In short, we have to abandon entirely the idea that conceptual fictions are errors, or sketches and aids, and that they precede rigorous concepts. Quite the opposite is true: conceptual fictions do not precede rigorous concepts, but follow them, and presuppose them as their own foundation. Were this not so, of what could they ever be fictions? To counterfeit or imitate something implies first knowledge of the thing which it is desired to counterfeit or to imitate. To falsify means to have knowledge of the genuine model: false money implies good money, not vice versa. It is possible to think that man, from being the ingenuous poet that he first was, raised himself, immediately, to the thought of the eternal; but it is not possible to think that he constructed the smallest conceptual fiction, without having previously imagined and thought. The house, the rose, the cat, the triangle, free motion presuppose quantity, quality, existence, and we know not how many other rigorous concepts: they are made with iron instruments great and small, which logical thought has created, and which come to be used with such rapidity and naturalness that we usually end by believing that we have proceeded without them. Whoever makes conceptual fictions, has already taken his logical bearings in the world: he knows what he is doing and reasons about it; progress with his conceptual fictions depending upon progress with his rigorous concepts, and being continuously remade, according to the new needs and the new conditions which are formed. Now that the concept of miracle or witchcraft has been destroyed, the conceptual fictions relating to the various classes and modes of miraculous facts and acts of witchcraft are no longer constructed; and since the destruction of the belief in the direct influence of the stars upon human destinies, the astrological and mathematical fictions, which arose upon those conceptual presuppositions, have also disappeared.