Maybe it is missing your pet theory, but the article has a definite point and Priest argues it at length. You seem not to have grasped the article because you refer to logic as something singular that should not be deemed superior to other modes of thought, while the article demonstrates there are many different, mathematically rigorous conceptions of logic. Epicycles are a non-sequitur here, because there is not a particular proposition that you set out to prove with whatever explanation you can find. Rather the goal is to find a logic that does not break down when presented with paradoxes.