Elsewhere (and in my dissertation), I've argued at length that "Liar sentences", like:
(1) The sentence marked (1) is not true.
or
(2) The sentence marked (2) is either false or meaningless.
...and, for precisely, the same reason, "Truth-Teller" sentences, like:
(3) The sentences marked (3) is true.
....and, of course, conditionalized truth-tellers (better known as "Curry sentences"), like
(4) If this sentence is true, the author of the blog post it appears in is a dialetheist.
.....are quite literally meaningless. "Wait," I can hear you asking, "doesn't that make (2) true?" I've written extensively about that question in the past, but the short answer is "no." A sentence with the grammatical form of a disjunction and a "second disjunct" that, if the same words in the same order were split off into a sentence of their own, would constitute a meaningful-and-true sentence, does not thereby become a meaningful sentence, much less a true one. For example, take (5), adapted from the classical example of a meaningless-but-"well-formed" sentence:
(5) Either colorless green ideas sleep furiously or snow is white.
There is, clearly, no contradiction in asserting both (6):
(6) (5) is meaningless.
....and (7):
(7) Snow is white.
....at the same time. Now, this is a very unpopular solution to the paradoxes--which is part of what makes it interesting enough to spend years developing arguments for!--but one which there are few extensive arguments against. Many theorists interested in the paradoxes--especially those interested in non-classical approaches--just brush it off out of hand as not worth taking seriously. Graham Priest derisively refers to it in In Contradiction as "the heroic solution." Hartry Field says in the introduction to Saving Truth From Paradox that people who endorse meaninglessness solutions must mean the term "meaningless" in "some special technical way", so that what they're saying must amount to a strangely-expressed version of his own paracomplete solution.
(I've always tried to be clear that I mean the word "meaningless" is precisely the ordinary mundane sense. As a result of my version of extreme deflationism about truth, I take the sentences that JC Beall calls "TTruth-inelimable" to be literally meaningless in precisely the same sense as a string of nonsense syllables, or "Colorless green ideas sleep furiously." Click on the link above for a less abbreviated explanation, but, basically, I agree with and take literally Quine's claim that sentences that ascribe truth to other sentences mean nothing above and beyond what the original sentences mean--that's the original metaphor behind the term "disquotationalism," that the upshot of prefixing a quoted sentence with the words 'it is true that' is to "remove the quotation marks"--and I generalize this to the claim that all truth-ascribing sentences necessarily inherit their meaning from the sentences to which they ascribe it. Thus, for example, "'colorless green ideas sleep furiously' is true" ends up being meaningless, because it inherits no meaning from the sentence to which it tries to ascribe truth. For precisely the same reason, "this sentence is true" is meaningless. And, of course, as Carnap was fond of pointing out, the negation of nonsense is nonsense.)
In the same spirit as Field's disguised-paracompleteness objection, when I met a regular reader of this blog, at the Eastern APA before last, we chatted about the Liar Paradox and he said he'd have to wait to "see the technical details" before he knew if it would "work."
I have, of course, a philosophical argument for the claim, and a lot of responses to various actual and potential objections, by the very nature of the solution, there aren't and can't be any "technical details." (There's plenty of nit-picky precision work--particularly when it comes to formulating and responding to "revenge paradoxes"--but that's not what most Liar specialist mean when they talk about "technical details.") The necessary absence of technical details strike right at the heart of the difference between the meaninglessness solution and more standard ones--that nothing technical needs to be revised in any way, shape or form on account of the semantic pardoxes is one of the chief selling points of the solution! We get to keep "the naive theory of truth" rather than any of the elaborate 'technical' theories that have proliferated in the post-Tarski/post-Kripke era. We get to keep classical logic, classical T-in and T-out rules, and, in short, we get to keep everything except for the intuition that many professional philosophers report having about the semantic status of the sentences in question.
So no, no "technical details" of the kind fashionable in theories of the Liar. There are not and could not be special rules (whether thought of as logicially revisionary or placed 'on top of' the logical edifice regulating particular predicates or operators related to truth or meaninglessness) about, say, the precise behavior of M(P) and ~M(P), because, if a sentence is meaningless, to symbolize it with a letter and trying to perform logical operations on it is to commit the same nonsensical category mistake which would be committed if some very confused logician tried to do the same to a cough or a string of nonsense syllables or a bit of burning candle wax.
The most common argument against the meaninglessness sentence is a simple foot-stamping appeal to intuition. Sadly, X-phi has not yet provided us with any empirical evidence about how widely shared the intuitions in question are, so it's hard to know whether those who take it as obvious that such sentences are meaningful are right when they assert that it's generally obvious to everyone pre-philosophically, but whether they're right or wrong, it's clearly possible for competent speakers of a natural language to be mistaken about questions of meaningfulness. For example, the philosophers of the Vienna Circle were competent speakers of German, but they mistakenly took many perfectly meaningful German sentences about metaphysical subjects to be meaningless. In fact, even if we *wanted* to be semantic Cartesians, holding idealized views about the privileged access of competent speakers to the status of sentences as meaningful or meaningless, we couldn't, because there are disputes in which, whoever is right, someone is a competent speaker making this mistake. For example, Graham Priest and I are both competent speakers of English, and we disagree about the meaningfulness of Liar sentences. Whichever one of us is right, the other one is a competent speaker of a natural language who has made a mistake about meaningfulness.
