that series is "The Normans conquered England in 1066." Juan's sentence inherits its meaning from Jose's, Jose's from Jake's, Jake's from Jack's, Jack's from John's and finally John's from Jill's.

My view, then, isn't that "this sentence is true" means "this sentence", but that any instance of the combination of words "this sentence is true" means whatever the sentence being referred to with the phrase "this sentence" means. If "this sentence" is intended to refer to itself, "this sentence is true" means nothing at all.

Moving on to the final paragraph:

"As you agreed earlier, we can use 'this sentence is true' in clearly meaningful ways. I think you want to distinguish these meaningful cases with the Liar Paradox by claiming that 'this' in P lacks content (in the relevant contexts). But I don't see how you are establishing that."

We agree that the words "this sentence is true" can be used in meaningful ways. If one accepts Quine's point about "'snow is white' is true"--and doesn't hold the odd view that truth-attributions work in a fundamentally different way depending on whether one bothers to quote the whole sentence to which one is attributing truth or just uses a short-hand device like 'that sentence' or 'Sentence X' or whatever--an obvious consequence of Quine's view is that there are obviously, unambiguously meaningless instances of the combination of words "this sentence is true", which are just the instances in which "this sentence" refers to a meaningless sentence. Given that the existence of both categories of instances of "this sentence is true"--meaningful ones where the 'this sentence' refers to a meaningful sentence and meaningless ones where the 'this sentence' refers to a meaningless sentence--the interesting question is that of which category "this sentence is true" falls into where the "this sentence" is intended to refer to the sentence in which it appears. My view is that truth-attributions don't start working in a fundamentally different way in self-references cases. In all cases, truth-attributions inherit their meaning from the sentences to which they attribute truth. An infinite series of sentences like:

Sentence 1: Sentence 2 is true.
Sentence 2: Sentence 3 is true.
Sentence 3: Sentence 4 is true.
....and so on into infinity....

....never reaches a non-truth-attributing sentence from which all the truth-attributing sentences in their series can inherit their meaning, so they are meaningless. The self-referential "this sentence is true" has the same problem, and is similarly meaningless. Adding the word "not" to a meaningful sentence doesn't make it meaningful, and the relationship between the self-referential "this sentence is true" and the self-referential "this sentence is not true" (or, equivalently, "this sentence is false") is no exception.

8 comments:

Emil said...

"In Part II, I argued against that competent speakers are fallible on questions of meaningfulness"

you meant infallible, right?

Ben said...

I did. Corrected. Thanks.

(I also cleaned up the appalling sentence construction there.)

Jason Streitfeld said...

I accept a number of your criticisms, but I'm not sure I've made my point as clearly as possible. My main concern is with your approach to meaning.

You say "colorless green ideas sleep furiously" is meaningless. My view is that whether or not that sentence is meaningful depends entirely on how it is being used. It is clearly not a standard sentence in the English language, so if it were to be used in our day and age, it would have to be taken metaphorically. I can imagine it being used to mean something like, "ideas which support the preservation of our ecosystem (green ideas) but which are strongly drawn in black-and-white terms (colorless) may exist in a society without playing an explicit role in the lives of its people (sleep) while causing tension and unrest in their psyches (furiously)."

Of course, that reading is very poetic, and I have no doubt that the sentence has rarely, if ever, been used to mean that, or anything even remotely similar. In fact, I wager the sentence has mostly only been used as an example of a meaningless sentence. But the reason it can be used as an example of a meaningless sentence is this: Most people have no memory of that sentence ever being used, and it takes a good deal of poetic work to find a good use for it.

I'm a contextualist about meaning. I'm not sure if you are or not, but your approach seems to be different. I thought you wanted to claim that sentences which only have "is true" or "is false" as their predicate cannot be meaningful. Yet, as I observed, this is not true. Sentences which have "is true" and "is false" can be meaningful, depending on the context.

Is your position that sentences are meaningless if they lack a referent? That view doesn't seem attractive to me, because "The present king of France is bald" seems meaningful, but lacks a referent. Also, "logically impossible entities do not exist" seems meaningful to me.

In any case, "This sentence is false" does have a referent, even when it is being used to refer to itself.

I think your argument is that it is meaningless (when self-referential) because it ultimately only refers to a truth-attributing sentence. Your claim is that truth-attributions can only be applied to sentences which ultimately refer to something other than truth-attributing sentences. But what is the argument for this position? Why should anyone accept it?

Jason Streitfeld said...

I think my last comment is waiting for approval. In the meantime, here are a few more thoughts.

First, I never meant to imply that only well-constructed sentences could be meaningful, though I concede that I did not express myself very well. The point I was trying to get at was that disquotation doesn't seem to work for cases where the subject of the truth predicate is not a well-constructed sentence. For example, the case of "what she says is true" is problematic, since there are plenty of cases where "what she says is true" does not mean "what she says." For example:

Jennifer: I disagree with her.
Joan: Do you mean you disagree with her as a person, or that you disagree with what she says.
Jennifer: What she says.

In this case (and countless others), "what she says" does not mean "what she says is true." Furthermore, "What she says is true" does not seem to mean, "'What she says' is true." The latter, in fact, is a very unusual thing to write, and I cannot imagine many good uses for it.

