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This article analyses some paradoxes linked to the academic and sceptical uses of the concepts of katalepsis, akatalèpsia, and akatalèptos. It tries to show that it is possible to deny the possibility of katalepsis without contradiction and that Academics and Sceptics managed to avoid some infamous paradoxes (which we will call the “paradox of dissolvable dogma” or the “paradox of distinct indiscernibles”). We will show that the Academics and Sceptics were able to demonstrate their gnoseological pessimism through argumentative strategies sometimes paradoxical, but not contradictory, and best suited to our state of “ignorant ignorance”, which is an absolute ignorance that is not aware of itself.