Forms of knowledge and literary-didactic forms.
And this is just the occasion to make clear the distinction that we have on several occasions employed, between forms of knowledge andliterary 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 Encyclopædias, Natural Histories, and so on. Authors, even outside strictly scholastic limits, used formerly to consider it convenient sometimes to isolate, sometimes 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 formations 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 thesolidity of these mixtures, which have become traditional.
Prejudices arising from these last.
But it is not an easy matter. Those mixtures 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 dividenaturalgroupings and not to introduce among them our owncaprice.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 ancientrichnessof thesciences is destroyed by these simplifications, and call the confusion richness.
Methodical prologues to Scholastic Manuals and their powerlessness.
It is true that in order to obviate the evil of confusion and the defective consciousness of the various kinds of research which have been mingled together, many authors are in the habit of prefixing to their books theoretic introductions, about themethod,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 introductions, 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 oncein 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 historica events and disquisitions on the place of Economics in the system of the sciences."Il s'agit d'unchapon et non point d'Aristote,"as the judge in thePlaideurssaid to the advocate who went back in his speech to thePoliticsof 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 sophisma dicto simpliciter ad dictum secundum quid.
The capricious multiplication of the sciences.
Further, the specialist has his pride, which leads him to exaggerate what he practises and fail to recognize its true nature and limits. The multiplication of theSciencesin our days has no other origin than this; the philosopher contemplates it with astonishment; it is a truly miraculous multiplication of the seven loaves of bread and five small fishes. Anew scienceis announced, whenever a crude idea passes through the brain of a professor. We are made gladwithSociologies, social Psychologies, Ethnopsychologies, Anthropogeographies, 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 theconceptof Genealogy, and proceeds to study its relations with history, with the natural sciences, with zoology, with physiology, with psychology and psychiatry, and with the knowable universe.
The sciences and academic prejudices.
Finally, the specialist is generally a teacher, 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 ofpersonifyingscience, and telling this imaginary person what he has to do, without regard to whether the assignment of the taskaccords 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.
THE FORMS OF ERRORS AND THE SEARCH FOR TRUTH
Error as negativity, and impossibility of treating specially of errors.
Error has sometimes been called privation ornegativity.It is commonly defined as a thinking of the false, as the non-conformity of thought 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 thesynthesis 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 mainspring 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 existing errors.
Nevertheless, we all know errors, distinguishable from truth and existing for themselves. The evolutionist affirms the biological formation of thea 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 preachesthe 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 unreality? They may not exist as truth, but they may perfectly well exist as errors.
Positive errors as practical acts.
There is no way of escaping from this antithesis between the inconceivability of the 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 something 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 goesto 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 todeed; 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. Theoretical 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 not practical errors.
Practical act and not practical error, or Evil; 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 convincedthat 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 æsthetic 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:un sot trouve toujours un plus sot pour l'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.
Economically practical, not morally practical.
This does not, on the other hand, mean that they are moral; they are rational, economically rational but not moral. Morality demands that man should think the true. Producers of errors evade, or rather, do not elevate themselves tothat duty. Still intent upon the demands of practical lifequa 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 discontent, 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 theoretical error to that which considered in itself must be called a simple economic act.
Doctrine of error, and doctrine of the necessary forms of error.
The doctrine here expounded is developed from what has been said above, or from developments 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, onmoral responsibility for such error, on the content 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 presupposed, 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 products 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 animproper combinationof 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 ofSophismsor of sophistical refutations: it has the formalist, verbalist, empirical character common to all that Logic. In our Logic, it must have a philosophic character, that is to say, it must depend upon the already distinguished forms of the theoreticspirit, and deduce from them the arbitrary combinations 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 of all theoretic errors.
