These appellations I have chosen advisedly, in order that we might not
lose sight of the distinctions in respect of the evidence and the
employment of these principles. It will, however, soon appear that—a
fact which concerns both the evidence of these principles, and the à
priori determination of phenomena—according to the categories of
quantity and quality (if we attend merely to the form of these), the
principles of these categories are distinguishable from those of the
two others, in as much as the former are possessed of an intuitive, but
the latter of a merely discursive, though in both instances a complete,
certitude. I shall therefore call the former mathematical, and the
latter dynamical principles.[27] It must be observed, however, that by
these terms I mean just as little in the one case the principles of
mathematics as those of general (physical) dynamics in the other. I
have here in view merely the principles of the pure understanding, in
their application to the internal sense (without distinction of the
representations given therein), by means of which the sciences of
mathematics and dynamics become possible. Accordingly, I have named
these principles rather with reference to their application than their
content; and I shall now proceed to consider them in the order in which
they stand in the table.
[27] All combination (conjunctio) is either composition (compositio)
or connection (nexus). The former is the synthesis of a manifold, the
parts of which do not necessarily belong to each other. For example,
the two triangles into which a square is divided by a diagonal, do not
necessarily belong to each other, and of this kind is the synthesis of
the homogeneous in everything that can be mathematically considered.
This synthesis can be divided into those of aggregation and coalition,
the former of which is applied to extensive, the latter to intensive
quantities. The second sort of combination (nexus) is the synthesis of
a manifold, in so far as its parts do belong necessarily to each
other; for example, the accident to a substance, or the effect to the
cause. Consequently it is a synthesis of that which though
heterogeneous, is represented as connected à priori. This
combination—not an arbitrary one—I entitle dynamical because it
concerns the connection of the existence of the manifold. This, again,
may be divided into the physical synthesis, of the phenomena divided
among each other, and the metaphysical synthesis, or the connection of
phenomena à priori in the faculty of cognition.
1. AXIOMS OF INTUITION.
The principle of these is: All Intuitions are Extensive Quantities.
PROOF.