Chapter II: æstheticism, Empiricism and Mathematicism

[Sidenote: _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.

[Sidenote: _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 develop the 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 true _instrument_ of 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 of _intuitionism,_ or again as _pure 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.

[Sidenote: _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 the true 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.

[Sidenote: _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 of _positivism_ and 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 already _philosophic determinations,_ and could only in this way be admitted as _historically ascertained. Psychologist_ is also positivism; positivism, that is to say, more properly applied to the group of the so-called mental and moral sciences. _Neocriticism_ can 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 of _a philosophy founded upon the sciences,_ or of an _inductive 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 rightly feels 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 on _familiar terms_ with 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 the practical 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.

[Sidenote: _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 true _philosophy 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 but _a 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.

[Sidenote: _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 side with the rights of thought, the rights of _feeling,_ 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 of _spiritualism._ 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.

[Sidenote: _Evolutionist positivism and rationalist positivism._]

Empiricism has certainly sought to cure its own insufficiencies, of which it was more or less conscious, and _evolutionist positivism_ must be numbered among these attempts. This form proposed to correct the anti-historical character of positivism by providing a _history_ of reality. But this history was always based upon empirical 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 of _rationalist 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. True _reason_ abhors _rationalism,_ if it be rationalism of that sort.

[Sidenote: _Mathematicism_]

_Mathematicism_ is 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.

[Sidenote: _Symbolical mathematics._]

We cannot properly consider as mathematicism that form of philosophy which appeared in antiquity as _Pythagoreanism_ and _Neopythagoreanism_ and 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.

[Sidenote: _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 their ideas 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.

[Sidenote: _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 mathematicist treatment 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 the _ennui_ of 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, only then, 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 of _n_ dimensions, they end by treating these constructions as conceivable realities, and seriously discuss bi-dimensional beings or four-dimensional worlds.

[Sidenote: _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 and over-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.