It's the barber that shaves all men (and only men) who don't shave themselves. Who shaves the barber? He can't shave himself, because he can't shave men who shave themselves. Similarly, he can't not shave himself, because then he falls into the class of men he has to shave.

So, if the octopus wearing the nametag starts out touching itself, then it falls into the set of octopii it shouldn't touch, so it stops touching itself, thus becoming an octopus it should touch, so it touches itself, thus becoming an octopus it shouldn't touch ... etc.

jai.
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