That theoretical error is always at bottom logical error. This is an important proposition, which merits explicit statement, because it is customary to speak of æsthetic, naturalistic, mathematical and historical errors side by side with those that are properly logical or philosophical. We too have spoken and will speak thus, when more subtle distinctions and more precise determinations are not necessary. But in truth, a fact likehumano capiti cervicem equinam jungere,orsimulare cupressumin the sea where the shipwrecked struggles in the waves, does not constitute in itself that practical act, called æsthetic error, unless there be added to it the false affirmation that the object produced is an æsthetic 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 asort of play of the imagination, such as occurs in fancy, in idleness and in dream. The extrinsic combination of a fancy and a concept is also altogether innocent, as in the case of allegory, which, in itself, is not unsuccessful art, but becomes so only when it is affirmed that the two heterogeneous elements form only one; or rather, it then becomes, not unsuccessful art, but bad philosophy. In the same way, a mathematical error (for example, the formula 4 x 4 = 20) is nothing but aflatus vocis,such as is made in jest or to loosen the tongue. Only when we add the logical affirmation that in thisflatus vocisan effectual multiplication has been expressed, do we have a mathematical error, which is therefore a logical error. It is not possible to consider and to condemn as a theoretical error a combination which does not intend to deceive any one as to its proper nature; neither those to whom it is shown, nor him who has made it. Thus, among æsthetic, naturalistic, mathematical, historical, logical and practical productions, combinations without cognitive content are quite possible and constantly to be found; but they do not become theoretical errors unless they are crowned with an improper logical affirmation, or rather with an arbitrary judgment formed upona logical affirmation. Indeed, even illogical combinations of philosophic concepts are not, as such, logical or theoretical errors, since they can be made tentatively, in order to see whether the two concepts combine or no. To make them errors, the arbitrariness of a special act of judgment is necessary. That arbitrariness consists in a lying to others or to ourselves, in order to satisfy an interest of our merely individual life, and it is impossible to lie without employing an affirmation, which is always a logical product.
History of errors and phenomenology of error.
In this way the problem of determining the various forms of theoretical errors, according to the already distinguished forms of knowledge, becomes transformed and circumscribed in the other problem of determining the various forms oflogical errors,in relation to the various forms of knowledge, that is to say, of determining the necessary forms of philosophic errors. Certainly, every individual errs in his own way, according to the conditions in which he finds himself; just as every individual according to those conditions discovers truth in his own way. But Philosophy in the strict sense (in the form of a philosophical treatise) cannot complete the examination of all individual errors. This is the task of all philosophies as they are developed in the ages andof the thought of all thinking beings, who have been, are, and will be.Itstask is to illuminate the eternal ideal history of errors, which is the eternal ideal history of truth, in its relations with the eternal forms of the practical spirit. The Philosophy of the spirit, as a treatise of philosophy, cannot give the history of errors; but must limit itself to giving theirphenomenology.In this sense is to be understood the enquiry concerning the fundamental forms of philosophical errors. These forms may be briefly deduced as follows.
Deduction of the forms of logical errors. Forms deduced from the concept of the concept, and forms deduced from the other concepts.
The pure concept, which is philosophy, can be incorrectly combined and mistaken either for the form that precedes it, pure representation (art), or for that which follows it, the empirical and abstract concept (natural and mathematical sciences); or it can be wrongly divided in its unity of concept and representation(a priorisynthesis), and wrongly again combined—either the concept may be taken as representation, or the representation as concept. Hence arise the fundamental forms of errors which it will be useful to denominate asæstheticism, empiricism, mathematicism, philosophism,andhistoricism(ormythologism). On the other hand, the other distinctions of the concept, or distinct concepts, can beincorrectly combined among themselves in a series of false combinations, corresponding to the series of the other particular philosophic sciences, and hence arise the forms of the other philosophic errors. But in Logic it is sufficient to show the possibility of these last forms of errors, and to adduce certain cases as examples, because a complete determination of them would demand that complete exposition of the whole philosophic system, which cannot be furnished in a treatise on Logic.
Errors arising front errors.
