A. B-san, may I ask you a question?
B. Please do.
A. Thank you. Are you an idiot?
B. That question is hardly of the intellectual calibre that I have come to expect from you, but I shall answer it nevertheless. No, A-san, I am not an idiot.
A. Are you entirely sure? I believe that I can demonstrate that you are indeed an idiot.
B. Are my trousers unbuttoned? Have I forgotten your birthday? If I have made some careless mistake you could tell me kindly rather than with insults.
A. Other than being somewhat old and ill-fitting, your trousers are fine. And my birthday is not for 3 months, as I believe you know. I do not have any such mistake in mind. Rather, I claim that I can demonstrate that you are an idiot using only this pen and paper. What is more, you will be forced by your own words to accept it. May I try?
B. I suppose so.
A. Very well. I shall write a sentence on this paper, and you must tell me whether or not you believe it.
B. What if I don’t know?
A. If you don’t know, then say you don’t believe it.
B. Hmm. It’s going to be one of those sentences which asserts its own falsity, isn’t it? Like that Cretan who said “all Cretans always lie”. Utterances like that can’t sensibly be called either true or false.
A. A good point, but my sentence is fully capable of supporting a truth value. Indeed, I shall attempt to persuade you that the sentence is true. And very likely I shall succeed. Nevertheless you will continue to insist that you do not believe it.
B. What? You say I will be convinced of your sentence’s truth, but at the same time I will refuse to believe it? That would indeed make me a supreme idiot.
A. Exactly! [Writes something down and hands it to B.]
B. [Reads] “Only idiots believe this sentence.”
A. So, do you believe it?
B. If I believe it, then I must be an idiot.
B. But I maintain that I am not an idiot. So, no, A-san, I do not believe this sentence.
A. That’s what I said when I first read it. And that’s what C-san and D-san said too. In fact, I expect your reaction is the same as that of any intelligent person.
B. I agree. Anyone who read that sentence and declared that they believed it would be a self-admitted idiot.
A. In other words, B-san, you are saying that only idiots believe that sentence.
A. Ok! Now read it again.
B. [Reads it again. Thinks.] Bollocks.
A. And B-san?
A. Your trousers are undone.