From November 3, 2011, “The intolerant antinomy revisited”
“If it’s what I think it is,” said Lenore, “it’s a sort of joke. A what do you call it. An antinomy.”
“An antinomy?”
Lenore nodded. “Gramma really likes antinomies. I think this guy here,” looking down at the drawing on the back of the label, “is the barber who shaves all and only those who do not shave themselves.”
Mr. Bloemker looked at her. “A barber?”
“The big killer question,” Lenore said to the sheet of paper, “is supposed to be whether the barber shaves himself. I think that’s why his head’s exploded, here.”
“Beg pardon?”
“If he does, he doesn’t, and if he doesn’t, he does.”
— David Foster Wallace, The Broom of the System
Sometimes I can’t get the thermos open. This is frustrating because: A) There is coffee in the thermos, and I want coffee; and B) I twisted the thermos lid shut myself, and thus it seems logical to expect that I should also be strong enough to untwist it myself.
This recalls a popular antinomy involving the idea of an omnipotent God. If such a being is all-powerful, it asks, then can this God create a rock so heavy that even He can’t lift it? (The omnipotent deity of this antinomy always seems to be masculine.)
Like Gramma Beadsman’s paradoxical barber, that’s an entertaining little semantic pretzel. If he can, he can’t, and if he can’t he can, etc.
But unfortunately most of the time this antinomy is invoked, the speaker doesn’t seem to realize, as Lenore Beadsman did, that it’s “a sort of joke.” They seem to think they’re saying something — neither I nor they can figure out quite what — about omnipotence or about God. But this little sort-of-joke antinomy is no more about God or omnipotence than Gramma Beadsman’s puzzle is about barbers or shaving. The big killer questions of such antinomies have nothing to do with whatever subjects they latch on to as pretexts. Those pretexts are incidental to their real subject — the inadequacy of language itself.
It’s tempting to try to answer such questions on their own terms. I sort of want to say that the barber shaves himself for the same reason that 1 is a prime number. But the point isn’t to try to answer such questions correctly, the point is that there cannot be a correct answer. These antinomies imitate the form of yes-or-no questions, but they’re actually neither-yes-nor-no questions semantically constructed as to make either, or any, answer impossible.
Such sort-of-jokes can be quite fun and the source of musings both playful and profound (see, for example, Lewis Carroll and Wittgenstein, respectively, and vice versa). But it’s less fun when the artfully deliberate nonsense of such antinomies is conscripted by those who mistakenly believe they are scoring points in some kind of debate.
As in, “Oh yeah, well if you’re so tolerant, how come you can’t tolerate my intolerance. Hah!”
As with the bit about the all-powerful God and the unliftable rock, the people citing the intolerant antinomy seem to have no idea that they’re not really saying anything at all about tolerance or intolerance, but merely providing yet another illustration of the elasticity and limits of language. They’re really just presenting another illustration of Russell’s paradox, the set of all normal sets, which Bertrand Russell himself illustrated with the example of the barber above.
I think the unwitting (or half-witting) invocation of the intolerant antinomy involves a more aggressive form of stupidity than the bit with the unliftable rock because tolerance is a much easier concept to understand than omnipotence. When you encounter someone who boasts of their inability to understand the concept of tolerance it’s difficult to imagine that they’re not just being willfully obtuse. Omnipotence, on the other hand, is the sort of transcendent concept that’s bound to force us up against the limits and inadequacy of language. (That’s what “transcendent” means, after all.)
Like most Christians, I believe that the Almighty is, you know, all-mighty. That means: A) I believe that God is omnipotent; and B) I cannot really comprehend precisely what that might mean.
To be honest, I don’t really spend much time trying to comprehend precisely what that might mean. “All-powerful” is not the attribute of God that ought to concern us most since it doesn’t seem to be the attribute of God that concerns God the most. “All-loving” — that’s the attribute that matters most when it comes to what God is actually doing. As handy as omnipotence might be, it’s nearly useless when it comes to redemption and reconciliation.
I try to remember that whenever my patience is tried by the gleeful morons congratulating themselves every time they mistakenly cite the intolerant antinomy as some kind of rebuttal of the virtue of tolerance. Reminding myself that love trumps power helps keep me from wanting to crush them beneath the Almighty’s unliftable rock.
Oh, and as for the thermos, I find running hot water over the lid for a bit usually does the trick.
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