Logic as the Science of the Pure Concept

by Benedetto Croce

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.

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.

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.

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.

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.