Wednesday, April 6, 2011

Some Objections to the Meaninglessness Solution to the Liar Paradox, Part III of IV

My view is that, as my boy Willard Van put it, truth is disquotation. When I prefix the words 'it's true that' to a quoted sentence, the effect of what I've done is to remove the quotation marks. Moreover, I see no principled distinction between this way of ascribing truth to a sentence (quoting it within the larger sentence in which one applies the truth operator to it), or other standard ways of ascribing truth, like saying "that's true" in response to someone else's statement, or the more formal device of writing down a pair of numbered sentences like (14) and (15):

(14) Snow is white.
(15) Sentence (14) is true.

In all of these, the function of the truth predicate/operator is exactly the same.

A good analogy in contemporary informal English is "What he said."

Imagine the following, fairly mundane interaction:

An evolutionary biologist, Jane, is drinking at a bar with her boyfriend John (a humanities major with a shaky but more or less accurate grasp on her field) and her loveable-but-frustrating cousin Jack, a fundamentalist Christian (who's just ordering coca cola and bar nachos while his heathen cousin and the man she's living in sin booze up). At some point, Jack brings up evolution and runs through some creationist talking point about missing links in the fossil record or some such. Jane sighs, orders another drink and carefully runs through the scientific explanation of what Jack's talking about. In the end, both cousins stop talking and turn to John, who just tilts his head towards his girlfriend and says "What she said."

This is a normal and immediately familiar usage--note, BTW, that John's sentence isn't syntactically "well-formed", but it's meaningful all the same, "well-formed"-ness in natural language contexts not being necessary for, sufficient for, or even especially relevant t meaningfulness--and we all get what's going on here. "What she said" is a linguistic device John is using as a shorthand method of asserting exactly what Jane just asserted. He could be using it for a variety of reasons--most obviously, using this handy abbreviation is far easier than repeating the entire explanation Jane just gave, but it could also (in this case quite plausibly) be that he doesn't remember every detail of what he means to be asserting. Certainly, there's very little temptation here to think that John means anything above and beyond, or different from, what Jane said. The point of the phrasing is, in fact, to draw attention to the fact that he means to say exactly what, well, "she said."

The word 'true' has various advantages over its functionally kindred linguistic device 'what she said'--for one thing, one can use it on written sentences, and more tellingly, on sentences whose source is unclear--but the point, I think, is the same. Instances of "what she said" are presumably meaningful if the sentence it's applied to are meaningful and meaningless otherwise (John: "Colorless green ideas sleep furiously", Jane: "What he said"), and the same goes, I would argue for truth. The general principle is that truth talk is only *parasitically* meaningful. Prefixing "it's true that" to a *quoted* sentence has the effect of removing the quotation marks--i.e. "it's true that 'snow is white'" means precisely the same thing as "snow is white"--but putting "it's true that" at the beginning of a sentence already outside of quotation marks has no semantic impact at all. (It might add emphasis, but it doesn't change the meaning.) "(16) is true" has no independent meaning not supplied by whatever sentence (16) means. An obvious consequence of this view is that if "(16) is true" inherits no meaning from sentence (16), then it means nothing at all. Hence, if sentence (16) is "snow is white", "(16) is true" does nothing but attribute whiteness to snow, and if (16) is (16) is true, it means nothing at all. Putting a "not" in the mix is never, of course, enough to change a meaningless jumble of words into a meaningful one.

At the end of Part I, I considered one of the most worrying objections to this position. Isn't it manifestly possible to 'reason' about these sentences? Doesn't someone like me, who takes Liar sentences to be meaningless, come to this position on the basis of careful consideration of various other approaches to the paradox? Isn't part of the process of arguing for this solution going to be a matter of arguing against competing solutions, and won't that, in turn, be to a considerable extent a matter of arguing about "what follows" from various Liar sentences, in combination with added premises taken from a proposed solution? (For example: "You say that standard Liar sentences are meaningful but that they do not express propositions. What, then, about a sentence that says of itself that it does not express a true proposition? Surely, if it doesn't express a proposition at all, it doesn't express a true one, right?" or "I don't see how a gap theorist can get around the revenge paradox about a sentence that says of itself that it's either false or gappy" or "How does the dialetheist deal with a sentence that says of itself that it is just false and not true?") If one plays this game as well as anyone, doesn't that show that, like everyone else one grasps the meaning of the sentences in question? After all, isn't this game of generating unappetizing inferences from alternate solutions a matter of drawing out the entailments of the content of these sentences?

In Part II, I responded to this objection by pointing out that the same problem could arise for sentences that everyone takes to be meaningless, drawing out a scenario in which many people might infer contradictions from the sentence "Colorless green ideas sleep furiously" and ways that the hypothetical philosophical debate about this "Greenness Paradox" could closely mimic the actual philosophical debate about the Liar Paradox.