Finally, since it is impossible that any form whatever of these errors, whether specifically logical or generically philosophic, should satisfy the mind, which asks for the true and does not lend itself to deception or mockery, each one of these forms tends to convert itself into the other, owing to its arbitrariety and untenability, and all mutually destroy one another. When the attempt is made to preserve both the true form and the insufficient form, or all the insufficient forms, we have gnoseological dualism; but with the decline to complete destruction, we have the error ofscepticismand ofagnosticism.Finally, if, having been by these led back to life and being deprived of every concept that should illuminate it back to life as a mystery, we affirm that truth lies in that theoreticmystery, in living life without thought, we have the error ofmysticism.Dualism, scepticism (or agnosticism) and mysticism thus extend both to strictly logical problems (that is to say, to the possibility, in general, of knowing reality), and to all other philosophic problems. Hence we can speak of a practical dualism, of an æsthetic or ethical scepticism, and of an æsthetic or ethical mysticism.
Professionalism and nationality of errors.
Such, stated in a summary manner, is the deduction of philosophic errors, which we shall now proceed to examine in detail. Upon their forms, which represent so many tendencies of the human spirit, is based this other fact, which is constantly striking us, and which may be called theprofessionalismof errors. Every one is disposed to use in other fields of activity those instruments that are familiar to him in the field which he knows best. The poet by vocation and profession dreams and imagines, even when he should reason; the philosopher reasons even when he should be poetical; the historian seeks authority, even when he should seek the necessity of the human mind; the practical man asks himself of what use a thing is, even when he should ask himself what a thing is; the naturalist constructs classes, even when he should breakthrough them, in order to think real things; the mathematician persists in writing formulae, even when there is nothing to calculate. If the narrowness of theEsprits mathématiqueshas been denounced, it must not be believed that the other professions have not also got their narrownesses. The philosopher's profession is no exception to this, for he should surpass all one-sided views, but does not always succeed. It is one thing to say and another to do, and if a man forewarned is half saved, he is not therefore altogether saved. That professionalism of error, which we observe in individuals, is also to be observed on a large scale among peoples. Thus we speak of peoples as antiartistic, antiphilosophical, or antimathematical: of speculative Germany, of intellectualist and abstract France, of empiricist England, of Italy as artistic in the centre and the north, and as philosophic in the south. But peoples, like individuals, are changeable and can be educated: so much so that in our days, the traditional Anglo-Saxon empiricism begins little by little to lose ground before the speculative education of the English people, due to classical German thought; France that was abstractionist becomes intuitionist and mystic. Germany leaves the vast dominion of the skies assigned to her byHeine for that of industry and commerce, and philosophizes somewhat unworthily; Italy, which in greater part was a country of artists, poets and politicians, is traversed in every direction by religious and philosophic currents. Were it not for this capacity for education of individuals and peoples, History would not be a free development, but determinism and mechanism, and each of us would possess less of that courage for social activity which each one exhibits with great ardour according to his own convictions.
Definition of these forms.
Æstheticism is the philosophic error which consists in substituting the form of intuition for the form of the concept, and of attributing to the former the office and value of the latter. Empiricism is the analogous substitution of the empirical concept, by means of which philosophic function and value is attributed to the empirical and natural sciences. Finally, mathematicism is the presentation of the abstract concept as concrete concept and of mathematics as philosophy.
Æstheticism.
We have met with æstheticism and with empiricism at the beginning of our exposition, and again here and there throughout its course; and we have sufficiently determined the nature of both and demonstrated the contradictions in which they become involved. In every one of their movements they presuppose the pure concept and the philosophy of which they mean to take the place. At the same time, they do not developthe philosophy which they have presupposed, because they suffocate it in the vapour of the intuitions and in the chilly waters of naturalistic concepts. They are not therefore effective thought, but an adulteration of thought with heterogeneous elements, which by a misuse of words are said to be furnished with theoretic and logical value.
