| We shall now proceed to fulfil this duty, and thereby throw not a little light on the question as to the determination of the proper business of the understanding. |
| 1. Identity and Difference. |
| When an object is presented to us several times, but always with the same internal determinations (qualitas et quantitas), it, if an object of pure understanding, is always the same, not several things, but only one thing (numerica identitas); but if a phenomenon, we do not concern ourselves with comparing the conception of the thing with the conception of some other, but, although they may be in this respect perfectly the same, the difference of place at the same time is a sufficient ground for asserting the numerical difference of these objects (of sense). |
| Thus, in the case of two drops of water, we may make complete abstraction of all internal difference (quality and quantity), and, the fact that they are intuited at the same time in different places, is sufficient to justify us in holding them to be numerically different. |
| Leibnitz regarded phenomena as things in themselves, consequently as intelligibilia, that is, objects of pure understanding (although, on account of the confused nature of their representations, he gave them the name of phenomena), and in this case his principle of the indiscernible (principium identatis indiscernibilium) is not to be impugned. |
| But, as phenomena are objects of sensibility, and, as the understanding, in respect of them, must be employed empirically and not purely or transcendentally, plurality and numerical difference are given by space itself as the condition of external phenomena. |
| For one part of space, although it may be perfectly similar and equal to another part, is still without it, and for this reason alone is different from the latter, which is added to it in order to make up a greater space. |
| It follows that this must hold good of all things that are in the different parts of space at the same time, however similar and equal one may be to another. |
| 2. Agreement and Opposition. |
| When reality is represented by the pure understanding (realitas noumenon), opposition between realities is incogitable--such a relation, that is, that when these realities are connected in one subject, they annihilate the effects of each other and may be represented in the formula 3 - 3 = 0. On the other hand, the real in a phenomenon (realitas phaenomenon) may very well be in mutual opposition, and, when united in the same subject, the one may completely or in part annihilate the effect or consequence of the other; as in the case of two moving forces in the same straight line drawing or impelling a point in opposite directions, or in the case of a pleasure counterbalancing a certain amount of pain. |
| 3. The Internal and External. |
| In an object of the pure understanding, only that is internal which has no relation (as regards its existence) to anything different from itself. |
| On the other hand, the internal determinations of a substantia phaenomenon in space are nothing but relations, and it is itself nothing more than a complex of mere relations. |
| Substance in space we are cognizant of only through forces operative in it, either drawing others towards itself (attraction), or preventing others from forcing into itself (repulsion and impenetrability). |
| We know no other properties that make up the conception of substance phenomenal in space, and which we term matter. |
| On the other hand, as an object of the pure understanding, every substance must have internal determination and forces. |
| But what other internal attributes of such an object can I think than those which my internal sense presents to me? |
| That, to wit, which in either itself thought, or something analogous to it. |
| Hence Leibnitz, who looked upon things as noumena, after denying them everything like external relation, and therefore also composition or combination, declared that all substances, even the component parts of matter, were simple substances with powers of representation, in one word, monads. |
| 4. Matter and Form. |
| These two conceptions lie at the foundation of all other reflection, so inseparably are they connected with every mode of exercising the understanding. |