My friend asked the following and we were unable to figure out the type of paradox it constitutes :

Name the paradox which means that - if I answer this question, the question will be invalidated.

For example : Could you name 3 things that only you know about yourself.

We looked up on the wiki without any luck.

• Some form of performative contradiction but I'm not too satisfied with this answer myself. Sep 8, 2014 at 12:57
• You could say it's a variation on Russell's barber paradox, but that doesn't really agree with the example. But the rule and the example are not identical (latter is much more specific as a type) Sep 8, 2014 at 13:17
• Explanation about the example - as soon as I tell you what is the thing that only I know, it is no longer the thing which only I know. Sep 8, 2014 at 13:25
• @pat_nafs On second thought: Maybe it is a performative contradiction. It is, if you don't focus on the question but on the answer: "Listen, this is something, only I know about me: ..." Sep 8, 2014 at 13:32
• @Einer - Thanks! Wikilink on performative contradiction lead me to Self-refuting idea - "ideas or statements whose falsehood is a logical consequence of the act or situation of holding them to be true". I think this is what we were looking for. Let me know your thoughts / answer it. Sep 8, 2014 at 15:02

I believe this may be related to the Berry Paradox.

The Berry Paradox asks : What is the smallest number not nameable in under ten words?

We can answer this by saying "the smallest number not nameable in under ten words".

But by saying that we have expressed this number in under ten words - a contradiction, thus invalidating the question.

EDIT

The reason we can answer Berry's question the way we do is due to the well-ordering of the natural numbers. Every set of natural numbers has a least member.

• ...or then "What is the smallest natural number not nameable in under eleven words" Oct 17, 2014 at 2:05
• @AndrewC Quite right. I was a bit sloppy in my statement of the paradox.
– nwr
Oct 17, 2014 at 2:13

The Identity Question. As a Cretan, I know all Cretans are liars; I swear it is true.

• The identity paradox comes from scripture - "One of themselves, even a prophet of their own, said, The Cretians are alway liars, evil beasts, slow bellies 13 This witness is true..."[Titus 1:12-13]. When the writer testifies "This witness is true" He verifies the paradoxical aspect of true/false veracity. Oct 22, 2014 at 19:45