Of course, there's nothing wrong with appeals to intuition--we can hardly do without them entirely--but, given a good argument and a good error theory, initial intuitive assessments are often shown to be false. Arrogantly enough, of course, I take myself to have both.
What about, however, the following more sophisticated variant on this sort of objection? (It was presented to me by a junior faculty member at the University of Miami a year or so ago, and I don't think I took it seriously enough at the time.) Someone like me, who says that Liars are meaningless, has presumably been convinced of it by prolonged reflection on the paradox. In the course of this, they've sifted through various possible diagnoses of the sentences in question, thinking about consequences of various approaches, objections to failed solutions and so on. Right? Well, then, wait a damn second. Doesn't all of this involve reasoning about what does and doesn't follow from these supposedly meaningless sentences, in conjunction with various other claims. For example, to embrace the meaninglessness analysis is to reject the analysis that says that Liar sentences are meaningful but that they don't express propositions. Presumably, in explaining why the meaninglessness analysis is superior, its partisans want to bring up "revenge paradoxes" like (8). (At any rate, I certainly want to bring it up!)
(8) The sentence marked as (8) does not express a true proposition.
If (8) doesn't express a proposition, it doesn't express a true one, just as if a cat isn't a dog, it isn't a black dog. And anyone who endorsed the meaningful-but-not-expressing-a-proposition analysis presumably doesn't think a sentence can be true without expressing a true proposition--after all, if truth can exist without propositions, why clutter one's ontology with them? Thus, the solution under consideration collapses into contradiction.
Now, while I tend to lean skeptical on the subject, I'm officially agnostic about the existence of propositions. I take its neutrality on this topic to be a big selling point of my preferred approach. (For the sake of simplicity, I usually talk about "sentences", but wherever I talk about "sentences" being true or false, an enthusiast for propositions can always mentally subsitute some phrase about the propositions expressed by those sentences being true or false...and, of course, presumably, if propositions exist at all, only meaningful sentences can express them, so if I'm right that Liars are meaningless, it follows that they don't express propositions any more than bits of burning candlewax express propositions.) If, however, I abandoned my agnosticism in favor of a full-throated embrace of propositions, I'd presumably be forced to classify (8) as meaningless as well. (If I abandoned it in the opposite direction, matters would be quite different. After all, if there are no such things as propositions, it's true of every sentence that it doesn't express one!) Certainly, I view more common revenge paradoxes, like (9):
(9) The sentence marked as (9) has some status other than 'true.'
....or the familiar anti-dialetheist revenge paradox (10):
(10) This sentence is just false, rather than being both true and false.
.....as being meaningless, and still deploy them against the approaches to the paradoxes that I reject, using standard Liar reasoning, like everyone else does. Doesn't the fact that I'm able to play this game as well as anyone else, that we all understand and can use the rules against each other, proof that the sentences are meaningful, that, after all, we all understand what they mean?
To which I say.......
Good question. Tune in on Wednesday!
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22 comments:
For example, the philosophers of the Vienna Circle were competent speakers of German, but they mistakenly took many perfectly meaningful German sentences about metaphysical subjects to be meaningless.
Well, while I'm sympathetic to your argument I'm inclined to think your argument about judgments of meaningfulness needs a bit of tightening up. As Schlick himself recognized, what this amounted to was that the logical positivist simply said to metaphysician, "I don't understand you"; i.e., t could be that by some means not in view the metaphysician's claim could be verified, but on Schlick's view the logical positivist's position was that the logical positivist couldn't see how. Conceivably other logical positivists took stronger positions, but this would make judgments of meaninglessness provisional. That seems a different sort of judgment about meaninglessness than you are suggesting.
But of course, that's a judgment about meaninglessness, and it's almost trivial that people can at least temporarily think that meaningful claims are meaningless, because it can take time to see the meaning of it. Are there any uncontroversial cases where a large group of competent speakers insisted that something was meaningful when it was really meaningless?
Hey Ben, 'regular reader' here. I'd like to try to convince you that advocates of the 'meaninglessness solution' have a burden to say something more. Let's forget about 'fashionable' technicalities for a moment and focus on an issue of more humble origins. Say you're speaking a language rich enough to do arithmetic. Then, unless there are unexpected features of your language it will be Godel-codable, and such a coding will suffice for the Diagonalization/Fixed-Point lemma to hold, i.e.
(DIAG) for any predicate P(x) of the language free in one variable, there exists a sentence S with code [S] such that: S is provably equivalent to P([S]).
This affords a kind of self-reference, such Godel sentences S 'saying of themselves' that they exemplify the corresponding predicate P (loosely speaking, of course, but close enough to the literal truth of what's going on with Godel sentences that it suggests the importance of this theorem as it pertains to the paradoxes).
Unless you think there is something defective about such languages *per se* you seem to be stuck in the following situation. You've just told me that you accept standard in/out rules for the use of a truth predicate and (correct me if I'm wrong, but...) that looks like it commits you to an untyped truth predicate. Now entertain the scenario in which we want to talk about the truth and falsity of sentences of our codable, arithmetic language. The presence of a truth predicate T(x) in a language in which (DIAG) holds entails the existence of a sentence analogous to the Liar, i.e. a sentence L provably equivalent to ¬T([L]).
