Tuesday, January 25, 2011

Liars, Divine Liars, and Semantics revisited

Divine Liar arguments aim to show that there’s no omniscient being—that no one knows all that’s true—in the following way. Suppose I say “No omniscient being knows that what I’m now saying is true.” If (as I believe) no one is omniscient, then no omniscient being exists, to know anything. So in that case, what I said was true. What I said was therefore an assertion, whether it was true or not. And if it wasn’t true—if it’s not the case that no omniscient being knows that what I said was true—then some omniscient being knows that what I said was true, despite it not being true, which is impossible (knowledge being of truths). So I asserted a truth; and so either that was a truth that some omniscient being doesn’t know, which is also impossible, or else there’s no such being.
 ......However, resolutions of the Liar Paradox might show that such arguments are invalid, e.g. according to Daniel J. Hill (2007: ‘The Divine Liar Resurfaces’, The Reasoner 1(5), 11–12) and my earlier article (2008: ‘Liars, Divine Liars and Semantics’, The Reasoner 2(12), 4–5). So, suppose I say “What I’m now saying isn’t true.” If what I said was true then, as I said, what I said wasn’t true. Does it follow that what I said wasn’t true? The paradox is that if so, then since that’s what I seem to have said, I seem to have said something true. The resolution defended earlier by me (2008) takes my utterance to have been meaningless, so that I didn’t really say anything. But we may then wonder how it was that it seemed so clear what my utterance would have meant had it been true; and my Divine Liar utterance was even more obviously meaningful. Another popular resolution would regard my Liar utterance as equivocal, with the word ‘true’ naming many different predicates in Hill’s (2007) Tarskian hierarchy. But formal languages can only be defined via natural language; and my informal Divine Liar utterance wasn’t obviously that equivocal.
 ......Questions of truth are essentially questions of how well our words are describing the world. So insofar as my Liar utterance wasn’t meaningless, it was asserting that it wasn’t describing itself very well, not well enough for it to have been true. And since it was nothing if not self-contradictory, it certainly wasn’t describing itself very well. But therefore, in view of what it was asserting, it seems to have been describing itself quite well after all. Was it describing itself well enough for it to count as true? I’m reluctant to call it ‘true’ as follows. If it was true because it wasn’t, then it was true and not true, but surely something’s only not some way if it’s not the case that it is. Nor do I want to say that it was neither true nor not true, as that’s just to say that it was not true and also true. Nevertheless, my utterance wasn’t describing itself very well, and was therefore describing itself quite well; so perhaps it was only partially true. If so then calling it either ‘true’ or ‘not true’ would both be inaccurate, would both be only partially true.
 ......We naturally focus upon whatever truth we can find in what people say, or upon an obvious untruth. And things are usually described accurately enough for some obvious purpose, or not accurately enough. But would it be unrealistic to think of truth (descriptive accuracy) as a matter of degree? The classic example is that of Vann McGee (1991: Truth, Vagueness, and Paradox, Hackett, 217): If “Harry is bald” is true insofar as Harry is bald, ‘true’ should be at least as vague as ‘bald’. And quite generally, why should we believe that our words are much better defined than our purposes have required them to be? Maybe natural language has a ubiquitous—since usually unobtrusive—vagueness. (That would explain why the discovery of a contradiction so naturally triggers an attempt to clarify our terminology.) And in particular, the Liar Paradox might be revealing this ordinarily obscure vagueness of ‘true’. That’s because if my Liar utterance was only partially true, then it would follow from what I said only that it was also partially not true, which clearly coheres with it being only partially true. There’s no inconsistency—no more paradox—and it seems that much the same could be said of any Liar sentences.
 ......And if that is how the Liar Paradox should be resolved, then my Divine Liar utterance would have been only partially true if there is an omniscient being. My Divine Liar argument was therefore fallacious, because arguments should have premises that are unequivocally true enough to count as true under all relevant hypotheses. But if you asked an omniscient being whether my Divine Liar utterance was true, she might say that it contained an element of truth. That might be a more informative—more true and less misleading—answer than a simple ‘yes’ or ‘no’.
 ......Similarly, the best answer to the question “Is this colour blue or not?” could be to say that it’s vaguely bluish. Ordinary objects are almost always either blue or not, but colours don’t really divide into those that are blue and those that aren’t. On the two sides of any such line, between the blue and the other colours of some spectrum, would be colours that were indistinguishable. So there’s no such division; and so there’s some colour of which, rather than saying that it’s blue, or that it isn’t, we ought to say that it’s bluish. Note that such a colour might look blue against a background of colours that weren’t blue, or even if you just wondered whether it belonged to that class of colours, and so postulated it amongst them (cf. what we find paradoxical about the Liar Paradox).
 ......Incidentally, some formal work on ‘true’ as a vague predicate is well described as Fuzzy Logic.

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