One possible problem here might have to do with distinctions among meaningless sentences. In the comments on Part I, ParisW suggested that there might be quantitative degrees of, or qualitatively different types of meaningfulness, and that different meaningless sentences might interact with logic in different ways. Now, I don't words in his mouth, and the line of thought would have to be developed a bit first anyway, but the general idea could be that it's not legitimate to pick out a meaningless sentence, show how it interacts with logic, and make sweeping generalizations about how Liars interact with logic or fail to do so if they are meaningless.

Now, personally I have trouble seeing how this could get off the ground--"means something"/"means nothing" look pretty clearly binary to me--but maybe the possibility of the "Greenness Paradox" is a consequence of "Colorless green ideas sleep furiously", despite its distinguished history as a stock example of a meaningless sentence, just isn't meaningless enough. How about "blorks geblork"? We could have the following conversation:

Person 1: "Blorks geblork!"
Person 2: "That's false."
Person 1: "So you think blorks don't geblork?"
Person 3: "That doesn't follow from what 2's point that it's not the case that blorks geblork. It could be that there are no blorks."

Clearly, there's something absurd about these three people going through the motions of reasoning about a combination of nonsense syllables. Equally, clearly, Person 1's gloss on Person 2's statement commits some sort of further mistake, correctly highlighted by Person 3's comment, and this further mistake is something that goes above beyond the basic category mistake of applying truth talk to a meaningless string of nonsense syllables and going on to "reason" about them.

Again, one might think this has something to do with degrees or kinds of meaninglessness. The string of nonsense syllables in question, after all, still has an apparent subject-predicate form, which is the entry point for all this.

Take a different example. Let's say I just sneezed. I've made a sound that doesn't sound at all subject-predicate-ish, and that no one who heard it and understood what it was would mistake for a claim about anything. Now, if some strange person did say that my sneeze was "true", a tempting way to correct them would be to say, "no no no, it wasn't true or false. Sneezes are just the wrong kind of thing to be able to count as either."

Once we combine a natural way of symbolizing the first sentence of my "correction" with two banally orthodox assumptions about truth and logic, we have all the ingredients of what we can call the Sneeze Paradox:

Premise 1: For every P, T(P) iff P..
Premise 2: For every P, T(P) or F(P).
Premise 3: Ben's sneeze (S) is neither true nor false. [~T(S) & ~F(S)]

By a series of relative simple steps I'll leave as an exercise for the reader, we get to:

Conclusion: S & ~S

One could imagine an (unlikely) scenario where no one ever figured out what was wrong here, and dialetheists used the Sneeze Paradox to argue for true contradictions, gap theorists used it to argue against Bivalence, sophisticated logicians with mostly orthodox premises found all kinds of ingenious ways of twiddling with or conceptually re-thinking the rational role of the logical architecture to avoid the conclusion and so on. Inevitably, various participants in this debate would make various reasoning mistakes.

Of course, we know that the at-bottom mistake underlying the whole debate is a nonsensical category mistake, not a factual mistake of any kind. If my statement "my sneeze wasn't true or false" is true, it's because I don't mean to literally assert the negation of the disjunction of the claim that it is true and the claim that it is false. If I'm talking sense in any sense, it's because what I really mean by the sloppy shorthand "it's not true or false" is "it's not the kind of thing to which 'true' and 'false' can be meaninfully applied, which is a different kettle of fish entirely. Still, on he way to realizing this, we'd doubtless want to nit-pick the arguments of the normal participants in the debate, catch them out on 'errors.'

So, how can we possibly conceptualize these 'errors'? And won't any analysis we give of the nature of these apparent "errors in reasoning" inevitably spawn new revenge problems for the meaningless solution, along the lines of (17)?

(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.

To which all I can say is, stay tuned for the exciting conclusion of our quadrilogy to find out!


Jonas said...

This might be a really silly question, but I cannot figure out if it actually is, so here goes...

Take the following sentence (Q):

(Q) 'This sentence is surrounded by quotation marks' is true

What do disquotationalists say about such sentences?

Ben said...

Hi Jonas,

Nice example. I like that.

Off the top of my head, I guess I'd say that the point about 'removing quotation marks' is converting mention to use. Normally, if S is some sentence, sentences of the form "'S' is X" mention S but don't use it....unless X is "true."

Now, in the case of your sentence Q, it seems like it's already in 'use' mode, despite the quotation marks. Or, put differently, the quotation marks are part of the sentence itself rather than a device allowing it to be merely mentioned. To attribute truth (or anything else) to it, I'd think you'd need an extra set of quotation marks, e.g. the sentence:

'"'This sentence is surrounded by quotation marks'" is a sentence which is surrounded by quotation marks.'

(Granted, English conventions about quotation marks make that look funny, since they aren't designed for infinite iterability the way parentheses and brackets in logical languages are.)