'So what?' you are probably saying. Well, here's the concern. Consider other Godel sentences of the language in question. These will include what is often referred to as 'the Godel sentence' G which is appealed to in standard proofs of the First Incompleteness Theorem, i.e. the sentence that roughly says 'This sentence is not provable'. I imagine you don't want to say that G is meaningless, but to my mind the only discernable difference between that sentence and the Liar is the *predicate* involved. One of them involves a proof predicate and one involves a truth predicate, but they are otherwise of the same provenance. I imagine you also don't want to finger the truth predicate as the culprit since that would lead you toward a Tarskian view. What I mean is that, if I am right about your commitment to an untyped truth predicate, then I gather you aren't inclined to say that any and all combinations of self-reference and truth are defective or meaningless.
Call it what you want -- technical, non-technical, I don't care -- the question is: what makes G meaningful and L meaningless? Because I for one cannot discern any difference between them which could be blamed for such a difference in content.
I'm afraid "Either colorless green ideas sleep furiously or snow is white" strikes me as meaningful and in fact true.
I also don't agree that the contrary of nonsense is nonsense (where nonsense includes meaninglessness), which you seem to assume based on the authority of the Vienna Circle. "It is not the case that colorless green ideas sleep furiously" seems meaningful and true to me.
Why not then just introduce a less loaded term such as "contentless," since this seems to be what you mean in any case? You will now to need to explain why contentlessness is contagious in disjunctions, without the crutch of the green ideas example, but since I don't think this example works anyway, that would be positive. It seems doable to me, certainly in the context of the strict disquotional sense you ascribe to truth.
Just to add a point. It seems that contagiousness in disjunction depends on the type of (as you would say) meaninglessness. For instance, "xxx yyy zzz" is meaningless, and "xxx yyy zzz or snow is white" is I guess best classified as meaningless. On the other hand, "colorless green ideas ... " does not rise to this level, or at least I wouldn't say that it does. So, while you *can* argue that "this statement is false or this statement is meaningless" is in fact meaningless, I don't think you can use the green ideas example to show it. And, if that's right, the "xxx" example itself will only show how it's possible to have contagion; it's not in and of itself conclusive evidence to make your point about "this statement is false or meaningless" because, in order to appeal validly to the "xxx" example, you need first to provide a reason why "this statement is false" is more like "xxx yyy zzz" than "colorless green ideas..." (and prime facie, it seems more like the second rather than the first, hence the need of a good explanation).
Since the type of meaninglessness is important for contagion, best I think to give your own term to this type (e.g. contentlessness), and argue from there.
Brandon,
Thanks for your comments. This definitely helps sharpen a couple of points.
"Are there any uncontroversial cases where a large group of competent speakers insisted that something was meaningful when it was really meaningless?"
Well, the obvious flippant response would that, if they involved a *large* group of speakers who disagreed with the assessment, then it pretty much follows that they wouldn't be uncontroversial.
Less flippantly, I think there are at least two or three different distinctions buried in that question that are worth separating out:
(1) A "large group" of competent speakers as opposed to a small one. (The popularity of the intuition.)
(2) That the speakers insisted that "something was meaningful when it was really meaningless". (That the case involves false positives instead of false negatives.)
(3) That they "insisted." (That, in other words, the intuition runs deep as well as just being widely held.)
So, before fishing around for another case that combines all three so as to set a precedent for the Liar, we should probably ask whether the Liar itself combines all three features. It would certainly be a case of (2) and (3) certainly describes the reported reactions of a handful of professional philosophers, given how vehemently some Liar specialists brush off the very idea that the meaningfulness of the Liar could be in doubt, but on (1), I'd have to say that the jury's out. X-phi has yet to settle the question of how widely shared the intuition is, and, while awaiting the empirical data, I'd be hesitant to be too sure. (The track record of philosopher's armchair guesses about what nonphilosophers intuitions will be being demolished by the evidence is getting to be a bit too much to ignore.) That said, (1) *might* be true, and even if not (3) being true of the Liar (even without (1) being true as well) does underline the need for a good error theory. Whether it's a handful of professional philosophers, or the overwhelmingly popular intuition of The Folk, why do people's intuitions serve them poorly on the meaningfulness of the Liar?
I'd suggest that part of the answer has to do with the fact that we're used to going through the motions of reasoning about it--see Part II on that subject--which might seem to settle the issue of meaningfulness. After all, surely we grasp its meaning if we can see what follows from it!
(continued)
Another relevant feature of the situation here is that Liar sentences fall into the intersection of several general categories of sentences that are generally meaningful. While I take it to be pretty easily showable from counter-examples that a sentence being syntactically 'well-formed' (i.e. being made up exclusively of standard words of natural language vocabulary, strung together without violating the rules of that language's grammar) is neither necessary nor sufficient for it to be meaningful, it's certainly true that the overwhelming majority of 'well-formed' and even almost-well-formed sentences we encounter in ordinary contexts are meaningful. (The ocassional clear example of a well-formed-but-meaningless sentence like "colorless green ideas sleep furiously" is most likely to come up when it's being used as an example of something!) By contrast, non-'well-formed' strings of words are comparatively more common in ordinary experience--think of scrambled up word magnets on a refridgerator, or a cat walking over your keyboard.
Another category of generally meaningful sentences are self-referential sentences. There are clearly a great many predicates P such that sentence of the type "This sentence is P" is unambiguously, obviously meaningful. Consider "being five words long" or "being meaningful." (On pain of contradiction, "this sentence is meaningful" had best be true and "this sentence is meaningless" false.) While it's true that most sentences of this type are likely to come up as a matter of playful example-mongering, even most examples intrudoced in that spirit are going to be meaningful.
