Wednesday, August 11, 2010
My Take on the Liar Paradox (Part II of IV)
In Part I, I provided what I take to be a principled, non-ad hoc motivation for what, in In Contradiction, Graham Priest refers to as the “heroic solution” to the Liar Paradox. I claim that sentences of the type “this sentence is true”, “this sentence is false” and so on are meaningless.
Many people are so initially confused by this proposal that they try to charitably interpret it away. Early last year, while I was discussing my dissertation with some faculty members in my PhD program who were not on my committee, one junior professor wrinkled his forehead and said, “wait, you don’t think that the Liar is meaningless the way that ‘colourless green ideas sleep furiously’ is meaningless, do you?”
In the same spirit, in his book Saving Truth From Paradox, Hartry Field (who, a couple of years after that book came out, was on my dissertation committee!) says that those who claim that sentences like the Liar are meaningless must be using the term meaningless “in some special technical sense” that’s distinct from ordinary use of the term, and that, as such, such talk probably amounts to a confusing way of formulating something like his own “paracomplete” approach to the paradoxes.
So, to be clear, no, I don’t mean ‘meaningless’ in some non-standard way. I take sentences which (a) seem to say of themselves or other sentences that they are ‘true’ (or ‘false’ or whatever) but which (b) can’t be paraphrased into some set of base-language sentences which don’t use ‘true’ or its negation, as (c) literally meaningless, in precisely the same way that ‘colourless green ideas sleep furiously’ is meaningless. “‘Snow is white’ is true” doesn’t mean anything above and beyond what “snow is white” means, and “this sentence is true” doesn’t mean anything at all.
A major factor that seems to drive the incredulous stares often directed at meaninglessness solutions to the paradoxes is the notion that competent speakers of natural languages are infallible about questions of meaningfulness. (We could call this the Strong Principle.)
Now, one could claim that the underlying principle behind the incredulous stares is not the Strong Principle, but just the notion that it’s very unlikely that ordinary competent speakers could be wrong about issues of meaninglessness, and that we should have a strong presumption in favor of their initial intuitions. (We can call this the Weak Principle.)
Now, I actually agree with the Weak Principle, but I don’t think it explains the strength of the incredulous stare reaction meaninglessness solutions often receive.
Anecdotally, it is often the case that people react with incredulity to the claim that Liar-like sentences could be meaningless despite not being sure where to object to the reasoning that delivered that conclusion, or even having originally assented to that reasoning. If it’s very un-common for Croatians to drink single malt whiskey, and our strong default assumption for any given Croatian is that they don’t do so, but you notice a half-empty bottle of Laphroaig on Emil’s kitchen table and you smell peat on Emil’s breath, the strong statistically-based assumption becomes irrelevant. If one acknowledges the possibility of error about meaningfulness by competent speakers but finds it unlikely and subscribes to a strong default assumption against it, and then one is confronted by a good argument that a certain category of initially meaningful-seeming sentences are meaningless, then the probability becomes irrelevant.
The Strong Principle, on the other hand, seems to be trivially easy to falsify. The philosophers of the Vienna Circle were surely all competent speakers of the German language, but they mistakenly held many perfectly meaningful German sentences about various metaphysical topics to be literally meaningless, nonsense, “like music,” etc. Linguistically competent Wittgensteinians have incorrectly held contradictions to be meaningless rather than false. I flatter myself to think that I speak, read and write reasonably passable English, but, if the majority opinion on this issue is correct, I’m mistaken about the meaningfulness of Liar-like sentences.
In fact, the fun part of all of this is that, for all of the debates just mentioned, whichever side turns out to be right, given the disagreements, some otherwise competent speaker must be making a mistake about meaningfulness!
Maybe, however, the Strong Principle is implausibly strong, but something stronger than the Weak Principle is still plausible. Given standard, orthodox views on all the subjects just mentioned, one could propose the Still Fairly Strong Principle, that, while false negatives of meaningfulness are possible, cases where ordinarily competent speakers mistakenly take meaningful statements to be meaningless, false positives are still impossible.