Æstheticism has few representatives, because complete abstention from reflection and reason is too obviously contradictory. Even when art was considered to be a trueinstrumentof philosophy, in the Romantic period, this affirmation was put forward in a confused manner, intuition being finally distinguished from intuition, art from art. This amounted at bottom to a radical change and an abandonment of the original thesis. We have seen æstheticism reappear in our times under the name ofintuitionism,or again aspure experience:an experience which is taken to be not posterior, but anterior to every intellectual category, and should therefore be called nothing but pure intuition.
Empiricism
The representatives of empiricism are on the other hand most numerous, now as in the past; so much so that empiricism sometimes seems to be the sole adversary of philosophy, and thetrue origin of all philosophic errors. This opinion is without doubt inexact, but it finds support in the fact that philosophy is obliged to defend itself from the incessant assaults of empiricism, more than from any other enemy. The confusion between pure and empirical concepts is, indeed, easy, since both have the form of universality (though the universality of the second is falsely assumed) and both refer to the concept (though in the second the concept is something arbitrarily limited). The empiricist is like the philosopher, in so far as he immerses himself in facts and constructs concepts.
Positivism, philosophy founded upon the sciences, inductive metaphysic.
The last great historical manifestation of empiricism is that which, from the system of Auguste Comte, took the name ofpositivismand by its very name expressed the intention of basing itself upon facts (that is, upon facts historically certified), in order to classify them, thus reducing philosophy to a classification. This, like all classifications, proceeded from the poorest to the richest, from the abstract gradually to the less abstract, though never to the concrete. Positivism did not seem to be aware that the facts from which it proposed to proceed and which it believed to be the rough material of experience, were alreadyphilosophic determinations,and couldonly in this way be admitted ashistorically ascertained. Psychologistis also positivism; positivism, that is to say, more properly applied to the group of the so-called mental and moral sciences.Neocriticismcan be almost altogether identified with positivism, although its upholders generally possess some knowledge of philosophical history (which is altogether lacking to the pure positivists), and this confers a more specious polish on their doctrine. Neocriticism, indeed, tends to eliminate every speculative element from the Kantian criticism, and by so doing approaches positivism—so as almost to become confounded with it. It is no wonder, therefore, that from the camp of the neocritics should have originated the proclamation and programme ofa philosophy founded upon the sciences,or of aninductive metaphysic.This is simply and solely the reduction of philosophy to the sciences, because a scientific philosophy, an inductive metaphysic, is not speculation, but classification, or as those who advocate it ingenuously declare, a systematization of the results obtained by the sciences. Here too are kindled the most comical quarrels between scientists and philosophers. For when it is only a question of classifying and systematizing those results, the scientist rightlyfeels that he can dispense with the labours of the philosopher, indeed, he feels that he alone, who has obtained the results, knows what these exactly are and how they should be treated in order to avoid deformation. And the philosopher, who by making himself an empiricist, a positivist, a psychologist and a neocritic, has renounced his autonomy, approaches the scientists and offers with little dignity services that they refuse. He elaborates scientific expositions, which they call compilations and mistakes, he proposes additions or corrections at which they mock as superfluous or foolish. Nevertheless, the philosopher does not grow weary nor become offended at these repulses and jests; he returns to the charge and indeed it is only when someone wishes to redeem him from this voluntary servitude and abjection that he turns upon him with fury, saying that philosophy should live onfamiliar termswith the sciences. As if the relations that we have faithfully described were relations of reciprocal respect and harmony! The truth is that the majority of empirical philosophers are failures in science and unsuccessful in philosophy, who out of their double incompetence compound a logical theory, thus furnishing another proof (if further proof were needed) in confirmation of thepractical origin of errors. For our part, we recognise the justice of the accusation of parasitism, which is brought against a philosophy of this character, and we will willingly afford our aid to the scientists in driving out these intruders, who dishonour philosophy in our eyes not less than in theirs they dishonour the sciences.
Empiricism and facts.