(continued)
Finally, we have the category of "sentences that do nothing but ascribe truth or its negation to a sentence." The vast majority of sentences one is likely to ever encounter starting with "it's true that" or ending with "is true" or "is not true" or whatever are meaningful. In fact, often we assume, because we have no reason to think otherwise, that they're meaningful, even though we have no idea what they mean! (Consider sitting on the subway and hearing a bunch of instances of "that's true" without hearing the other half of the conversation.)
This last category is particuarly relevant. Given Quine's "nothing above and beyond" principle (asserting that it's true that 'snow is white' means nothing above and beyond attributing whiteness to snow), a sentence like "Sentence X is true" could mean any number of entirely different things, depending on what Sentence X is. It could be "snow is white", it could be "snow is green", it could be "colorless green ideas sleep furiously" and it could be "Sentence X is true." If attributing truth to "snow is white" means nothing above and beyond attributing whiteness to snow, then to say "Sentence X is true" where Sentence X is "colorless green ideas sleep furiously" is to say nothing above and beyond attributing furious sleep to colorless green ideas. To say it, in other words, is to say something meaningless.
Similarly, I'd argue, for the case where Sentence X *is* "Sentence X is true", for the reasons I argued for in Part I. But, given that it takes a bit of thought to realize this, and for most values of Sentence X we'd expect to run into in the normal course of things, "Sentence X is true" is perfectly meaningful, and discovering that it's self-referential doesn't immediately solve anything, given that most self-referential statements are meaningful and even true, and that the great majority of syntactically well-formed statements we ordinary encounter are true, it gets very easy to see how someone could assume that Liars were meaningful, especially if one gets used to going through the motions of reasoning about them (thus creating a sense of grasping the specific meaning, because one can see what 'follows'), and *most* especially if one is used to interacting with others who take the assumption as basic. And, after all, if properly taken to be defeasible, these sorts of statistical inferences (almost all sentences-of-type-X are meaningful, so all else being equal, we should assume this one is) are perfectly reasonable. That the "all else being equal" clause is sprung here is, after all, something established by philosophical argumentation, not immediate apprehension.
I'd think that's enough of an error theory to account for (3) being true of the Liar, even *if* later empirical research confirms that (1) is true of it as well. Of course, that still leaves the matter of (2)....
(continued)
I think an easy case of a non-philosophical false positive--indeed, one where the speaker of the sentence can reasonably be excused for taking his own words to be meaningful even though they aren't--is the 'bored dinner date' scenario. Jack and Jill are eating at a restaurant and Jack is bored by what Jill is saying. After a while, he tunes out completely and starts ag reeing with her on auto-pilot: He thinks about other things, but, every time he's cued by the rising and falling of her voice and the pauses in her conversation, he slips in a "good point" or "I agree" or "that's true." Eventually, Jill catchs on. To test him, in a normal tone and pace, her voice rising and falling in a normal way, she says "blork glork gerk, derk dark geblork lork" and he says "that's true." Jack has every reason to assume that, whether what he said was true or not (and, after all, as Professor Frankfurt explains in his little book about bullshit, we often say things without having any idea whether or not they're true and not caring a bit), it was at least *meaningful.* But, pretty clearly, if "it's true that blork glork gerk, derk dark geblork lork" is not meaningless, meaninglessness has no meaning. Finally, on verificationism:
"As Schlick himself recognized, what this amounted to was that the logical positivist simply said to metaphysician, "I don't understand you"; i.e., t could be that by some means not in view the metaphysician's claim could be verified, but on Schlick's view the logical positivist's position was that the logical positivist couldn't see how."
Again, I'd argue that there are two distinct issues worth disambiguating here:
(1) That Schlick was (appropriately) fallibilistic, as anyone should be about any judgment of meaningfulness or meaninglessness once we realize that competent speakers are fallible about these matters, &
(2) That he was doing something other than telling the metaphyiscian "I don't understand you."
It seems to me that normally implicit in "I don't understand you" or "I don't understand what you mean" is the tentative extension of the charitable assumption that the person being spoken to means *something* and that perhaps if the respondent knew everything relevant to this that the original speaker knew, he would understand *what* the original speaker meant. By contrast, "that doesn't mean anything" contains a *judgment* (whether fallibilistic or not) that the respondent knows everything relevant that the original speaker knows, and that they've come to the conclusion that the original statement was meaningless. And *that* seems to be precisely what Schlick and his co-thinkers were saying to the metaphysician.
Colin,
"You've just told me that you accept standard in/out rules for the use of a truth predicate and (correct me if I'm wrong, but...) that looks like it commits you to an untyped truth predicate."
Most definitely, yes.
"...if I am right about your commitment to an untyped truth predicate, then I gather you aren't inclined to say that any and all combinations of self-reference and truth are defective or meaningless."
Nope.
I think that all sentences that Beall would call "TTruth-ineliminable" are meaningless. Self-refential truth ascriptions (or the negations of the same) are an instance of that general assessment. If all truth-ascriptions must inherit their meaning from the sentences to which they ascribe truth, then "orphaned" truth-ascriptions, without any 'true'-free sentences from which to directly or indirectly inherit their meaning, don't end up having any meaning at all. All of the sentences, without exception, that Beall would call "Ttruth-ineliminable" are thus meaningless. This category includes self-referential cases, as well as those like Yablo that don't involve any self-reference.
"I imagine you also don't want to finger the truth predicate as the culprit since that would lead you toward a Tarskian view."
