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. [Sidenote: _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. [Sidenote: _Series in the abstract concepts._]