Neoclassical economic theory holds, with apparent certainty, that the model of perfect competition is an idealized form of real markets. Although difficult to find, it is of enormous importance as a scientific concept and as a guide to practice. In this article we propose that this statement is partially incorrect. Neither is perfect competition an idealized form of real markets, nor can it serve as an adequate guide for an economic policy on the ordering of markets. Instead, perfect competition and other similar concepts are topological variants of spontaneous order. From the two previous considerations, a set of paradoxes and inconsistencies derive that, however, do not totally invalidate the search for transcendental concepts, if we correctly locate their place in the social sciences.