Logic as the Science of the Pure Concept

by Benedetto Croce

or universals void of representations

The conceptual fictions of the triangle and of free motion have an analogous but opposite defect. With them, it appears, we emerge from the difficulties of representations. The triangle and free motion are not something which begins and ends in time and of which we are not able to state exactly the character and limits. So long as thought, that is to say, thinkable reality, exists, the concept of the triangle and of free motion will have validity. The triangle is formed by the intersection of three straight lines enclosing a space and forming three angles, the sum of which, though they 'vary from triangle to triangle, is equal to that of two right angles. It is impossible to confuse the triangle with the quadrilateral or the circle. Free motion is a motion, which we think of as taking place without obstacles of any sort. It is impossible to confuse it with a motion to which there is any particular obstacle. So far so good. But if those conceptual fictions let fall the ballast of representations, they ascend to a zone without air, where life is impossible; or, to speak without metaphor, they gain universality by losing reality. There is no geometric triangle in reality because in reality there are no straight lines, nor right angles nor sums of right angles, nor sums of angles equal to that of two right angles. There is no free motion in reality, because every real motion takes place in definite conditions and therefore among obstacles. A thought, which has as its object nothing real, is not thought; and those concepts are not concepts but conceptual fictions.

Critique of the doctrine which considers them to be erroneous concepts,

Having made clear, by means of these examples, the character of concepts and of fictional concepts, we are prepared to solve the question as to whether the second are legitimate or illegitimate products, and if they merit the reproach which seems to attach to their name. And certainly, a view which has had and still has force does not hesitate to consider those fictions as nothing but erroneous concepts, and declares a war of extermination against them, in the name of rigorous thought and of truth. If it follows from what we have said, that the cat or the house or the rose are not concepts, and that the geometrical triangle or free motion are not so either, the conclusion seems inevitable that we must free ourselves from these errors or misconceptions, and affirm that there is neither the cat nor the rose nor the house, but a reality all compact (although it is continuously changing) which develops and is new at every instant; nor is there either the triangle or free motion, but the eternal forms of this reality, which cannot be abstracted and fixed by themselves, and deprived of the conditions which are an integral part of them. But a single fact suffices to invalidate this conclusion and to confute the premiss upon which it rests, that conceptual fictions are erroneous concepts. An error once discovered cannot reappear, at least until the discovery is forgotten, and there is a falling back into the conditions of mental obscurity similar to those antecedent to the discovery. When, for example, the position has been attained that morality is not a phenomenon of egoism and that it has value in itself, or one has become certain that Hannibal was ignorant of the disaster that befell his brother Hasdrubal on the Metaurus, it is impossible to continue believing that morality is egoism, or that Hannibal has been informed of the arrival of Hasdrubal and had voluntarily allowed him to be surprised by the two Consuls. But with conceptual fictions similar to those in the example the case is otherwise. Even when we are persuaded that the triangle and free motion correspond to nothing real, and that the rose, the cat, and the house have nothing precise and universal in them, we must yet continue to make use of the fictions of triangles, of free motion; of houses, cats, and roses. We can criticise them, and we cannot renounce them; therefore, it is not true that they are, at least altogether and in every sense, errors.

or imperfect concepts preparatory to perfect concepts.

This indispensability of conceptual fictions to the life of the spirit, finds acknowledgment in a more temperate form of the doctrine which considers them as erroneous concepts; that is, in the thesis that they are erroneous, but at the same time preparatory to, and almost a first step towards, the formation of true and proper concepts. The spirit does not issue all at once from representations and attain to the universal; it issues from them little by little, and prior to the rigorous universal, it constructs others less rigorous, which have the advantage of replacing the infinite representations with their infinite shades, through which reality presents itself in æsthetic contemplation. Conceptual fictions, then, would be sketches of concepts, and therefore, like all sketches, capable of revision and annulment, but useful. Thus it would be explained how they are errors, and errors made for a good reason. But this moderate theory also clashes noisily with the most evident facts. Above all, it is not true that the spirit issues little by little from the representations, passing through a series of grades; the procedure of the spirit, in this regard, is altogether different, and when philosophers have wanted to find a comparison for it, they have been obliged to come back to that very 'leap' which they wanted to avoid: "Spirit (said Schelling, for example,) is an eternal island, which is not to be reached from matter, without a leap, whatever turns and twists be made." And, for this very reason, conceptual fictions are not good passages to rigorous concepts: to think rigorously, we must plunge ourselves again into the flood of representations and think immediate reality, clearing away the obstacles that proceed from conceptual fictions. And always for the same reason, rigorous concepts, when they find themselves confronted with conceptual fictions as rivals in the same problem, do not claim their assistance, nor correct, nor refine upon them, in order partially to preserve them, but combat and destroy them. What the rigorous concepts are unable to do, is to prevent the others from reappearing; because the spirit, as has been seen, preserves, without correcting them, although it has recognized their falsity: it preserves them, that is to say, not fused and rendered true in the rigorous concepts, but outside and after these.

Posteriority of conceptual fictions to true and proper concepts.

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.

Those who have seen errors or sketches of truth in conceptual fictions have certainly seen something: because (without incidentally anticipating at this point the theory of errors, or that of sketches or aids to the search for truth) it may at once be admitted, that conceptual fictions also sometimes become both errors and obstacles, and suggestions and aids to truth. But because a given spiritual product is adopted for an end different from that which rightly belongs to it (thereby becoming itself different and giving rise to a new spiritual product), we must not omit to search for the intrinsic end, which constitutes the genuine nature of this product. The portrait of a fair lady, white as milk and red as blood, which the prince of the story finds beneath a cushion by the help of the fairy, may serve as an incentive to make him undertake the journey round the world in search of the woman in flesh and blood, who is like the portrait and whom he will make his wife; but that portrait, before it is an instrument in the hands of the fairy, is a picture, that is to say, a work of art, which has come from the hands, or rather from the fancy, of the painter; and must be appreciated as such. Thus conceptual fictions, before they are transmuted into errors or into expedients, into obstacles or into aids to the search for truth, have, before them, a truth already constructed, toward the construction of which, therefore, they cannot serve; whereas that truth has served them, for they would not otherwise have been able to arise. They are, therefore, intrinsically neither obstacles nor aids to truth, but something else, that is, themselves; and what they are in themselves it is still necessary to determine.

Practical character of conceptual fictions.