lofty spheres we take m individual differences), as we gradually descend into what is called nature or inferior reality. On this is founded the illusion that nature is invariable and without history. And it also explains why mathematics has seemed more applicable to the globus naturalis than to the globus intellectualis, and in the globus naturalis, to mineralogy more than to zoology, to physics more than to biology. Still, mathematics is equally applicable to the globus intellectualis, as, for instance, in Economics and Statistics. And, on the other hand, it is inapplicable to both spheres, when they are considered in their effective truth and unity as the history of nature or the history of reality, in which nothing is repeated and therefore nothing is equal and identical. Beneath that difference of applicability there is nothing but a consideration of utility. If the grains of sand on which we tread can be considered (although they are not) equal to one another, it happens less frequently that we regard MATHEMATICS 377 MATHEMATICS 377 those with whom we associate and act in the same light. Hence the decreasing utility of naturalistic constructions (and of mathematical calculation), as we gradually approach human life and the historical situation in which we find ourselves. Decreasing but never non-existent, for otherwise, neither empirical sciences (grammars, books on moral conduct, psycho logical types, etc.) nor calculations (statistics, economic calculations, etc.,) would continue in use. A constructor of machines needs little intuition, but much physics and mechanics. A leader of men needs very little mathematics, little empirical science, but much intuitive and' perceptive faculty for the vices and value of the human individuals with whom he has to do. But both little and much are empirical determina tions; the Spirit, which is the whole spirit in every particular man and at every particular instant of life, is never composed of measurable elements.
VII THE CLASSIFICATION OF THE SCIENCES The theory THE explanations given as to the various forms of the forms of knowledge of knowledge are also explanations concerning andthe doctrine r Of the categories. fa^ categories of the theoretic and theoretic- practical spirit: the intuition, the concept, historicity, type, number; and also quality and quantity and qualitative quantity, space, time, movement, and so on. They form part of that doctrine of the categories, in which the account of philosophy in the strict sense is completed. To ask what mathematics or history is, means to search for the corresponding categories; to ask what is the relation between history and mathe matics, and in general how the various forms of knowledge are related to one another, means to develop genetically all these forms, which is precisely what we have attempted.
But the difficult enquiry as to the forms of knowledge as categories has not been much in favour in recent times. Another problem has, on PART II SCIENCES 379 the other hand, acquired vogue. It has seemed The problem of the more easy, but that is not so, because though classification of the sciences artfully disguised, it is at bottom identical with anrda^cal the preceding problem. Instead of putting the nature- question in the manner indicated above, which implies seeking out the constitution of the theoretic spirit, a modest request has been made for a classification of the various forms of knowledge, a classification of the sciences.
Scant confidence in philosophic thought, and excessive confidence in naturalistic methods, have so operated that, unable to renounce the necessity of dominating the chaos of the various competing sciences and not wishing to have recourse to philosophic systematization, an attempt has been made to classify the sciences like minerals, vegetables, and animals. Even now there exist writers occupying professorships who claim to be specialists in classifying sciences. Volumes on this theme appear with an unprofit able frequency and abundance.
Certainly, if such writers and professors were False . ^ philosophic to proceed in an altogether empirical manner, character corresponding with their declarations, nothing could be said against their labours, beyond advising them not to discuss them philosophically in order that they may not waste time in mis- 380 LOGIC 380 LOGIC understandings, and to recognize their slight utility. But, as a fact, none of them contains himself within empirical limits, but each gives some philosophic and rational basis to the classi fication which he proposes. Thus there appear bipartitions of the sciences into concrete and abstract, into historical and theoromatic (or nomotechnical), into sciences of the successive and sciences of the coexistent, or into real and formal\ or tripartitions, into sciences of fact, of law and of value; into phenomenalist, genetic and systematic sciences; and into similar parti tions and groups, of which some are old acquaintances and correspond to functions of the spirit that we have already distinguished, while others, on the contrary, must be held to be false, because they confuse under the same name functions that are different and divide functions that are unique. But all of them, true or false, leave the empirical and direct themselves to the problem of Logic and of theoretic Philosophy. This is not the place to criticize them, because substantially it has already been done in the course of the exposition of our theories; and what is left would reduce itself to a criticism of minute errors, which finds a more suitable place in reviews dealing with books of the day than SCIENCES 381 in philosophic treatises. So true is it that those classificatory systems pass with the day that witnessed their birth.
We are concerned only to demonstrate more coincidence of that problem clearly that the demand inherent in such attempts with the search 3 for the is identical with that which leads to the establish- categories, when ing of a doctrine of the categories or a philosophic system. It is indeed possible to discover now and then in the demands for a classification of the sciences, two demands, the one limited, the other wider. The first takes the form of a demand for a classification of the forms of know ledge, as in the Baconian system, and in the others which repeat the type. Here the sciences are divided according to the three faculties, memory (natural and civil history), imagination (narrative, dramatic and parabolical poetry), and reason (theology, philosophy of nature and philosophy of man). The other tends to a classification not according to gnoseological forms alone, but according to objects, according to all the real principles of being, as in the system of Comte and in those derived from it. Now a classification of the first kind coincides with researches relating to the forms of the theoretic spirit, and the problems that it exposes cannot be solved save by penetrating into the problems PART 382 LOGIC PART 382 LOGIC of these forms. Otherwise it is not possible to say if, for example, the Baconian classification be exact or no, and if not, where it should be corrected. But in passing to the other form of classification, according to objects or to the real principles of being, we pass from the sea to the ocean, because that coincides with the entire philosophic system. The classification of Comte, for example, is his positivism itself, and it is not possible to accept or refute or evaluate the one, without accepting or refuting or submitting to examination the other. There are people who ingenuously believe that they ^ can understand things by representing them on a sheet of paper, in the form of a genealogical tree or of a table rich in graphic signs of inclusion and exclusion. But when we seriously engage upon the work, we perceive that in order to draw up the tree and construct the table, it is above all things needful to have understood them. The pen falls from the hand and the head is obliged to bend itself in meditation, when it does not prefer to abandon the dangerous game and amuse itself in other ways. Forms of And this is just the occasion to make clear knowledge and literary- the distinction that we have on several occasions didactic forms.
employed, between forms of knowledge and „ SCIENCES 383 literary or didactic forms of knowledge, between the orders of knowledge and books. The arrangement of books is not always determined solely by the demand for the strict treatment of a determinate problem; very frequently, its motive is supplied by the practical need of having certain different pieces of knowledge collected together, in order not to be obliged to go and search for them in several places, that is to say, in their true places. Thus, side by side with scientific treatises properly so-called, are to be found scholastic compilations and manuals. Such are Geographies, Pedagogies, juridical or philological Encyclopaedias, Natural Histories, and so on. Authors, even outside strictly scholastic limits, used formerly to con sider it convenient sometimes to isolate, some times to unite certain orders of knowledge, and to baptize the mutilation or mixture with a particular name. It is evident that when dealing with these hybrid compilations and for mations the philosopher and the historian of the sciences, who seek not books, but ideas, must carry out a series of analyses and syntheses, of disassociations and associations, without allowing themselves to be seduced by the authority of the writers or by the 384 LOGIC PART solidity of these mixtures, which have become traditional. Prejudices But it is not an easy matter. Those mixtures arising from these last. are no longer ingenuous, nor are the practical motives that have determined them apparent. Around them has grown up a dense forest of philosophemes, of capricious distinctions, of false definitions, of imaginary sciences, of prejudices of every sort. Any one who has succeeded in discerning the genuine connections and attempts to separate the interlaced boughs, to isolate the trees and to show the different roots, any one who sets an axe to those wild tree-trunks, is horrified by cries and complaints, not less resonant than those that drove Tancred from the enchanted wood. And there is the traditionalist who admonishes us severely not to divide natural groupings and not to introduce among them our own caprice. Thus he calls the capricious natural and the natural capricious. "What?" (has recently written the shocked Professor Wundt) "for the excellent reason that the search for the individual is historical search, must Geology be considered history and research relating to the glacial epoch be abandoned to the amiable interest of the historian? " And others lament that the ancient richness of the SCIENCES 385 SCIENCES 385 sciences is destroyed by these simplifications, and call the confusion richness.
It is true that in order to obviate the evil Methodical prologues to of confusion and the defective consciousness of scholastic Manuals the various kinds of research which have been and their powerlessness.
mingled together, many authors are in the habit of prefixing to their books theoretic introductions, about the method, as they call it, of their science. The special logic of the individual disciplines is to be sought (they say) in the books that treat of these. Manuals in the German language are especially notable for this arrangement, preceded, as they are, by the heaviest intro ductions, which occupy a great part of the volume or of the volumes of the book. They present a contrast to French and English books, which usually enter at once in medias res. This arrangement seems preferable: the German type has against it the sensible observation of Manzoni, that one book at a time is enough, when it is not more than enough. He who opens a historical book in order there to learn the particulars of an event, or a book on economics in order to learn how an economic institution works, should not be obliged to read the theory of historical events and disquisitions on the place of Economics in the system of the sciences. "// sagit dun PART 386 LOGIC chapon et non point d'Aristote" as the judge in the Plaideurs said to the advocate who went back in his speech to the Politics of Aristotle. But, besides the literary contamination, there is also here the other inconvenience, that science and the theory of the sciences being different operations and demanding different aptitudes and preparations, the specialist who is competent in the first is usually not at all competent in the second; though he may be believed to be so, owing to a confusion of names. Why, indeed, should an expert on banking and Stock Exchange business be versed in the gnoseology of economic science? The affirmation of competence in the one on the strength of competence in the other constitutes a true and proper sophism a dicto simpliciter ad dictum secundum quid. The capricious Further, the specialist has his pride, which multiplication.
multiplication.
of the sciences, leads him to exaggerate what he practises and fail to recognize its true nature and limits. The multiplication of the Sciences in our days has no other origin than this; the philosopher con templates it with astonishment; it is a truly miraculous multiplication of the seven loaves of bread and five small fishes. A new science is announced, whenever a crude idea passes through the brain of a professor. We are made glad SCIENCES 387 with Sociologies, social Psychologies, Ethno- psy etiologies, Antkropogeographies, Criminologies, comparative Literatures, and so on. Some years ago, an eminent German historian, having observed that some use might be made of genealogical and heraldic studies, generally abandoned to the cultivators and purveyors of the mania for birth and titles, instead of limiting himself to publishing his little collection of minute observations at once proclaimed Genealogy as a science, Genealogie als Wissenschaft, and provided the appropriate manual. This begins by determining the concept of Genealogy, and proceeds to study its relations with history, with the natural sciences, with zoology, with physio logy, with psychology and psychiatry, and with the knowable universe.
Finally, the specialist is generally a teacher, The sciences and therefore accustomed to identify eternal ideal science with his real and contingent chair, and the organism of knowledge with that of the university faculties. Hence arises a fashion of conceiving the nature and scope of the sciences that has become habitual in the academic world. It consists of personifying science, and telling this imaginary person what he has to do, without regard to whether the assignment of the task PART 388 LOGIC PART 388 LOGIC accords or no with the quality of the function. " Logic will be occupied with this, but yet will not neglect this other thing; it will benefit by casting a look on this third thing also, which is extraneous to its task, but not to its interest; nor will it fail to aid, with due regard, the student of an analogous matter, by giving to him suggestions, if not even rules." Whoever reads the scientific books of our times will recognize in this example, not a caricature, but a plan constantly repeated and applied. It was said of the poet Aleardo Aleardi that he treated the Muse like his maid servant, since he was at every instant addressing himself to her and asking her something. The professor ends by treating Science like his steward, or at least his respectable consort, with whom he naively comes to an agreement regarding the portions that are to form the meals of the day, and other matters concerning the management of the family.
THIRD PART THE FORMS OF ERRORS AND THE SEARCH FOR TRUTH ERROR AND ITS NECESSARY FORMS ERROR has sometimes been called privation or Error as negativity, and negativity. It is commonly defined as a thinking impossibility of the false, as the non-conformity of thought sPecialfy of errors.
with its object, and in other similar ways. These are all reducible to the first, since, for example, thought which is of a different form from its object is false thought, which does not attain to its intrinsic end; and false thought is not thought, but privation of thought, negativity.
As negativity error gives rise to a negative concept, responding to the positive concept, which is truth. True and false, truth and error, are related to one another as opposite concepts. Now we know from the logical doctrines just stated that opposite concepts, far from being separable, are not even distinguishable, and when they are distinguished, they represent nothing but the abstract division of the pure concept, of the unique concept, which is the 392 LOGIC PART synthesis or dialectic of opposites. And we know from the whole of Philosophy that Reality, thought in the pure concept and of which the pure concept is also an integral element, genuine and truly real Reality, is a perpetual development and progress, which is rendered possible by the negative term intrinsic to the positive and constituting the main spring of its development.
If then, error is negativity, it is vain to treat it as something positive. No other positivity or reality belongs to it than just negativity, which is a moment of the dialectic synthesis and outside the synthesis is nothing. A treatment of error in this sense already exists quite complete in the treatment of logical truth; and there is nothing special to add here to that argument. As a fact, a form of the spirit distinguishable from the positive and real forms, error does not exist, and philosophy cannot philosophize upon what is not. Positive and Nevertheless, we all know errors, distinguishexisting errors.
existing errors.
able from truth and existing for themselves. The evolutionist affirms the biological formation of the a priori; the utilitarian resolves duty into individual interest; the Christian says that God the Father sent his son Jesus to redeem men from the perdition into which they had fallen through the sin of Adam; the Buddhist preaches m ERROR 393 the annulment of the Will. Are not these true and proper errors? Have they perchance no existence? Have they not been expressed, repeated, listened to, believed? Whoever does not admit the validity of the examples adduced can himself find others; there will certainly be no lack of examples in such a field. Do we wish to maintain that these errors do not exist, in homage to the definition of error as negativity and un reality? They may not exist as truth, but they may perfectly well exist as errors.
There is no way of escaping from this Positive errors antithesis between the inconceivability 01 the acts. existence of error and the impossibility of denying the existence of errors which the mind recognizes and the fact proves, save by the solution to which we have several times had occasion to refer. That error, which has existence, is not error and negativity, but some thing positive, a product of the spirit. And since that product of the spirit is without truth, it cannot be the work of the theoretic spirit. And since beyond the theoretic spirit there is nothing but the practical spirit, error, which we meet with as something existing, must of necessity be a product of the practical spirit. If every way of issue is closed, this one is open; it goes 394 LOGIC PART to the very bottom and leads to the place of rest.
Indeed, he who produces an error has no power to twist or to denaturalize or stain the truth, which is his thought itself, the thought ^ which acts in him and in all men; indeed, no sooner has he touched thought than he is touched by it: he thinks and does not err. He possesses only the practical power of passing from thought to deed', and his doing, in fact his thinking, is to open his mouth and emit sounds to which there corresponds no thought, or, what is the same thing, no thought which has value, precision, coherence and truth. It is to smear a canvas to which no intuition corresponds; to rhyme a sonnet, combining the phrases of others, which simulate the genius that is absent. Theo retical error, when it is truly so, is inseparable from the life of thought, which to the extent to which it perpetually overcomes that negative moment, is always born anew. When it is possible to separate and consider it in itself, what is before us is not theoretical error, but practical act.
