| [*Footnote; Apprehension is the Kantian word for preception, in the largest sense in which we employ that term. |
| It is the genus which includes under i, as species, perception proper and sensation proper--Tr] |
| Now that quantity which is apprehended only as unity, and in which plurality can be represented only by approximation to negation = 0, I term intensive quantity. |
| Consequently, reality in a phenomenon has intensive quantity, that is, a degree. |
| if we consider this reality as cause (be it of sensation or of another reality in the phenomenon, for example, a change), we call the degree of reality in its character of cause a momentum, for example, the momentum of weight; and for this reason, that the degree only indicates that quantity the apprehension of which is not successive, but instantaneous. |
| This, however, I touch upon only in passing, for with causality I have at present nothing to do. |
| Accordingly, every sensation, consequently every reality in phenomena, however small it may be, has a degree, that is, an intensive quantity, which may always be lessened, and between reality and negation there exists a continuous connection of possible realities, and possible smaller perceptions. |
| Every colour-- for example, red--has a degree, which, be it ever so small, is never the smallest, and so is it always with heat, the momentum of weight, etc. |
| This property of quantities, according to which no part of them is the smallest possible (no part simple), is called their continuity. |
| Space and time are quanta continua, because no part of them can be given, without enclosing it within boundaries (points and moments), consequently, this given part is itself a space or a time. |
| Space, therefore, consists only of spaces, and time of times. |
| Points and moments are only boundaries, that is, the mere places or positions of their limitation. |
| But places always presuppose intuitions which are to limit or determine them; and we cannot conceive either space or time composed of constituent parts which are given before space or time. |
| Such quantities may also be called flowing, because synthesis (of the productive imagination) in the production of these quantities is a progression in time, the continuity of which we are accustomed to indicate by the expression flowing. |
| All phenomena, then, are continuous quantities, in respect both to intuition and mere perception (sensation, and with it reality). |
| In the former case they are extensive quantities; in the latter, intensive. |
| When the synthesis of the manifold of a phenomenon is interrupted, there results merely an aggregate of several phenomena, and not properly a phenomenon as a quantity, which is not produced by the mere continuation of the productive synthesis of a certain kind, but by the repetition of a synthesis always ceasing. |
| For example, if I call thirteen dollars a sum or quantity of money, I employ the term quite correctly, inasmuch as I understand by thirteen dollars the value of a mark in standard silver, which is, to be sure, a continuous quantity, in which no part is the smallest, but every part might constitute a piece of money, which would contain material for still smaller pieces. |
| If, however, by the words thirteen dollars I understand so many coins (be their value in silver what it may), it would be quite erroneous to use the expression a quantity of dollars; on the contrary, I must call them aggregate, that is, a number of coins. |
| And as in every number we must have unity as the foundation, so a phenomenon taken as unity is a quantity, and as such always a continuous quantity (quantum continuum). |
| Now, seeing all phenomena, whether considered as extensive or intensive, are continuous quantities, the proposition; "All change (transition of a thing from one state into another) is continuous," might be proved here easily, and with mathematical evidence, were it not that the causality of a change lies, entirely beyond the bounds of a transcendental philosophy, and presupposes empirical principles. |