A paradox is a proposition in (alleged) contrast with common sense. All science is replete with paradoxes. Economics is not an exception. This paper is focused on two widely discussed paradoxes: the Mandeville paradox (and the associated idea of an ‘invisible hand’) and the Prisoners' Dilemma (with the allied literature on market failures). The main tenet of this paper is that they cannot be simultaneously paradoxical, because they state one the opposite of the other. If common sense contrasts with Mandeville, then it must agree with the Prisoners' Dilemma and vice versa. This is what I term the ‘paradox of paradoxes’ in economics, which is a simple consequence of the rarely noticed principle that two opposing propositions cannot be paradoxical at the same time. A tentative way out from this impasse is presented. I claim that economists would gain a better understanding of their profession if they devoted more time to the study of the intuitive or folk economics.