Our table of the categories suggests considerations of some importance, which may perhaps have significant results in regard to the scientific form of all rational cognitions. For, that this table is useful in the theoretical part of philosophy, nay, indispensable for the sketching of the complete plan of a science, so far as that science rests upon conceptions a priori, and for dividing it mathematically, according to fixed principles, is most manifest from the fact that it contains all the elementary conceptions of the understanding, nay, even the form of a system of these in the understanding itself, and consequently indicates all the momenta, and also the internal arrangement of a projected speculative science, as I have elsewhere shown.* Here follow some of these observations.
*In the Metaphysical Principles of Natural Science.
I. This table, which contains four classes of conceptions of the understanding, may, in the first instance, be divided into two classes, the first of which relates to objects of intuition- pure as well as empirical; the second, to the existence of these objects, either in relation to one another, or to the understanding.
The former of these classes of categories I would entitle the mathematical, and the latter the dynamical categories. The former, as we see, has no correlates; these are only to be found in the second class. This difference must have a ground in the nature of the human understanding.
II. The number of the categories in each class is always the same, namely, three- a fact which also demands some consideration, because in all other cases division a priori through conceptions is necessarily dichotomy. It is to be added, that the third category in each triad always arises from the combination of the second with the first.
Thus totality is nothing else but plurality contemplated as unity; limitation is merely reality conjoined with negation; community is the causality of a substance, reciprocally determining, and determined by other substances; and finally, necessity is nothing but existence, which is given through the possibility itself. Let it not be supposed, however, that the third category is merely a deduced, and not a primitive conception of the pure understanding. For the conjunction of the first and second, in order to produce the third conception, requires a particular function of the understanding, which is by no means identical with those which are exercised in the first and second. Thus, the conception of a number (which belongs to the category of totality) is not always possible, where the conceptions of multitude and unity exist (for example, in the representation of the infinite). Or, if I conjoin the conception of a cause with that of a substance, it does not follow that the conception of influence, that is, how one substance can be the cause of something in another substance, will be understood from that. Thus it is evident that a particular act of the understanding is here necessary; and so in the other instances.
III. With respect to one category, namely, that of community, which is found in the third class, it is not so easy as with the others to detect its accordance with the form of the disjunctive judgement which corresponds to it in the table of the logical functions.
In order to assure ourselves of this accordance, we must observe that in every disjunctive judgement, the sphere of the judgement (that is, the complex of all that is contained in it) is represented as a whole divided into parts; and, since one part cannot be contained in the other, they are cogitated as co-ordinated with, not subordinated to each other, so that they do not determine each other unilaterally, as in a linear series, but reciprocally, as in an aggregate- (if one member of the division is posited, all the rest are excluded; and conversely).
Now a like connection is cogitated in a whole of things; for one thing is not subordinated, as effect, to another as cause of its existence, but, on the contrary, is co-ordinated contemporaneously and reciprocally, as a cause in relation to the determination of the others (for example, in a body- the parts of which mutually attract and repel each other). And this is an entirely different kind of connection from that which we find in the mere relation of the cause to the effect (the principle to the consequence), for in such a connection the consequence does not in its turn determine the principle, and therefore does not constitute, with the latter, a whole- just as the Creator does not with the world make up a whole. The process of understanding by which it represents to itself the sphere of a divided conception, is employed also when we think of a thing as divisible; and in the same manner as the members of the division in the former exclude one another, and yet are connected in one sphere, so the understanding represents to itself the parts of the latter, as having- each of them- an existence (as substances), independently of the others, and yet as united in one whole.