In one episode, Homer asks Ned Flanders a question which is a parody of a well-known version of the omnipotence paradox, known as the stone paradox ("Could an omnipotent being create a stone so heavy that even he could not lift it?"):
The paradox is about a contradiction. To quote from Wikipedia: "If a being can perform any action, then it should be able to create a task that it is unable to perform. Hence, this being cannot perform all actions. On the other hand, if this being cannot create a task that it is unable to perform, then there is something it cannot do." The part before the "On the other hand" is already sufficient to see the contradiction and the paradox that ensues: a being is omnipotent if and only if it/he/she is not omnipotent. Or to put this differently still, if you can do anything you want, it means you can also not do anything you want. An all-powerful being must by necessity have restricted powers.
In another episode of The Simpsons, in which Homer takes part in a prison rodeo (don't ask), gets severely injured by a bull and is then taken care of in prison so that he can go home soon, we have the following exchange between Homer, his wife Marge and a prison warden:
Marge: How's your back, Homey?
Homer: I can't complain. [indicates a sign which reads, "No Complaining"]
Warden: Ah, that's for the prisoners. You can complain all you want.
Homer: Oh, God, my back! It hurts so much! And my job is so unfulfilling!
(cited from http://www.simpsonsarchive.com/episodes/CABF05.txt)
There is no true paradox here in Homer's "I can't complain" and his pointing at the "No Complaining" sign, but it nevertheless come close. If there's such a sign, the person this sign applies to cannot complain. But if you cannot complain, in the sense of not being allowed to, you have every reason to complain, being deprived of a basic right to vent your pain, emotions and, on top of that, your frustration at not being allowed to complain about this lack of permission, if you can still follow. So, if you can't complain, it's definitely not the case that you can't complain. This has a whiff of paradox, and it would be undeniably paradoxical if it weren't for the fact that can('t) is not used with the same basic meaning. If you can't complain, as per a fictitious "No Complaining" sign, there is a lack of permission. If you say that you can't complain, as we do in common usage to convey the idea that everything is reasonably okay, we use this modal verb in a rather different (though not wildly different) sense, namely that there's nothing about your situation that licenses you to complain with any justification.
My colleague Ilse Depraetere calls this latter kind of meaning "situation permissibility". Lack of permission ("I'm not allowed to complain") is not quite the same as absence of situation permissibility ("The circumstances are such that my complaining cannot be allowed to happen"). This can be described as a difference between small scope and wide scope modality:
My colleague Ilse Depraetere calls this latter kind of meaning "situation permissibility". Lack of permission ("I'm not allowed to complain") is not quite the same as absence of situation permissibility ("The circumstances are such that my complaining cannot be allowed to happen"). This can be described as a difference between small scope and wide scope modality:
I (not-possible(complain)) vs. not-possible(I complain)
For there to be a real paradox, there has to be no ambiguity in the predicates that make up the contradiction of the general form "if X does Y, then X doesn't Y". It should be about the same kind of (not) doing Y.
In the second example from The Simpsons, the scope difference is subtle, perhaps so subtle that we fail to appreciate the difference. After all, if I don't have the permission to complain, the net result is the same as when the situation of me complaining is not permissible: most likely, I will refrain from complaining in either case. For language users who fail to see this difference, the second example from The Simpsons should contain a paradox as well. The fact that we do perceive a strong comical contrast between something at first sight positive (the everyday sense of I can't complain) and then something negative (complaining is not allowed) without getting a sense of paradox is proof that the pragmatic meaning of I can't complain ('I'm fine'), as a kind of idiom, prevails over its literal meaning ('me complaining is a situation which is not in order here'), which may be too close to the meaning of the "No complaining" sign to prevent paradox from flooding in.
Of course, Homer only has the "No complaining" meaning in mind, so there can be no paradox in his utterance and what he's simultaneously pointing at. My point is that there could have be a potential paradox between the oddly prohibitive "No Complaining" sign and the way Marge first understood Homer's utterance, I can't complain. But there isn't really.
In the second example from The Simpsons, the scope difference is subtle, perhaps so subtle that we fail to appreciate the difference. After all, if I don't have the permission to complain, the net result is the same as when the situation of me complaining is not permissible: most likely, I will refrain from complaining in either case. For language users who fail to see this difference, the second example from The Simpsons should contain a paradox as well. The fact that we do perceive a strong comical contrast between something at first sight positive (the everyday sense of I can't complain) and then something negative (complaining is not allowed) without getting a sense of paradox is proof that the pragmatic meaning of I can't complain ('I'm fine'), as a kind of idiom, prevails over its literal meaning ('me complaining is a situation which is not in order here'), which may be too close to the meaning of the "No complaining" sign to prevent paradox from flooding in.
Of course, Homer only has the "No complaining" meaning in mind, so there can be no paradox in his utterance and what he's simultaneously pointing at. My point is that there could have be a potential paradox between the oddly prohibitive "No Complaining" sign and the way Marge first understood Homer's utterance, I can't complain. But there isn't really.
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