Empiricism owes the greater part of its influence upon the minds of many to its continual appeal to reality and facts. This leads to the belief that speculative philosophy wishes to neglect reality and facts and to build, as the saying is, upon clouds. But we have here an ambiguity and a sophism with which we must not allow ourselves to be deceived. Not only does speculative philosophy also base itself upon facts and have the phenomenal world as its point of departure; but speculative philosophy truly founds itself upon facts and empiricism does not. The first considers facts in their infinite variety and in their continuous development; the second, a certain number of facts, collected at certain epochs and among certain peoples, or at all epochs and among all peoples empirically known; chat is to say, it considers a limited number of facts. Speculative philosophy, presupposing the pure phenomenon, transforms it into (historical)fact and is a truephilosophy of fact; empiricism, without being aware of it, presupposes the facts that it accepts, which are already, though with little criticism, historically ascertained and interpreted. This unconsciousness of what it is doing makes its condition worse, so that it can give nothing buta philosophy of classifications,which are taken for facts only through habitual lack of reflection. Speculative philosophy, therefore, can answer the claim and the boast of empiricism that it is based upon facts, by accepting the claim but denying the boast, as one to which empiricism has and can have no right, and by appropriating this achievement to itself.
Bankruptcy of empiricism: dualism, agnosticism, spiritualism and superstition.
But the bankruptcy of empiricism in all its forms and under all its synonyms is clear in the dualism to which it leads, of appearance and essence, phenomenon and noumenon. For while it professes that there is nothing knowable but the phenomenon, it also postulates an essence, a noumenon, something that is beyond the phenomenon and unknowable. It is all very well to say that this unknowable is not, for it, a proper object for science and philosophy, but it is not to be driven from the field of reality merely by removing it from science and philosophy. Every empiricism, then, recognises side by sidewith the rights of thought, the rights offeeling,and thus the circle of reality comes to be broken at one or more points. When it is wished to continue working empirically upon the unknowable residue, we have those various attempts, which can all of them be summarized beneath the name ofspiritualism.Here the hidden truth is sought by means of experiments of a naturalistic type and spirit is reduced to matter more or less light and subtle. Empiricism ends in superstition. This has always happened; in the decadence of ancient civilization, when philosophers took to converting themselves into thaumaturges; at the eve of the French Revolution, after a century of empiricism and sensationalism, when all sorts of fanatics and schemers appeared and were the favourites of a society of most credulous materialists; in our times, when they have been favoured by a less credulous public of positivists, or of ex-positivists.
Evolutionist positivism and rationalist positivism.
Empiricism has certainly sought to cure its own insufficiencies, of which it was more or less conscious, andevolutionist positivismmust be numbered among these attempts. This form proposed to correct the anti-historical character of positivism by providing ahistoryof reality. But this history was always based uponempirical presuppositions, and was therefore a history of classifications, not of concrete reality; an extravagant caricature of the philosophy of becoming, from whose breast comes History rightly and truly so-called. Another attempt was that ofrationalist positivism,which sought to check the degeneration of positivism toward dualism, sentimentalism and superstition, by appealing to the absolute rights of reason. But this reason is nevertheless always empirical reason, limited to certain series of facts, extrinsic, classificatory, unintelligent. Absolute authority can well be attributed to it in words, but such an attribution does not confer the power of exercising it. This kind of positivism, therefore, meets in our day with favour in freemasonry (at least of the Franco-Italian sort). This is a sect, which is annoying, chiefly because, heedless of facts, it preserves and defends the habit of making use of empty formulas and phrases, and because when it has insulted some priestly vestment, it believes that it has successfully destroyed superstition and obscurantism in man, or when it has declaimed about liberty, it imagines that by this slight effort, liberty has been won and established. Truereasonabhorsrationalism,if it be rationalism of that sort.
Mathematicism
Mathematicismis much rarer than empiricism, because the confusion between thinking and calculating is less easy than that between thinking and classifying. Owing to its rarity and paradoxical character, mathematicism has something aristocratic about it, resembling in this the other extreme error, of æstheticism; whereas the intermediate error, empiricism, just because of its mediocrity, is popular and indeed vulgar.
Symbolical mathematics.