I’d argue that this proposal is falsified by what I think of as “bored dinner guest”-type examples. Imagine that two people, Jack and Jill, are at dinner. Jill goes on at length about subjects that Jack is bored to tears by, and, after a while, Jack completely tunes out. He contributes nothing to the conversation except for the occasional “yeah,” “I agree” or “that’s true,” dictated by the rising and falling of
Jill’s voice and the appropriate pauses. After a while, Jill catches on. To test him, she starts emitting a string of nonsense syllables like “glork bork de glork”, but she keeps her tone normal, and makes sure her voice rises and falls in the normal way. At the appropriate pause, Jack says “oh yeah, that’s true.”
Now, Jack has no idea whether he just “that’s true”-ed a true statement or a false one, so he doesn’t know whether his statement was true or false. He does, however, surely assume that it was one or the other, that he at least said something meaningful.
But, to paraphrase our previous President, if “it’s true that ‘glork bork de glork’” isn’t meaningless, then meaninglessness has no meaning. Jack is an ordinarily competent speaker of English who is mistaken about the meaningfulness of *his own* utterance. False positives are indeed possible.
(Moreover, remember, especially on standard deflationary stories about truth, such “blind endorsements” constitute one of the most important linguistic purposes for which the truth predicate exists.)
Now, one could water down the Still Fairly Strong Principle to the Not Terribly Weak Principle:
False negatives are possible across the board, but false positives are only possible when the competent speaker in question isn’t aware of the content of the sentence in question.
Now, to canvass a broad range of approaches here, I’ve left that word “content” intentionally ambiguous. If by “content”, one means something merely syntactic, such that “knows the content of a sentence” just means “is aware of which words appear in the sentence”, then the Still Not Terribly Weak Principle looks awfully implausible.
For one thing, I think an awful lot of linguistically-but-not-epistemically-competent people could be suckered into believing that “colorless green ideas sleep furiously” was not only meaningful but true…for example, Deepak Chopra could tell them that quantum physics had proved that colorless green ideas did that.
In response, one could interpret “knows the content” in a stronger, semantic way, where “knows the content” means “grasps the content.” It may be possible to fool people in various ways into thinking that “colorless green ideas means something” but it’s impossible to fool them into actually knowing what it means, because there’s nothing there to know.
Fair enough, but at this point deploying the (now entirely trivial) principle which we are still referring to as the Still Not Terribly Weak Principle against meaninglessness solutions to the Liar Paradox would utterly and transparently beg the question. No one would deny that, of course, if competent speakers (or, for that matter, even normally wildly incompetent speakers!) grasp the meaning of a sentence they take to be meaningful, their belief that it’s meaningful can’t be wrong. To base on objection to meaninglessness solutions on this, however, is to simply assume the precise bone of contention, which is whether Liar-like sentences have a content to grasp.
Perhaps, somewhere along this spectrum, there’s some remotely plausible principle that’s relevantly stronger than the Weak Principle, and as such justifies the “well, that’s just obviously ridiculous” unargued brush-off that some people use to refute meaninglessness solutions. If anyone has any candidates they’d like the propose in the comments section, I think that might be interesting.
Meanwhile, of course, showing that it’s possible for competent speakers of English to be mistaken about the meaningfulness of syntactically innocuous sentences formed out of English words is quite a different thing from showing that, in the case of the particular category of sentences under consideration, they actually are mistaken. In Part I, I sketched out an argument, but we need more than that. We also need an error theory to explain why many people have such a strong mistaken intuition. This obligation becomes more pressing as the number of mistaken people rises. If one ordinarily mathematically competent reasoner gets the wrong result for a simple algebra problem, then “he didn’t have enough coffee that morning” may be a plausible error theory. If, on the other hand, out of the thousands of ordinarily mathematically competent reasoners to have tried their hand at the problem, all but one have gotten the wrong answer, we need something a bit more robust to explain this away.
Now, many people make claims from the armchair that most speakers have the intuition that Liar-like sentences are meaningful, but I’ve never seen any concrete empirical evidence to back this up. (This has always sounded like a job for x-phi to me.) In fact, anecdotally, my impression is that, on first contact with the Liar and its ilk, some non-philosophers will respond in a way that indicates what may be precisely the opposite intuitions, having conversations like this one….
“This statement is false.”
“Wait, what statement is false?”
“Well, the one I just made.”
“Yes, but what did you say?”
“I said that what I said was false.”
….and so on. None of this, of course, adds up to a good reason to suppose that Liars are meaningless, but it might reflect a suspicion that this is the case.