Also, I don't think you quite got my point about "'Colorless green ideas sleep furiously' is true." I think that it is meaningful regardless of whether or not "colorless green ideas sleep furiously" is meaningful. So my point was not that "Colorless green ideas sleep furiously" is meaningful just in case somebody believes it is meaningful. Rather, my point is that we can understand what a person means who says it is true, even if we don't believe that "colorless green ideas sleep furiously" is meaningful. We might not understand the sentence which they claim is true, but we know what they mean when they claim it is true. They are not speaking nonsense.

Ben said...

Hey Jason,

Your previous comment ended up in the spam folder not the "awaiting moderation" one for some reason, but in any case, they're both up now. I'll try to reply in more depth sometime in the next day or two when I have a bit more time (I'mgetting ready to teach right now), but a few quick points as I skim through your comments:

(1) I agree that meaningfulness vs. meaninglessnes varies with context. In fact, that's pretty central to my view, since I think that "this sentence is not true" is sometimes meaningful and sometimes not, depending on what sentence the "this" is supposed to refer to.

(2) I ***don't**** think that sentences without referents are meaningless. Nor do I think that sentences with "is true" or "is false" in them are meaningless.

I think, however, that such sentences are only *parasitically* meaningful. In other words, my view is that sentences with "is true" in them inherit their meaning from the meaning of the sentences to which they are attributing truth, and sentences with "is false" in them inherit their meaning from the meaning of the negation of the sentences to which they are attributing falsity. Thus, in the following series:

(1) Sentence (2) is true.
(2) Sentence (3) is true.
(3) Sentence (4) is true.
(4) Grass is green.

....all four sentences are meaningful, and in fact, I would argue, they all mean the same thing. The meaning of (1) is entirely inherited from the meaning of (2), the meaning of (2) is entirely inherited from the meaning of (3), and the meaning of (3) is entirely inherited from the meaning of (4).

By contrast, if the series just went on forever, with each sentence attributing truth to the next sentence:

(1) Sentence (2) is true.
(2) Sentence (3) is true.
(3) Sentence (4) is true.
(4) Sentence (5) is true.

....and on forever like that, never reaching a 'true'-free sentence from which the rest of the sentences can derive their meaning, then all the sentences in that infinite list would, on my view, be meaningless.

An obvious consequence of this is that "this sentence is true" is meaningless if the "this" is meant to refer to itself. This isn't a matter of any sort of ban on self-reference--after all "this sentence has seven words in it" is perfectly meaningful and clearly true--but a consequence of the general view that sentences that use the truth predicate (or truth operator) ultimately derive their meaning from the meaning of whatever 'true'-free sentence or sentences (i.e. sentences that do not use the truth predicate or operator) to which they (directly or indirectly) attribute truth.

Jason Streitfeld said...

It might not be fair of me to comment again before you've had a chance to respond to all of my earlier points. But consider this:

(1) Sentence (2) is true.
(2) Sentence (3) is true.
(3) Grass is green.

What makes (2) true is the fact that (3) is true. But what makes (1) true is not simply the fact that (3) is true, but the fact that (3) is true and that (2) states that (3) is true.

In my understanding, the meaning of (1) is not dependent on whether or not (3) is true (or even meaningful), but on whether or not we make sense of (1). And we can make sense of it, even if there were no coherent (3) to speak of.

For example, I give you three pieces of paper. On one, I write

(1) Sentence (2) is true.

On the next, I write

(2) Sentence (3) is true.

On the next, I write

(3) Sentence (1) is false.

I give these to you sequentially. You understand the first piece of paper, in so far as you know you must find sentence (2) in order to determine it's truth value. Similarly with the second.

When you get to the third piece of paper, you realize you have a problem. But you had previously understood the first two pieces of paper.

We might distinguish between pragmatics and semantics here. Pragmatically, the sentences on the first two pieces of paper have meaning. You might say their semantic content is incomplete, or something like that. But it seems wrong to say that they have no meaning at all.

Jason Streitfeld said...

I hope my last comment wasn't treated as SPAM, too. In any case, one more point, or rather, question.

Would you agree that meaningless sentences are neither true nor false?

Ben said...

Jason,

Skipping ahead to that last point as a promissory note for a more complete reply in the future:

No, I would definitely not say that meaningless sentences are neither true nor false. I'd agree that someone would be making a mistake if they said of such sentences that they're true or if they said of them that they're false, but I'd argue that the mistake isn't a substantive mistake but a category mistake. I'd say meaningless-but-grammatically-declarative sentences--like questions, commands, sticks, stones, bits of burning candle wax and so on--simply aren't the sorts of things to which truth talk meaningfully applies. Like Carnap liked to point out, the negation of nonsense is nonsense. If the claim that some such sentence is true is meaningless, then the claim that it is not true is equally meaningless.

There's a loose way of talking according to which we might say that a coffee cup is "neither true nor false", as a slightlyy confused way of saying that it would be a mistake to say that it was true or false, but of course, given (a) Bivalence, and (b) standard intersubstitutivity rules for "P is false" and "not-P" and for "P is true" and "P", we can derive an outright contradiction from the claim that a coffee cup--or a meaningless sentence--is *literally* neither true nor false. I think it's significant that no dialetheist has ever tried to argue for true contradictions that way, even though it would be a lot easier than messing around with paradoxes.