I *do* want to finger the Truth predicate, though I don't see how this would lead me to a Tarskian view. The specific, disquotationalist story I told about why "ineliminable" uses of the truth predicate/operator are meaningless is *specific* to the truth predicate/operator. Of course, there may be other semantic properties about which an almost exactly similar story might be told--an obvious case would be "applies to itself", as in "the property of being a property applies to itself" and "the property of being a concrete physical object does not apply to itself", which might reasonably thought to be a shorthand way of saying "The property of being a property is a property" and "The property of being a concrete physical object is not a concrete physical object respectively", just as "that's true" in response to some long, elaborate statement subsitutes for repeating the original statement. Drawing out the conclusion that the meaning of sentences with the predicate "applies to itself" is parasitical on the meaning of the subjects of those sentences in the same way that the meanings of truth-ascriptions are parasitical on the meanings of the sentences to which truth is being ascribed, this has the added advantage of solving the "does not apply to itself" pardox that Field refers to as "Russell's Paradox for properties" in a way quite unified with the solution to the Liar Paradox. There are, however, going to be other cases where no remotely similar story can be told--an obvious case in this category is the meaningless predicate. In any case, there's no reason to think that very many predicates will be like this, and yes, I do finger the truth predicate as the culprit. I don't see, however, how this would lead me in a Tarskian direction. My claim is that, rather than a hierarchy of truth predicates, there's one truth predicate that's sometimes used in meaningful sentences and sometimes appears in meaningful ones. Why, in your view, should I have trouble getting away with this?
ParisW,
What, in your view, is the difference between the meaning of "snow is white" and the meaning of "snow is white or colorless green ideas sleep furiously"? I'm having a hard time seeing how something can be meaningless and yet add additional meaning to a sentence.
Would you agree that, at least in normal cases, the meaning of compound statements is a function of the meaning of the atomic statements within it--e.g. that "either Hitler won WWII or grass is green" and "either Hitler won WWII or snow is white" have different meanings? If so, I have a hard time seeing how you're going to get away with meaningful 'disjunctions' with meaningless 'disjuncts.'
As far as negation goes, the claim that adding "not" to something meaningless doesn't convert it into something meaningful isn't something I base on the authority of the Vienna Circle. I casually mentioned that as one obvious important debate in which it came up--and tellingly, I've *never* read a criticism of verificationism that challenged that assumption--but in general, as far as I can tell, that's about as uncontroversial an assumption about meaningfulness as one can possibly find. I've never seen it invoked in a debate where the other side disagreed. Have you?
If you'd grant that there are certain cases of meaningless 'disjunctions' with meaningless 'first disjuncts' and second disjuncts that, if split off into sentences of their own, I have a hard time seeing by what plausible principle you could possibly differentiate cases where sentences were meaningless 'enough' for this to be the case and others were not. It seems to me that 'contagion' is all or nothing.
Finally...
"Why not then just introduce a less loaded term such as 'contentless,' since this seems to be what you mean in any case?"
....seems to me to skirt on the edge of question-begging, given that I explicitly denied, at length, that I was using the term "meaninglessness" in some special technical sense, and explicitly spelled out the fact that I take sentences like "This sentence is true" and "This sentence is false" to be literally meaninglesss in the ordinary sense, exactly like "Blork gork beglork" or "Colorless green ideas sleep furiously."
You might find my argument for that claim unconvincing, the claim itself ludicrously implausible, or me delusional for holding it, but at least do me the courtesy of granting that I'm at *sincerely* deluded.
Part I
"What, in your view, is the difference between the meaning of "snow is white" and the meaning of "snow is white or colorless green ideas sleep furiously" ?
One asserts snow is white, the other asserts snow is white or colorless green ideas sleep furiously.
"If so, I have a hard time seeing how you're going to get away with meaningful 'disjunctions' with meaningless 'disjuncts.'" Well, it's difficult to help because you're leaving "meaningless" on an intuitive level, and intuitive concepts can be tricky if not incoherent. Anyway, I think you are reasoning in the wrong direction. Consider the sentence you gave, without any a prioris. [DISJ] "Snow is white or colorless green ideas sleep furiously" certainly sounds true. (Say it to yourself.) I think most people would say that have no idea about the second disjunct, but the first is clearly so, so the whole sentence is so. You may have a theory which says that it shouldn't be, but when theory hits brute fact, theory should lose out every time. If so then: either (1) true sentences can be meaningless; or (2) true, meaningful sentences can have a meaningless disjunct; or (3) "Colorless green ideas sleep furiously is actually meaningful. (2) seems to cause the least perturbation, so it seems the best alternative, but I'm not fixed on it religiously, because it all rests on intuition, which can give conflicting signals. But the brute fact is, DISJ seems true. Maybe you're right and it's not; again, I'm not even particularly wedded to it being true. But it's enough of a judgment call where I don't think it helps your explanation.
Let me put it this way. You have a theory that a meaningless disjunct renders the disjunction meaningless (and so impossible to be true). You say you have a hard time seeing how the contrary could happen. So the example of DISJ doesn't add anything. You're not reasoning *from* this example, you're reasoning *to* it. That is, you have a theory, and because of this theory, you can classify DISJ. You are not using DISJ to argue for the theory. (You're not saying, "Look, DISJ is meaningless, so a disjunction with a meaningless disjunct can be meaningless." You're saying, "A disjunction with a meaningless disjunct is meaningless, therefore DISJ is meaningless." So you should just leave it out, state the theory, and go directly to the Liar sentence. I think most people would say, doing that, that you haven't really provided much of an explanation, because the important part of the theory (disjunction of a meaningful sentence with a meaningless sentence is meaningless, and the Liar sentence is meaningless) depends too much on the meaning of "meaningless," and you're leaving that on an intuitive level.