Certainly, though, whatever the proportions might turn out to be at some point in the future when we’ve collected some empirical evidence, there’s no denying that plenty people, philosophically trained and otherwise, have the meaningfulness intuition, certainly enough that “Priest and Field don’t drink enough coffee”-type explanations won’t cut it.
I think one piece of the puzzle (although, to be clear, only a secondary one) is a matter of training. Intuitions are formed, changed and molded by one’s educational experiences. The people whose intuitions about the Liar we know the most about are professional philosophers. The Liar is an ancient and venerable philosophical difficulty, and even professional philosophers who have never thought in depth about it at least have years under their belt of being vaguely aware of it in a context in which one of the fundamental background assumptions to get the difficulty off the ground is that it is meaningful. (Moreover, as good rhetoricians have known since time immemorial, it’s often easier to influence people with the opinions you never get around to explicitly stating. Think about Mark Antony’s funeral speech in Shakespeare’s “Julius Caeser.”) So people’s intuitions are shaped by the shared assumptions of the people around them. Think about the way that, in the other direction from the case at hand (non-existence solutions to Russell’s Paradox being as popular as they are unpopular when it comes to the Liar), people who work on set theory, and who initially have ‘naïve’ intuitions, often claim to have new intuitions about what sorts of things sets are and which might exist, formed as a result of the experience of exclusively working in the cumulative hierarchy of ZFC or some similar system. So that’s surely part of the story, and I think it accounts for some of the strength and self-assured fervor of meaningfulness intuitions among professional philosophers.
For many reasons, however, this can only be a small part of the overall story. After all, how do we explain how meaningfulness assumptions initially came into the picture? Besides, it’s surely plausible that a great many people have the meaningfulness intuition on first contact with the Liar “in the wild,” even in eccentric circumstances where it isn’t presented to them as a famous and interesting puzzle.
I think that the first thing to notice is that odd and unusual sentences involving self-reference are usually meaningful—indeed, they’re usually obviously and unproblematically true or obviously and unproblematically false. Consider cases like...
“This sentence has seven words in it.”
When it comes, however, to sentences whose truth-value is utterly and stubbornly inaccessible to us, we usually have no reason to doubt that they are meaningful and that they thus have truth-values. Consider “Alexander the Great’s maternal grandmother’s paternal grandfather once had a splinter in his thumb at some point during the month after his sixth birthday.” Given, among other problems, the absence of time travel, no one has the slightest idea of how to find out whether this is true or false, but this doesn’t (and shouldn’t!) make us question whether it has a semantic content and that this content either lines up with the facts or fails to.
Finally (although it would certainly be possible to go on) the Liar is a syntactically “well-formed” sentence. Now, it’s easy to show with examples that being “well-formed” is neither necessary nor sufficient for being meaningful, and I’m somewhat inclined to think that the use of the phrase “well-formed” to describe natural language sentences relies on an exaggerated, idealized and un-helpful analogy between natural language and formal logical “languages,” but let’s put that to one side and acknowledge that sentences that are “well-formed” (i.e. composed entirely of normal natural language words, arranged in a way that conforms to grammatical rules, etc.) are at least less likely to turn out to be meaningless jumbles of words than other sorts of utterances, and that most of the grammatically innocuous assertion-style combinations of words we have cause to run into in the ordinary course of things are meaningful.
At this point, we can see that the Liar and its ilk sit at the intersection of several categories of sentences such that the overwhelming majority of members of each category are meaningful. It is, then, fantastically unsurprising that most people’s initial intuitive reaction is that it is meaningful. (If, indeed, this turns out to be the case.) Moreover, even when subjecting that intuition to critical scrutiny, it’s perfectly rational to apply a bit of simple probabilistic inference here and argue that, all else being equal, it’s reasonable to infer that a sentence that participates in a lot of categories of typically-meaningful sentences is itself meaningful.
All else is, in this particular case, simply not meaningful, as established by the argument from the disquotationalist principle that quotation marks and ‘is true’ don’t jointly add anything to the content of a sentence to the conclusion that a sentence that attempts to apply truth talk to itself won’t be meaningful. This is a substantive discovery in the course of reasoning about difficult problems, not something that one would expect to be immediately pre-reflectively obvious.
Coming up next time: