heyhey! Paradoxes my friend are many, each with their own snazzy names and history...I think the one you are talking about (didn't/did) is like the one in my signature: it is QUINE'S PARADOX (related to the LIAR PARADOX ie 'this is not a sentence'), a paradox concerning truth values, such as in my signature where, in simple terms, the sentence implies that it is false, which is paradoxical - for if it is false, what it states is in fact true.

----The next sentence is true. The previous sentence is false----