"that's about as uncontroversial an assumption about meaningfulness as one can possibly find."
Sorry, but "It's not the case that colorless green ideas sleep furiously" sounds clearly true to me, much more, and I mean much more, than DISJ. I mean, it's just not the case. Clearly. Even more, it's just clearly meaningful; it's saying that something is not so which is not so. So maybe you want to say that "colorless green ideas sleep furiously" is meaningful, or maybe you want to say that the contrary of a meaningless sentence can be meaningful. Whatever.
I'm a bit surprised you saying that's it's uncontroversial. Where's a good philosopher when you need them? Say I define b to be the largest even number. "b" is then not well-defined, and "b is even" is a better instance of meaninglessness than "Colorless green..." because b hasn't even been given a proper meaning. Yet I think most mathematicians would agree that "It's not the case that b is even" is meaningful and true.
Part II
"I explicitly denied, at length, that I was using the term "meaninglessness" in some special technical sense"
What I meant is that "meaninglessness" is a loaded term precisely because you are keeping it on an intuitive level. Intuition wants lots of things, at the same time, not always clearly or coherently. It exposes you to someone like me, relying on his intuition, who says, No that's not meaningless. If you're keeping it on an intuitive level, I get to use my intuition, right? It seems to me much better to introduce a technical term or at least a more technical term like "contentlessness," and argue from there. The Liar is contentless. A disjunction of content with contentlessness is contentless. etc. Use intuition, obviously, but don't use a word like "meaningless" where, apparently, honest people can differ as to whether a particular sentence is meaningless.
Sorry, just to be clear, "Where's a good philosopher when you need them?" is supposed to be a joke, playing on the idea that philosophers will argue any point, and so every point is controversial.
Hi, Ben,
Lots of comment there! I'm still digesting some of it. But three preliminary points after having read it through twice:
(1) I'm not sure I see your error theory here; that is, what you call your error theory does make sense of why people would think the Liar meaningful, but that's becuase it looks like a list of reasons to think the Liar really is meaningful. But I take it that an error theory has to be not a list of reasons why a reasonable person might accept the error, but an account of either why people aren't picking up on the fact that their reasons for the erroneous conclusion aren't themselves in error, or why they aren't picking up on the fact that their reasons don't actually support the erroneous conclusions. As it stands your error theory looks something like, "People falsely believe the Liar is meaningful because there are lots of reasons to think the Liar meaningful; the Liar just happens not to be meaningful."
(2) I don't think your track record objection to your (1) carries much weight here; we aren't talking about something that was proposed in the past few decades, which is where most of the actual proven splotchiness of intuitions is, but on something that has been around for dozens of centuries, crossed cultural and linguistic lines, and been treated as meaningful but a very large group of people. Conceivably it's comparable to the piddling things most X-Phi has handled so far, but that's far from clear. In any case, the claim is not an armchair one: it's a historical one, and there is evidence. What's more, I'm not convinced it has anything to do with intuitions: it's an empirical question about how people respond to statements, and while that does mean evidence is required, there is plenty of it. Do we know if the fourteenth century Parisian equivalent of the man on the Clapham bus held that the Liar was meaningful? No; but we don't need to know it -- the Liar has an extensive history, and thus there's lots of historical documentary evidence about how people have treated it. Most of them were philosophers of one type or another, true, but if we are making the assumption that philosophers don't count as competent speakers of language, we probably should quite while we're ahead. From the historical evidence we can gather quite a bit of information about judgments about Liars in a large number of languages by competent speakers. And certainly many of those did treat it as meaningful (in Middle Ages, for instance, although there was some variation, it was common to regard it as meaningful but necessarily false).
X-Phi studies would be interesting, in other words, but it would be incorrect to think that they would be adding evidence to a field that already has a great deal of evidence.
(3) I don't see how your blork glork gerk is supposed to be parallel. Jack doesn't have reason to think that "blork glork gerk" itself is meaningful; he has reason to think that what Jill says generally is meaningful. He doesn't have acquaintance, so to speak, with "blork glork gerk," having not really paid attention to it, to say that it itself is meaningful. Suppose somebody asks me whether the sentence they are pointing to in a book (a sentence I can't see at the moment) is meaningful; I would certainly say that it probably is -- most sentences in books are. But suppose the sentence were "The gostak is that which distims the doshes." I wouldn't have judged that that was meaningful, and I never had reason to think that that sentence in particular was meaningful, even though I had reason to think that sentences in the book generally were meaningful.
A correction -- this:
X-Phi studies would be interesting, in other words, but it would be incorrect to think that they would be adding evidence to a field that already has a great deal of evidence.
Should read:
X-Phi studies would be interesting, in other words, but it would be incorrect to think that they would be adding evidence where there was none, rather than to a field that already has a great deal of evidence.
ParisW,
First of all, I want to make a really important clarificatory point.
You say:
"Let me put it this way. You have a theory that a meaningless disjunct renders the disjunction meaningless (and so impossible to be true). You say you have a hard time seeing how the contrary could happen. So the example of DISJ doesn't add anything. You're not reasoning *from* this example, you're reasoning *to* it."
That's flatly wrong.
