An Idiotic Paradox

6th June, 2011

A.   B-san, may I aks 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.

A.   Precisely!

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.

B.   Yes!

A.   Ok! Now read it again.

B.   [Reads it again. Thinks.] Bollocks.

A.   And B-san?

B.   Yes?

A.   Your trousers are undone.


Categories: Logic, Nonsense | Permalink

7 Responses to “An Idiotic Paradox”

  1. From Minnie:

    June 6th, 2011 at 7:39 pm

    I just discovered that my trousers are undone. Perhaps we could found the undone trousers club!

  2. From JAM:

    June 6th, 2011 at 7:47 pm

    Bollocks indeed. There’s no getting out of that one.

  3. From Impress your friends with Richard’s paradox* « Blunt Object:

    July 28th, 2011 at 7:45 pm

    [...] An idiotic paradox (Richard Elwes) [...]

  4. From Jerzy:

    August 10th, 2011 at 8:10 am

    It would be only fair to add that this paradox was invented by the famous logician Raymond Smullyan.

  5. From Richard:

    August 11th, 2011 at 8:42 pm

    Really? That’s entirely possible, but I’ve not read it in his work (or have forgotten). Have you got a more specific reference?

  6. From Flippy Doodle:

    September 14th, 2011 at 4:08 pm

    Damn, I feel like a total idiot now!

    But this is fantastic, thanks for posting this.

  7. From alex:

    April 2nd, 2012 at 3:01 am

    how about this for a world wide blind spot
    i typed in “compulsive laughing robot” into google
    answer from google “no results”
    of course it is not logical to us

    have a look (the void may have been filled since i sent this to u) :)

    this is a way of using google for fun to see what people are not saying (textually)

    larry here is another one (but this just sounds funny)

    buddha=godels incompleteness theorem

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