Sunday, October 21, 2012

Revenge revisited

The obvious resolution of the Liar paradox is that such self-descriptions as “this claim is not true” are as true as not. That resolution is obvious because it follows immediately from the problem, which is that insofar as they are not true, such claims are true. That is how the problem should be expressed, rather than as paradoxical biconditionals, if truth might be a matter of degree. And if a uniformly coloured object is as blue as not, then prima facie “the object is blue” is as true as not, so that is a prima facie logical possibility. Indeed, since the Liar paradox is a paradox, its less obvious resolutions are all very implausible, and so it is itself an indication that truth is in general a matter of degree.
......But, there is a fly in the ointment. What about “this claim is not even as true as not”? Were that claim as true as not, it would be false that it was not even as true as not. That is the revenge problem for this resolution. The problem is that insofar as the revenge claim is at least as true as not, it is false. But it follows that, while it is a bit more false than true, it is still about as true as not. So where is the problem? The revenge claim is almost as true as not. Now, if we use “vaguely true” to mean about as true as not, then we have another revenge claim, “this claim is not even vaguely true”. Insofar as that claim is vaguely true, it is false. It follows that it is as false as it is vaguely true, though. So this claim is just a bit more vaguely true. Again, where is the fly?
......It is trapped in the bottle of ointment, loudly buzzing. The buzz is that it is clearly not the case that “this claim is not true” is true. Were it true, it would be as it says it is, it would not be true. So it is not true. Even if it is as true as not, it is still not true enough to count as simply true. And furthermore, if “this claim is not even vaguely true” is vaguely true, then it what it claims is simply not true. How could it help to talk of the more vaguely true when “vaguely true” is such a vague term? Or so the buzzing goes. But, it is precisely because “vaguely true” is vague that there is no contradiction. The buzzing is understandable, but it does not spoil the ointment. It is understandable because we tend to imagine that things are black-and-white when we try to think logically.
......Consider the uniformly coloured object that is, in some contexts, as blue as not. Of course, blue is not normally a matter of degree. Oxford blue is deeper, not bluer, than Cambridge blue. “Oxford blue is blue” is not truer than “Cambridge blue is blue”. But, as greenish blue shades into bluish green there is bound to be a colour that is about as blue as not. There would otherwise be a blue colour that was the same colour as a colour that was not blue. And of course, a blue-green object will in some contexts look blue, e.g. when surrounded by red balls. But our object is in a context where it is as blue as not, so it does not look very blue. So I do not want to say that it is blue. If anything, I want to say that it is not the case that it is blue. But tempted as I am to say that it is not blue, the fact is that “the object is not blue” is, like “the object is blue”, only as true as not.

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