Saturday, April 02, 2011

Liar statements are about as true as not

This post is the second part of Vaguely True Liars.

Things are usually described well enough, for some obvious purpose. E.g., if something is obviously blue, then we might call it ‘blue’ when referring to it. If, given a different object, some other description sprang to mind, well, maybe the object wasn’t blue. Or perhaps it was blue, but something else about it was more apposite. Another possibility is that it was as blue as not, however, because colours don’t 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; but of course, colours that appear identical will both be blue enough to count as blue if one is. So there’s no such dividing line; rather, there are colours that are vaguely bluish. Intuitively, ‘that’s blue’ said of such colours would be vaguely true. It would not be true enough to count as true, but being roughly as true as not, nor would it be more than vaguely false.

There are two basic logical possibilities, i.e. true, or not. Statements are true insofar as they describe how things are, as opposed to how they aren’t. And when a description isn’t true enough, we can usually replace it with a more detailed description. E.g. we can replace ‘that’s blue’, when it’s vaguely true, with ‘that’s vaguely bluish’. And we don’t always have to make things so explicit, because we naturally focus upon the pertinent elements of truth in what’s being said (or perhaps upon some obvious falsity). Indeed, that may well be why we have the concept of truth (and that of negation) [i]. Perhaps it’s also why we fall for the Liar paradox.

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. So you may well wonder if I really said anything, with my Liar utterance. But if not, then surely you would have found my utterance incomprehensible, rather than paradoxical, and so I think that the meaning of my utterance must have been fairly clear. It seems to me that I was saying that what I was saying wasn’t a good enough description of itself for it to count as simply true. Now, since it was nothing if not self-contradictory, it wasn’t describing itself very well. But therefore it seems to have been describing itself quite well after all. Still, perhaps its self-description was almost good enough to count as simply (or absolutely) true, but its self-contradictory nature meant that it fell just short enough to avoid paradox.

Much as ‘is heterological’ had to be as heterological as not, my Liar utterance seems forced to be about as true as not. I say ‘about’ in view of the underlying imprecision of natural language (and presuming more accuracy could lead to a ‘revenge’ paradox that would take us back to this position anyway). The paradoxical reasoning rules out the non-vague extremes, but it being vaguely true that what I said was not true implies only that what I said was vaguely untrue – vaguely false (since I was making an assertion) – which coheres well enough with it being vaguely true for there to be no more contradiction. And this resolution also explains why my utterance seemed true when thought of as false, and vice versa. By analogy, if you were given something blue-green, for example, you might wonder whether it was really more green than blue. But if it’s roughly as blue as not, then it would look bluer as you postulated it amongst – and hence saw it in your mind’s eye against – various shades of green. The contrast would enhance its bluishness. And if you thence thought of it as possibly blue, it would similarly seem not to be.

You may be wondering what exactly the element of truth would have been, were my statement vaguely true. Well, it would also have been vaguely false, so it would have been vaguely true that it was false. So we might say that the element of truth was that there was an element of falsity (and vice versa) [ii]. But more precisely, I’m suggesting that my statement wasn’t describing itself very well, that it was neither true enough to count as simply true, nor sufficiently false to be less than vaguely true. It may well have seemed untrue (if true) and then true (if untrue), but that was while those two inaccurate descriptions were being each other’s context. My statement had only the one context of its utterance. And it must have been about as true as not, if the alternatives are paradoxical. (To be continued.)

[i] The more usual reason given for why we have the concept of truth is that it allows such sweeping claims as ‘everything the Pope said was true’. For more on that reason, see John Collins, ‘Compendious Assertion and Natural Language (Generalized) Quantification: A Problem for Deflationary Truth’, in Cory D. Wright and Nikolaj J. L. L. Pedersen (eds.), New Waves in Truth (Basingstoke: Palgrave Macmillan, 2010), 81–96.

[ii] Elements of truth and falsity are often propositions. But it might be argued that Liar sentences express no proposition, in their paradoxical contexts; and doubts about emphasising propositions have, for example, been raised by W. V. Quine, Philosophy of Logic (Englewood Cliffs: Prentice-Hall, 1970), 8–13.

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