By Jon Cogburn
One of the benefits of being a philosophy professor is that there's never any trouble with playing Opposite Day with your kids. This is the game where the world has been transformed such that English (insert your language here) is now an idiolect where every sentence means "the opposite" of what it does in English. Most kids will play this at the lexical level, trying to come up with antonyms, e.g. "Look down at the ground!" instead of "Look up that the sky!" But this is a mug's game, at the level of your kids' art. Most words don't have "opposites." What's "the opposite" of bird? Cold-blooded invertabrate mammal who lacks feathers, wings, and beak?
But if you're a professor of analytic philosophy you've had your nose rubbed in so much Frege, Russell, and Quine that all you have to do is go sentential. Instead of saying "You mustn't look at that cold-blooded invertabrate mammal who lacks feathers, wings, and beak" all you have to say is "It is not the case that you should look at that bird." Sentential negation FTW.
Unfortunately though, if you've taken enough philosophy, then you start to notice a systematic problem with Opposite Day. At some point one of the players will invariably get flustered and say something to the effect of "O.K. It's not Opposite Day anymore." But of course, if it's Opposite Day, then the sentence that it is not the case that it is Opposite Day merely means that it is Opposite Day. Note that "It is not Opposite Day" is pragmatically analytic in the same way that "I am here" is. It is true whether it is Opposite Day or not. If it's not Opposite Day and you utter it, you are uttering something true. If it is Opposite Day, then (given what Opposite Day does to meanings) you are also uttering something true.
And of course "It is Opposite Day" is always false for the same reason. If it's not Opposite Day, the sentence is clearly false. But if it is Opposite Day, then the sentence means what we mean in non-Opposite Day English when we say "It's not the case that it's Opposite Day."