I'm doing exactly the opposite of what you say I'm doing.
I take it as obvious that the 'disjunction' in question is meaningless, and use those examples to argue for that other sentences with the syntactic form 'disjunctions' (or other compound statements) that include meaningless 'disjuncts' are similarly meaningless.
Of course, the persuasive power of the example depends on the expectation that most people will share my reaction to the example. Perhaps I'm deluding myself here--once again, a good dose of X-Phi would be interesting here--but I will say that, anecdotally, you're the first person I've ever encountered to express the contrary intuition.
Similarly for the negations of meaningless sentences being meaningless. This is one of the reasons I casually referenced verificationism by way of a reminder that in most contexts people take this as obvious. No one, to the best of my knowledge, has ever written an article accusing the verificationists of having made an elementary mistake--"Why does Carnap say that both the nominalist and the more inflationary metaphysician are saying meaningless things? If the inflationary metaphysician is saying something meaningless, then the nominalist, in asserting the negation of those meaningless sentences, is saying something *true*! Even if meaning is about verification, once we've shown the inflationary metaphysician's claims to be meaningless, we *have* verified their negations!"
You answer my question of what additional meaning and sentence lacking in meaning can add to a compound sentence by saying:
"One asserts snow is white, the other asserts snow is white or colorless green ideas sleep furiously."
You don't think that, if you brought up these two sentences ("snow is white" and "either snow is white or colorless green ideas sleep furiously") in some non-philosophical context and explained the difference, you'd have to expect a lot of response along the lines of...
"Wait wait wait. What?!? One asserts that snow is white. I got that. But I got totally lost with that second one. You said that it either asserts that snow is white or.....what? I have no idea what you mean by that second one."
...?
(continued)
That said, even if I'm wrong about all of this, you make a generalization about what follows from it:
"[W]hen theory hits brute fact, theory should lose out every time."
....that I can't go along with. Given that the "brute fact" we're talking about is ordinary-speaker-intuitions, and any semantic theory that might contradict some of them is presumably based on a different bunch of intuitions, the claim that the former 'always wins' seems totally wrong to me. Which one loses and which wins in the event of a conflict is a matter for a complicated process of reflective equilibrium, and it seems unlikely that we can make very many interesting and accurate generalizations about how such a process will turn out in absolutely every single case.
Finally:
"Use intuition, obviously, but don't use a word like 'meaningless' where, apparently, honest people can differ as to whether a particular sentence is meaningless."
Of course they can disagree. The subject at hand is one that people are going to disagree about. As with all subjects, our shaved-monkey epistemic faculties are imperfect, and, as tends to be the case when we come to interesting enough philosophical problems to inspire prolonged debate, different shaved monkeys are going to come to different conclusions even if they're all doing the best they can. That's just the deal, and changing the terminology won't change it.
Brandon,
Not sure what to say, re: error theories. Seems to me that, if, we're in a situation where many competent people say X, after arguing that X is mistaken on the grounds that Y, the task for an error theory is to explain why they made that mistake. In most cases, "well, in 99.99 of all cases like this, the equivalent of X would be true....you have to realize Y to realize that this isnt' one of them" seems to me to be a perfectly adequate explanation. The follow-up question--"why did they miss Y?"--is only pressing if we have reason to think that Y is obvious enough to be hard to miss. In this case, I think I have a good argument, and that the conclusion is right, but I'm not quite arrogant enough to think that *any* argument I've ever developed about *any* philosophical subject is so blindingly obviously on the money that there's an interesting further question about why philosophers in previous eras of human history weren't clever enough to see the truth of my conclusions.
On your historical argument for the claim that most people regard Liars as meaningful, I remain unconvinced. We're pretty much *exclusively* talking about philosophers, and even at that, there's an obvious self-selection dynamic. Although, to the best of my knowledge, the paradox has never been as popular and discussed as it's been in the last century or so, it's true enough that it's been around for a long, long time. Historical evidence, is, though, by definition, evidence from people who found the problem compelling enough to write about. In the absence of a thriving debate to respond to (e.g. because people were drawing conclusions from the paradox one found importantly wrong), the only people who would write about it are those who shared the intuition that the sentences were meaningful, from which the problem follows.
Of course, if you're just saying that this rather non-random sample is evidence that at least some people share the intuition, rather than that *most* people do, that's fair enough, but if so, it looks a bit redundant to me. Surely, a Jstor search of journal articles from the last year, or a look at comments left on posts here, should establish *that.* Why go into the history? The more interesting question--whether it's a *majority* intuition at all, much less the kind of overwhelming majority opinion that some philosophers seem to assume it is--would be something we'd need X-Phi for.
I actually think that anyone who's frequently been in the position of explaining the paradox to non-philosophers has lots of anecdotal evidence that should at least ground a reasonable suspicion that many a great many competent speakers don't share the intuition. I'm not just talking about otherwise intelligent people totally incapable of wrapping their minds around the opening lines of an explanation of the paradox--and people like that are *legion*--but also about some of the telling things people say when trying to articular their confusion ("*what* sentence is false?" "well, that sentence itself" "right, but what is it saying?" "that its false" "yeah, but I don't understand what...", etc.), and, of course, non-philosophers' reactions to an explanation of the meaninglessness solution in the rare instances where the discussion goes that far. My (again, anecdotal and quite possibly ridiculously eccentric) impression is that almost no non-philosophers find the suggestion that the sentences could be meaningless absurd, that this reaction is a good deal more common among philosophers who don't work on the paradox (although, among philosophers in that category, the "yeah, that makes sense" reaction to the meaninglessness solution" is *also* quite common) and extremely common among philosophers who work on the paradox.
