Let it be supposed that a composite thing (as substance) consists of simple parts. Inasmuch as all external relation, consequently all composition of substances, is possible only in space; the space, occupied by that which is composite, must consist of the same number of parts as is contained in the composite. But space does not consist of simple parts, but of spaces. Therefore, every part of the composite must occupy a space. But the absolutely primary parts of what is composite are simple. It follows that what is simple occupies a space. Now, as everything real that occupies a space, contains a manifold the parts of which are external to each other, and is consequently composite — and a real composite, not of accidents (for these cannot exist external to each other apart from substance), but of substances — it follows that the simple must be a substantial composite, which is self-contradictory.
The second proposition of the antithesis — that there exists in the world nothing that is simple — is here equivalent to the following: The existence of the absolutely simple cannot be demonstrated from any experience or perception either external or internal; and the absolutely simple is a mere idea, the objective reality of which cannot be demonstrated in any possible experience; it is consequently, in the exposition of phenomena, without application and object. For, let us take for granted that an object may be found in experience for this transcendental idea; the empirical intuition of such an object must then be recognized to contain absolutely no manifold with its parts external to each other, and connected into unity. Now, as we cannot reason from the non-consciousness of such a manifold to the impossibility of its existence in the intuition of an object, and as the proof of this impossibility is necessary for the establishment and proof of absolute simplicity; it follows that this simplicity cannot be inferred from any perception whatever. As, therefore, an absolutely simple object cannot be given in any experience, and the world of sense must be considered as the sum total of all possible experiences: nothing simple exists in the world.
This second proposition in the antithesis has a more extended aim than the first. The first merely banishes the simple from the intuition of the composite; while the second drives it entirely out of nature. Hence we were unable to demonstrate it from the conception of a given object of external intuition (of the composite), but we were obliged to prove it from the relation of a given object to a possible experience in general.
Observations on the Second Antinomy.
Thesis.
When I speak of a whole, which necessarily consists of simple parts, I understand thereby only a substantial whole, as the true composite; that is to say, I understand that contingent unity of the manifold which is given as perfectly isolated (at least in thought), placed in reciprocal connection, and thus constituted a unity. Space ought not to be called a compositum but a totum, for its parts are possible in the whole, and not the whole by means of the parts. It might perhaps be called a compositum ideale, but not a compositum reale. But this is of no importance. As space is not a composite of substances (and not even of real accidents), if I abstract all composition therein — nothing, not even a point, remains; for a point is possible only as the limit of a space — consequently of a composite. Space and time, therefore, do not consist of simple parts. That which belongs only to the condition or state of a substance, even although it possesses a quantity (motion or change, for example), likewise does not consist of simple parts. That is to say, a certain degree of change does not originate from the addition of many simple changes. Our inference of the simple from the composite is valid only of self-subsisting things. But the accidents of a state are not self-subsistent. The proof, then, for the necessity of the simple, as the component part of all that is substantial and composite, may prove a failure, and the whole case of this thesis be lost, if we carry the proposition too far, and wish to make it valid of everything that is composite without distinction — as indeed has really now and then happened. Besides, I am here speaking only of the simple, in so far as it is necessarily given in the composite — the latter being capable of solution into the former as its component parts. The proper signification of the word monas (as employed by Leibnitz) ought to relate to the simple, given immediately as simple substance (for example, in consciousness), and not as an element of the composite. As an element, the term atomus would be more appropriate. And as I wish to prove the existence of simple substances, only in relation to, and as the elements of, the composite, I might term the antithesis of the second Antinomy, transcendental Atomistic. But as this word has long been employed to designate a particular theory of corporeal phenomena (moleculae), and thus presupposes a basis of empirical conceptions, I prefer calling it the dialectical principle of Monadology.
Antithesis.
Against the assertion of the infinite subdivisibility of matter whose ground of proof is purely mathematical, objections have been alleged by the Monadists. These objections lay themselves open, at first sight, to suspicion, from the fact that they do not recognize the clearest mathematical proofs as propositions relating to the constitution of space, in so far as it is really the formal condition of the possibility of all matter, but regard them merely as inferences from abstract but arbitrary conceptions, which cannot have any application to real things, just as if it were possible to imagine another mode of intuition than that given in the primitive intuition of space; and just as if its a priori determinations did not apply to everything, the existence of which is possible, from the fact alone of its filling space. If we listen to them, we shall find ourselves required to cogitate, in addition to the mathematical point, which is simple — not, however, a part, but a mere limit of space — physical points, which are indeed likewise simple, but possess the peculiar property, as parts of space, of filling it merely by their aggregation. I shall not repeat here the common and clear refutations of this absurdity, which are to be found everywhere in numbers: every one knows that it is impossible to undermine the evidence of mathematics by mere discursive conceptions; I shall only remark that, if in this case philosophy endeavours to gain an advantage over mathematics by sophistical artifices, it is because it forgets that the discussion relates solely to Phenomena and their conditions. It is not sufficient to find the conception of the simple for the pure conception of the composite, but we must discover for the intuition of the composite (matter), the intuition of the simple. Now this, according to the laws of sensibility, and consequently in the case of objects of sense, is utterly impossible. In the case of a whole composed of substances, which is cogitated solely by the pure understanding, it may be necessary to be in possession of the simple before composition is possible. But this does not hold good of the Totum substantiale phaenomenon, which, as an empirical intuition in space, possesses the necessary property of containing no simple part, for the very reason that no part of space is simple. Meanwhile, the Monadists have been subtle enough to escape from this difficulty, by presupposing intuition and the dynamical relation of substances as the condition of the possibility of space, instead of regarding space as the condition of the possibility of the objects of external intuition, that is, of bodies. Now we have a conception of bodies only as phenomena, and, as such, they necessarily presuppose space as the condition of all external phenomena. The evasion is therefore in vain; as, indeed, we have sufficiently shown in our Aesthetic. If bodies were things in themselves, the proof of the Monadists would be unexceptionable.
The second dialectical assertion possesses the peculiarity of having opposed to it a dogmatical proposition, which, among all such sophistical statements, is the only one that undertakes to prove in the case of an object of experience, that which is properly a transcendental idea — the absolute simplicity of substance. The proposition is that the object of the internal sense, the thinking Ego, is an absolute simple substance. Without at present entering upon this subject — as it has been considered at length in a former chapter — I shall merely remark that, if something is cogitated merely as an object, without the addition of any synthetical determination of its intuition — as happens in the case of the bare representation, I— it is certain that no manifold and no composition can be perceived in such a representation. As, moreover, the predicates whereby I cogitate this object are merely intuitions of the internal sense, there cannot be discovered in them anything to prove the existence of a manifold whose parts are external to each other, and, consequently, nothing to prove the existence of real composition. Consciousness, therefore, is so constituted that, inasmuch as the thinking subject is at the same time its own object, it cannot divide itself — although it can divide its inhering determinations. For every object in relation to itself