Practical acts Practical act and not practical error, or Evil; not practical errors. for that practical act is altogether rational. Let him who doubts this cast a glance at those who produce errors. He will be at once convinced in ERROR 395 that they act with perfect rationality. The dauber produces an object which is asked for in the market by people who wish to have at home pictures of any sort, to cover the walls and to attest to their own easy circumstances or riches, and who are altogether indifferent to the aesthetic significance of those objects. The rhymer wishes to secure an easy success for himself among people who look upon a sonnet as a social amusement. The babbler who emits sounds instead of thoughts, often obtains in virtue of those sounds applause and honour denied to the serious thinker: ^tn sot trouve to^tjours un plus sot pour P admirer. If, by means of those so-called errors, provision is made for house, firing, food, children's clothes, or for the satisfaction of self-esteem, ambitions and caprices, who will say that they are irrational acts? Man does not live by bread alone, but he does live by bread; and if, by means of those acts, bread is provided, that is to say, if the wants of each one's individuality are met, they are well-directed, far- sighted, fruitful, and therefore most rational.
This does not, on the other hand, mean that Economically f practical, not they are moral; they are rational, economically morauy practical.
rational but not moral. Morality demands that man should think the true. Producers of errors evade, or rather, do not elevate themselves to 396 LOGIC PART that duty. Still intent upon the demands of practical life qua talis, they do not actualize in themselves the universal life, nor do they create in obedience to this last the ethical will and the will for truth. Therefore there arises in their souls, and in the souls of those who see them at work, the desire for another superior activity, which should supervene upon the preceding and complete it. They demand, not only to live, but to live well, to seek not only bread, but that " bread of the angels " with which, as the divine poet says, we are never sated. The expression of this desire manifests itself in a cry of dis content, of reprobation, of anguish, of longing; and therefore, with negative emphasis, it accuses of irrationality that inferior rationality which has to be surpassed, and gives the name theo retical error to that which considered in itself must be called a simple economic act. Doctrine of The doctrine here expounded is developed error, and error, and doctrine of the from what has been said above, or from developnecessary forms of error. ments given elsewhere in the Philosophy of the Spirit. We shall not therefore enlarge further upon the immanence of values in facts, upon evil as the stimulus and concreteness of the good, on the non-existence of evil in itself, on the practical character of theoretical error, on ERROR 397 moral responsibility for such error, on the con tent of desire exhibited by negative statements accompanying judgments of value, and so on. In an exposition of Logic the genesis of the theoretical error could be set aside as pre supposed, for in this didactic sphere any one among the common definitions which present error as a thinking of the false is sufficient.
A task in closer connection with Logic is that of enquiring as to the necessary forms of error, the task, that is to say, not of confuting all errors (which is performed by Philosophy as a whole), but of establishing in how many ways the pro ducts of the various forms of knowing and of knowledge can be practically combined, and what therefore are the gnoseological possibilities of error. If error is nothing but an improper com bination of ideas (as Vico said), we must see the number to which the fundamental forms of these improper combinations can be reduced. In traditional Logic, the theory of error appears as the doctrine of Sophisms or of sophistical refutations: it has the formalist, verbalist, empirical character common to all that Logic. In our Logic, it must have a philosophic char acter, that is to say, it must depend upon the already distinguished forms of the theoretic 398 LOGIC .
spirit, and deduce from them the arbitrary com binations of the errors which are formally possible. The ideas or concepts of the theoretic and theoretic-practical spirit are so many and no more, and so many and no more must be the possible improper combinations of them and the forms of theoretic error. Logical nature That theoretical error is always at bottom errors. logical error. 1 his is an important proposition, which merits explicit statement, because it is customary to speak of aesthetic, naturalistic, mathematical and historical errors side by side with those that are properly logical or philo sophical. We too have spoken and will speak thus, when more subtle distinctions and more precise determinations are not necessary. But in truth, a fact like humano capiti cervicem equinam jungere, or simulare cupressum in the sea where the shipwrecked struggles in the waves, does not constitute in itself that practical act, called aesthetic error, unless there be added to it the false affirmation that the object produced is an aesthetic object, that is to say, unless there be added a logical affirmation, so that the practical act becomes, by means of it, logical error. Taken in itself, the union of a human head with a horse's neck, or of a cypress with the sea is a ERROR 399