It is right to say whatever is affirmed or denied of the whole of a conception can be affirmed or denied of any part of it (dictum de omni et nullo); but it would be absurd so to alter this logical proposition as to say whatever is not contained in a general conception is likewise not contained in the particular conceptions which rank under it; for the latter are particular conceptions, for the very reason that their content is greater than that which is cogitated in the general conception. And yet the whole intellectual system of Leibnitz is based upon this false principle, and with it must necessarily fall to the ground, together with all the ambiguous principles in reference to the employment of the understanding which have thence originated.
Leibnitz’s principle of the identity of indiscernibles or indistinguishables is really based on the presupposition that, if in the conception of a thing a certain distinction is not to be found, it is also not to be met with in things themselves; that, consequently, all things are completely identical (numero eadem) which are not distinguishable from each other (as to quality or quantity) in our conceptions of them. But, as in the mere conception of anything abstraction has been made of many necessary conditions of intuition, that of which abstraction has been made is rashly held to be non-existent, and nothing is attributed to the thing but what is contained in its conception.
The conception of a cubic foot of space, however I may think it, is in itself completely identical. But two cubic feet in space are nevertheless distinct from each other from the sole fact of their being in different places (they are numero diversa); and these places are conditions of intuition, wherein the object of this conception is given, and which do not belong to the conception, but to the faculty of sensibility. In like manner, there is in the conception of a thing no contradiction when a negative is not connected with an affirmative; and merely affirmative conceptions cannot, in conjunction, produce any negation. But in sensuous intuition, wherein reality (take for example, motion) is given, we find conditions (opposite directions)—of which abstraction has been made in the conception of motion in general—which render possible a contradiction or opposition (not indeed of a logical kind)—and which from pure positives produce zero = 0. We are therefore not justified in saying that all reality is in perfect agreement and harmony, because no contradiction is discoverable among its conceptions.[39] According to mere conceptions, that which is internal is the substratum of all relations or external determinations. When, therefore, I abstract all conditions of intuition, and confine myself solely to the conception of a thing in general, I can make abstraction of all external relations, and there must nevertheless remain a conception of that which indicates no relation, but merely internal determinations. Now it seems to follow that in everything (substance) there is something which is absolutely internal and which antecedes all external determinations, inasmuch as it renders them possible; and that therefore this substratum is something which does not contain any external relations and is consequently simple (for corporeal things are never anything but relations, at least of their parts external to each other); and, inasmuch as we know of no other absolutely internal determinations than those of the internal sense, this substratum is not only simple, but also, analogously with our internal sense, determined through representations, that is to say, all things are properly monads, or simple beings endowed with the power of representation. Now all this would be perfectly correct, if the conception of a thing were the only necessary condition of the presentation of objects of external intuition. It is, on the contrary, manifest that a permanent phenomenon in space (impenetrable extension) can contain mere relations, and nothing that is absolutely internal, and yet be the primary substratum of all external perception. By mere conceptions I cannot think anything external, without, at the same time, thinking something internal, for the reason that conceptions of relations presuppose given things, and without these are impossible. But, as an intuition there is something (that is, space, which, with all it contains, consists of purely formal, or, indeed, real relations) which is not found in the mere conception of a thing in general, and this presents to us the substratum which could not be cognized through conceptions alone, I cannot say: because a thing cannot be represented by mere conceptions without something absolutely internal, there is also, in the things themselves which are contained under these conceptions, and in their intuition nothing external to which something absolutely internal does not serve as the foundation. For, when we have made abstraction of all the conditions of intuition, there certainly remains in the mere conception nothing but the internal in general, through which alone the external is possible. But this necessity, which is grounded upon abstraction alone, does not obtain in the case of things themselves, in so far as they are given in intuition with such determinations as express mere relations, without having anything internal as their foundation; for they are not things of a thing of which we can neither for they are not things in themselves, but only phenomena. What we cognize in matter is nothing but relations (what we call its internal determinations are but comparatively internal). But there are some self-subsistent and permanent, through which a determined object is given. That I, when abstraction is made of these relations, have nothing more to think, does not destroy the conception of a thing as phenomenon, nor the conception of an object in abstracto, but it does away with the possibility of an object that is determinable according to mere conceptions, that is, of a noumenon. It is certainly startling to hear that a thing consists solely of relations; but this thing is simply a phenomenon, and cannot be cogitated by means of the mere categories: it does itself consist in the mere relation of something in general to the senses. In the same way, we cannot cogitate relations of things in abstracto, if we commence with conceptions alone, in any other manner than that one is the cause of determinations in the other; for that is itself the conception of the understanding or category of relation. But, as in this case we make abstraction of all intuition, we lose altogether the mode in which the manifold determines to each of its parts its place, that is, the form of sensibility (space); and yet this mode antecedes all empirical causality.
[39] If any one wishes here to have recourse to the usual subterfuge, and to say, that at least realitates noumena cannot be in opposition to each other, it will be requisite for him to adduce an example of this pure and non-sensuous reality, that it may be understood whether the notion represents something or nothing. But an example cannot be found except in experience, which never presents to us anything more than phenomena; and thus the proposition means nothing more than that the conception which contains only affirmatives does not contain anything negative—a proposition nobody ever doubted.
If by intelligible objects we understand things which can be thought by means of the pure categories, without the need of the schemata of sensibility, such objects are impossible. For the condition of the objective use of all our conceptions of understanding is the mode of our sensuous intuition, whereby objects are given; and, if we make abstraction of the latter, the former can have no relation to an object. And even if we should suppose a different kind of intuition from our own, still our functions of thought would have no use or signification in respect thereof. But if we understand by the term, objects of a non-sensuous intuition, in respect of which our categories are not valid, and of which we can accordingly have no knowledge (neither intuition nor conception), in this merely negative sense noumena must be admitted. For this is no more than saying that our mode of intuition is not applicable to all things, but only to objects of our senses, that consequently its objective validity is limited, and that room is therefore left for another kind of intuition, and thus also for things that may be objects of it. But in this sense the conception of a noumenon is problematical, that is to say, it is the notion of that it that it is possible, nor that it is impossible, inasmuch as we do not know of any mode of intuition besides the sensuous, or of any other sort of conceptions than the categories—a mode of intuition and a kind of conception neither of which is applicable to a non-sensuous object. We are on this account incompetent to extend the sphere of our objects of thought beyond the conditions of our sensibility, and to assume the existence of objects of pure thought, that is, of noumena, inasmuch as these have no true positive signification. For