(continued)
If I'm right about this, one could of course explain it different ways. Maybe Liar specialists, given their intimate familiarity with the subject, are more likely to realize things that even other philosophers, much less non-philosophers, will miss. On the other hand, maybe those for whom the meaningfulness intuition is strongest in the first place are most likely to gravitate to the field, and in any case those intuitions are constantly re-enforced by their constant exposure to arguments in which all sides take that assumption for granted. As Chomsky explains so well in his media critiques, there are few more effective forms of propaganda than framing a vigorous debate in a way that simply assumes the point point being propagandized for.
(Without neglecting the very important differences between the two, a *somewhat* parallel case is phil of religion. Philosophers who work on phil of religion are vastly more likely to be theists than philosophers who work in other areas. It could be that they know the arguments better and are thus more likely to be convinced by theistic arguments, or it could just be that people with theistic convinctions derived from extra-philosophical sources are most likely to find the subject compelling.)
(continued)
To be clear, though, the X-Phi/range-of-reactions-to-the-suggestion-meaningless thing is a side issue. While I do suspect that many competent speakers display what, from the perspective of solution, are good instincts on the question, I wouldn't be shocked if it turned out that a large majority came down on the other side here. I just that, if this is the case, the statistical point looks to me like all the error theory we really need.
Hi again. I now see the point about T-ineliminability, or what (I think equivalently) is usually called ungroundedness following Kripke. I was too quick to say that fingering the truth predicate would lead you toward Tarskianism. I think what I had in mind when I said that was a more crude gesture that rules out truth-plus-self-reference across the board. That gets back to the spirit of my original question so let me try framing it differently.
If I follow, you seem to think that the reason the 'meaninglessness solution' to the paradoxes does *not* require a technical model (or some such) is because it does not introduce any concepts that have an impact on logical theory, formal semantics, etc. Saying the Liar, et. al. are meaningless is in part to say that they are not the right kind of thing to apply logic to. So in effect, by cordoning off the Liar we get to keep standard logic and T-rules without further comment.
Here's one way of posing my question. Recursion theorists seem to think that Godel-coding affords a kind of self-reference which, in the presence of antecedently given predicates 'suitable to reason with' produces sentences that are also suitable to reason with. We don't rule out deductive reasoning about the Godel sentence 'I'm unprovable' just because it has the funny feature of 'Proof-Predicate-ineliminability'. We don't rule it out even when we discover that it compels us to accept the (classically uncomfortable) position that some deductively closed theories are incomplete. What has gone wrong with the dual thought that the Liar sentence, having similar provenance, must be similarly meaningful even though it compels us to accept inconsistent theories? Where is the analogy breaking down?
To put the point more simply: if you thing that meaningless sentences are the kinds of things that logic does not apply to (hence no need for a technical solution...) then how can you even reason about the Liar? If it really lacks content, according to you, how can you reason to conclusions like 'the Liar would be true if and only if it were false'?
Hey Colin,
"I now see the point about T-ineliminability, or what (I think equivalently) is usually called ungroundedness following Kripke."
For 99% of the time that I was writing my dissertation, I expressed my view by talking about 'grounding out' a la Kripke, but my experience has been that it introduces unnecessary confusion in some quarters. (For example, people who work on technically revisionary solutions in the great Kripke-to-Field tradition often assume that the meaning of groundedness is going to be given by a familiar sort of technical apparatus, and I've had people argue that there's some ambiguity there about which sentences count as 'grounded' w/o such an apparatus.) Since I've never heard anyone criticize Beall's "ineliminability" terminology on similar grounds, I'm just as happy to simply use that.
"We don't rule out deductive reasoning about the Godel sentence 'I'm unprovable' just because it has the funny feature of 'Proof-Predicate-ineliminability'. We don't rule it out even when we discover that it compels us to accept the (classically uncomfortable) position that some deductively closed theories are incomplete. What has gone wrong with the dual thought that the Liar sentence, having similar provenance, must be similarly meaningful even though it compels us to accept inconsistent theories? Where is the analogy breaking down?"
Well, first, I've never said that the Liar was meaningless because it compelled us to accept inconsistent theories. That would, first, be an odd fit with my central claim about it. Secondly, the context I'm often concerned with is arguing with dialetheists, where of course "it's meaningless because it leads us to inconsistency" would be hopelessly question-begging. I think it's meaningless because uses of the truth predicate (or the truth operator) are only parasitically meaningful--e.g. to say that 'snow is white' is true is to say something that doesn't mean anything above and beyond ascribing whiteness to snow--and sentences that (a) use the truth predicate (or the truth operator) and (b) have no sentence that does not do so from which to inherit their meanings never end up meaning anything at all.
Secondly, when it comes to 'Proof-Predicate-ineliminability' vs. truth-ineliminability, I'd say that the analogy breaks down if and because, when we apply the proof predicate P to some sentence S, "S" and "S is P" would seem to mean quite different things.
Finally....
"To put the point more simply: if you thing that meaningless sentences are the kinds of things that logic does not apply to (hence no need for a technical solution...) then how can you even reason about the Liar? If it really lacks content, according to you, how can you reason to conclusions like 'the Liar would be true if and only if it were false'?"
Well, that, happily enough, is the sole subject of Part II, which I just posted a few minutes ago!
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