We have already seen that the arbitrary concept differs from the pure concept in that, of necessity, it produces two forms by the two acts of empiricism and emptiness and thereby gives rise to two different types of formations, empirical and abstract concepts. Empirical concepts have this property, that in them unity is outside distinction and distinction outside unity. And it is natural: for if it were the case that these two determinations penetrated one another, the concepts would be, as we have already noted, not arbitrary, but necessary and true. If the distinction is placed outside the unity, every division that is given of it is, like the concepts themselves, arbitrary; and every enumeration is also arbitrary, because those concepts can be infinitely multiplied. In exchange for the rationally determined and completely unified distinctions of the pure concepts, the pseudoconcepts offer multiple groups, arbitrarily formed, and sometimes also unified in a single group, which embraces the entire field of the knowable, but in such a way as not to exclude an infinite number of other ways of apprehending it.
In these groups the empirical concepts simulate the arrangement of the pure concepts, reducing the particular to the universal, that is to say, a certain number of concepts beneath another concept. But it is impossible in any way to think these subordinate concepts, as actualizations of the fundamental concept, which are developed from one another and return into themselves; hence we are compelled to leave them external to one another, simply co-ordinated. The scheme of subordination and co-ordination, and its relative spatial symbol (the symbol of classification), which is a right line, on the upper side of which falls perpendicularly another right line, and from whose lower side descend other perpendicular and therefore parallel right lines, is opposed to the circle and is the most evident ocular demonstration of the profound diversity of the two procedures. It will always be impossible to dispose a nexus of pure concepts in that classificatory scheme without falsifying them; it will always be impossible to transform empirical concepts into a series of grades without destroying them.
The definition in the empirical concepts, and the notes of the concept.
In consequence of the scheme of classification, the definition which, in the case of pure concepts, has the three moments of universality, particularity, and singularity, in the case of empirical concepts has only two, which are called genus and species; and is applied according to the rule, by means of the proximate genus and the specific difference. Its object indeed is simply to record, not to understand and to think, a given empirical formation; and this is fully attained when its position is determined by means of the indication of what is above and what is beside it. In order to determine it yet more accurately, the doctrine of the definition has been gradually enriched with other marks or predicables, which, in traditional Logic, are five: genus, species, differentia, property, accident. But it is a question of caprice upon caprice, of which it is not advisable to take too much account. And as it would be barbaric to apply the classificatory scheme to the pure concepts, so it would be equally barbaric to define the pure concepts by means of marks, that is, by means of characteristics mechanically arranged.
Series in the abstract concepts.
Where the thinker forgets the true function of the empirical concepts and is seized with the desire to develop them rationally, and thus to overcome the atomism of the scheme of classification and of extrinsic definition, he is led to refine them into abstract concepts, in which that scheme and that method of definition are overcome: the classification becomes a series (numerical series, series of geometrical forms, etc.), and the definition becomes genetic. But this improvement not only makes the empirical concepts disappear, and is therefore not improvement but death (like the death which the empirical concepts find in true knowledge when they return or mount up again to pure thought); but such improvement substitutes for empiricism emptiness. Series and genetic definitions answer without doubt to demands of the practical spirit; but, as we know, they do not yield truth, not even the truth which lies at the bottom of an empirical concept or of a falsified and mutilated representation. Hence, here as elsewhere, empirical concepts and abstract concepts reveal their double one-sidedness, and exhibit more significantly the value of the unity which they break up; the distinction, which is not classification, but circle and unity; the definition, which is not an aggregate of intuitive data; the series, which is a complete series; the genesis, which is not abstract but ideal.