We cannot properly consider as mathematicism that form of philosophy which appeared in antiquity asPythagoreanismandNeopythagoreanismand has reappeared in our days as a doctrine of the mathematical relations of the universe and the harmony of the world. In this conception, numbers are not numbers, but symbols; the numerical relations are not arithmetical, but æsthetic. The pretended mathematical philosophers of this type are neither philosophers nor mathematicians, nor are they arbitrary combiners of these two methods. They would be better described as poets or semi-poets.
Mathematics as demonstrative form of philosophy.
Nor again can we consider to be mathematicism the attempt made by some philosophers to expound their own ideas by a mathematical, algebraical or geometrical method. If theirideas were ideas and not numbers, the method to which they had recourse necessarily remained extrinsic, and possessed no mathematical character beyond the verbal complacency with which they adopted certain formulae of definitions, axioms, theorems, lemmas, corollaries and certain numerical symbols, These formulas and symbols could always be replaced by others, without any inconvenience whatever. It is possible to discuss, it has indeed been discussed, whether such modes of exposition are in good or bad literary taste, or of greater or less didactic convenience. They can be condemned, as they have been condemned, and caused to fall into disuse, as they have fallen; but the quality of the philosophic truth thus expressed, remains unaltered and is never changed into mathematics. Neither the system of Spinoza, who employed the geometrical method, nor that of Leibnitz, who desired the universal calculus, are mathematical systems. If they were so, modern philosophy would not owe some of its most important idealist concepts to those two systems.
Errors of mathematicist philosophy.
Better examples of mathematicism than the treatises and systems developed according to its rules are found in the unfulfilled programmes of such treatises and systems, or in the mathematicisttreatment of certain philosophie problems. Such, for instance, is that concerning the infinity of the world in space and time, a problem which, treated mathematistically, becomes insoluble and makes many people's heads turn. It is impossible to comprehend the world in one's own mind with the mathematical infinite; and either to give or to refuse to it a beginning and an end. Hence the exclamations of terror before that infinite, and the sense of sublimity which seems to arise in the struggle joined between it, which is indomitable, and the human mind which wishes to dominate it. It has, however, already been observed with reason, that such sublimity is not only very near to the ridiculous, but falls into it with all its weight; and that such terror could not in truth be anything but terror of theennuiof having to count and recount in the void and to infinity. The mathematical infinite is nothing real; its appearance of reality is the shadow projected by the mathematical power which the human spirit possesses, of always adding a unit to any number. The true infinite is all before us, in every real fact, and it is only when the continuous unity of reality is divided into separate facts, and space and time are rendered abstract and mathematical, onlythen, if the complete operation be forgotten, that the desperate problem arises and the anguish of never being able to solve it. Another and more actual example of this mathematicist mode of treatment is that of the dimensions of space. Here, forgetting that space of three dimensions is nothing real that can be experienced, but is a mathematical construction, and on the other hand finding it convenient for mathematical reasons to construct spaces of less or more than three dimensions, or ofndimensions, they end by treating these constructions as conceivable realities, and seriously discuss bi-dimensional beings or four-dimensional worlds.
Dualism, agnosticism and superstition of mathematicism.
With affirmations such as those of infinites incomprehensible to thought, and of real but not experienceable spaces, mathematicism also creates a dualism of thought and of reality superior to thought, or (what amounts to the same thing) of thought which meets its equivalent in experience and thought without a corresponding experience. The unknowable here too lies in wait and falls upon the imprudent mathematicist philosopher, who feels himself lost before a second, third, fourth and infinite worlds, excogitated by himself, superior or inferior worlds to those of man, underworlds and overworlds andover-over worlds. He then becomes even spiritualist and asks with Zollner, why spiritualist facts should not possess reality and be produced in the fourth dimension of space, shut off from us. The contradiction of the mathematicist attempt, like that of the æsthetic and empiricist, is clearly revealed in the dualistic, agnostic and mystical consequences to which, as we shall see more clearly further on, all of them necessarily lead.