"Reaffirmation through denial" is an identification of the fact that axiomatic truths are necessary to any and all knowledge - including any attempts at denying its truth. It is an interesting characteristic of Axioms, yet not a validation of them. It validates an axiom qua axiom, not qua truth.
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    Take "existence exists", for instance. The truth of this statement is self-evident - every single perception you have, is a perception of something, therefore, something exists. Nothing but direct awareness is necessary to establish the truth of that statement.
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    Not every self-evident statement, however, is axiomatic. "Facebook exists" is self-evident to anyone reading these paragraphs - you can see, directly, that it exists. Yet this knowledge is not necessary to all other knowledge. One could say "Facebook doesn't exist" without having to assume the existence of Facebook to do so.
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    A mystic who claims that "Nothing exists", - and that claim is particularly common among eastern mystics - unlike our hypothetical facebook-denier, must implicitly assume a great number of things that contradict his very claim. He must assume that he exists, that his claim exists, that all he is basing his claim on exists, and that the person to whom he is making the claim exists - he must assume that something (existence) exists.
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    When people attempt to deny an axiom, it usually entails an attempt to sound profound. "Reaffirmation through denial" shows that it is actually one of the silliest things someone can do.