In Academic Questions XXVI, Cicero says that all the challenges against the possibility of knowledge fall into one of four categories about which the schools had split and been arguing for hundreds of years. Over time it would be good to develop some kind of chart explaining these and the Epicurean response to each:
However, to abridge the controversy, consider, I pray you, within what narrow bounds you are confined. There are four principles which conduct you to the conclusion that there is nothing which can be known, or perceived, or comprehended;—and it is about this that the whole dispute is. The first principle is, that some perceptions are false; the second, that such cannot be perceived; the third, that of perceptions between which there is no difference, it is not possible that some of them can be perceived and that others cannot; the fourth, that there is no true perception proceeding from the senses, to which there is not some other perception opposed which in no respect differs from it, and which cannot be perceived. Now of these four principles, the second and third are admitted by every one. Epicurus does not admit the first, but you, with whom we are now arguing, admit that one too,—the whole contest is about the fourth.