Is there a word or idiom describing a situation where a rebuttal to an argument is evidence to it (especially when it is ironic/meta)?
A very simple example:
John: “You can talk!”
Mary: “No I can't!”
John put forth an argument, and Mary rebutted it; in doing so, she inadvertently gave evidence to the contrary.
The word is self-refuting (or self-defeating).
In his Introduction to Logic, Harry Gensler defines a self-refuting statement as “[A] statement that makes negative claims so sweeping that it ends up denying itself.”
For instance, Truth does not exist (Is that a true statement?); Nothing is absolute (Is that absolutely true?); "I cannot speak a word of English”
There is a difference between self-contradiction and self-refutation.
Are you asleep? yes (self-refutation).
I am sleeping and not sleeping. (self contradiction)
This situation is best described as a catch-22, or a logical paradox which can be escaped only by denying its premise. The eponymous novel by Joseph Heller, Catch-22, contains the following illustration:
One must seek a declaration of insanity to be exempt from combat duty.
Those who go into combat duty are insane.
Therefore, to seek exemption from combat duty is tacit proof of one's own sanity. Under these circumstances, no declaration of insanity can ever be granted, but there is no recourse but to seek one.
The situation you set up between John and Mary is not exactly the same, because in reality Mary has a valid rebuttal available to her. She could respond with silence, and thereby disprove John's statement. Assuming you had constrained the situation so that only verbal rebuttals were acceptable, however, then I believe the word/idiom you're looking for is catch-22.
You may be thinking of paralepsis or aphophasis -- 'mentioning by not mentioning'.
