This conclusion is quite correct: if there is only composite and we imagine everything composite removed, then nothing remains; we may grant this, but this tautological superfluity might be spared, and the proof might begin with what follows, namely : —
“Either all composition cannot be mentally removed, or, it being removed, something subsisting without composition — namely, the simple — must remain.”
“But in the first case again the composite would not consist of substances (for with these compositeness is only a contingent relation of the substances,! and they must be capable of existing as persistent beings without it). — But this case is contradictory to the hypothesis, and thereiore only the second remains: namely, that all composite substance consists of simple parts.”
The reason which is the main point, compared with which all that has been said is quite superfluous, is relegated to a parenthesis. The dilemma is this : — That which persists is either the composite or else the simple. If the first (the composite) were that which persists, then that which persists is not the substances, for in these compositeness is a contingent relation; but the substances are that which persists, therefore that which persists is the simple.
It is evident that the apagogic detour might be avoided, and
' Here redundance of language it added to redundance in proof, — “for with these (to wit, the substances) compositeness is only a contingent relation of Its
that to the Thesis (“Composite substance consists of simple parts”) this reason might immediately be added as proof, namely that compositeness is merely a contingent relation of the substances, external to and not concerned with them. — If compositeness is in truth contingent, then the essence is of course the simple. But this contingency, which is the sole point at issue, is not proved but simply assumed (in parenthesis) as though it were obvious or beside the point. It is, of course, self-evident that compositeness is the determination of con¬ tingency and externality; but, if we were only about to deal with a contingent juxtaposition instead of continuity, it was not worth while to set up an antinomy about it, or, rather, it was impossible ; in that case it is mere tautology (as was said) to assert that the parts are simple.
Thus in the apagogic detour we see that the very assertion which is to be its result already occurs. Thus the proof might more briefly be put as follows : —
Let it be assumed that substances do not consist of simple parts, but are composite. Now all composition can be thought away (since it is a merely contingent relation) ; it being removed, therefore, no substances remain unless they consist of simple parts. But we must have substances, since we assumed their existence ; everything must not vanish, something must remain ; for we have presupposed that some such persistent entity (which we called substance) exists. Therefore this something must be simple.
To complete matters, we must consider the conclusion, which runs as follows : —
“Hence it follows immediately that all the things in the world are simple essences, that compositeness is a condition merely external to them, and that reason must consider the elementary substances to be simple essences.”
Here the external, that is, the contingent, nature of com¬ positeness is cited as a consequence, after having already been introduced parenthetically and used in the proof.
Kant protests much that he is not looking for sophisms in the conflicting propositions of the antinomy, in order to effect (as the phrase is) an advocate’s proof. Indeed, this proof is not really to be accused of sophistry so much as of a forced and useless tortuosity, which serves only to produce the outer form
of a proof, not allowing it to be perfectly transparent that that which should stand out as conclusion is the (parenthetic) hinge of the proof, and that there is no proof but only an assumption.
“No composite thing in the world consists of simple parts, and nothing simple anywhere exists in it.”
The proof again has the apagogic turn, and in another manner is as faulty as the previous.
“Assume,” it runs, “that a composite thing as substance consists of simple parts. Now all external relation (and therefore also the composition of substances) is possible only in space, and therefore the space which it occupies must consist of as many parts as those of which the composite thing consists. Now space does not consist of simple parts, but of spaces. Therefore each part of the composite thing must occupy one space.”
“But the absolutely first parts of every composite thing are simple.”
“Now every reality which occupies a space comprehends a manifold of mutual externalities ; it is therefore composed (of substances), and thus the simple would be a substantial com¬ posite, which is self-contradictory.”
This proof may be called a perfect nest (to use an expression which is elsewhere employed by Kant) of faulty procedure.
First, the apagogic turn is a baseless fabric. The assumption that whatever is substantial is spatial, while space does not consist of simple parts, is a direct assertion which is made the immediate foundation of that which is to be proved ; after this there is no need for further proof.
Next, this apagogic proof begins with the proposition “that all composition of substances is an external relation,” but, strangely enough, immediately forgets it. For the further con¬ clusion is made that composition can take place only in space, that space does not consist of simple parts, and that therefore the reality occupying a space is composite. If once composite¬ ness has been taken as an external relation, then spatiality itself (since composition is supposed to be possible in it alone) is for that very reason a relation external to the substances, which does sot concern them nor touch their nature any more than
does all the rest that can be inferred from the determination of spatiality. For this very reason the substances should not be placed in space.
Further, it is assumed that the space into which the sub¬ stances are here transplanted does not consist of simple parts ; since it is an intuition (that is, according to Kant’s determina¬ tion, a sensuous representation) which can be given only by one single object, and is not a so-called discursive concept. — This distinction of Kant’s between intuition and concept has, of course, led to the abuse of the former, and, in order to save the labour of achieving the latter, its value and sphere have been extended to all cognition. What is relevant here is this, that space, like intuition itself, must be conceived if we would have any concept at all. And thus the question would arise whether space, though simple continuity for intuition, might not conceptually have to be taken as composed of simple parts, since otherwise space would be affected by that same antinomy into which substance only was transplanted. Indeed, if the antinomy is taken in the abstract, it extends to all Quantity (as was said above) and therefore also to Space and Time.
Now in the proof it is assumed that space does not consist of simple parts ; and this should have been sufficient reason for not transplanting the simple into this element, which is inade¬ quate to the determination of the simple. — Here also the con¬ tinuity of space comes into collision with compositeness ; these two are confused, and the former is inserted in the place of the latter (which results in a Quaternio Urminorum in the con¬ clusion). Kant expressly determines space as being one, its parts being based only on limitations, so that they do not precede space, sole and all-comprehending, as its component parts from which it could be put together. ( Critique of Pure Reason, Second Ed., p. 39.) Here continuity is predicated of space, very justly and definitely, in opposition to its compositeness out of parts. In the proof, on the other hand, the transplanting of the sub¬ stances into space is to involve “a manifold of mutual exter¬ nalities,” which, further, is “therefore composite.” Yet we have quoted what shows that the manner in which a manifold exists in space is expressly designed to exclude compositeness and parts which precede its unity.
In the Note to the proof of the Antithesis, the other Junda-
mental notion of the critical philosophy is further expressly adduced, namely, that we have a concept of bodies only as phenomena, which, as such, necessarily presuppose space as the condition of the possibility of all external manifestation. If by substances mere bodies are meant, such as are seen, felt, tasted, and so forth, then there is really no question of their concep¬ tual meaning : sense-perception only is in question. The proof of the Antithesis might then be put in brief thus : — All visual, sensory, and other experience shows us only what is composite; the best microscopes and the keenest knives have never yet allowed us to hit on anything simple. Therefore Reason, too, should not want to hit on anything simple.
And thus when now we regard more closely this opposition of Thesis and Antithesis, liberating their proofs of all idle superfluity and tortuousness, we find that the proof of the Antithesis, by transplanting the substances into space, contains a dogmatic assumption of Continuity, and that the proof of the Thesis, by assuming Compositeness as the class of relation sub¬ sisted between the substances, contains the dogmatic assump¬ tion of the contingency of this relation — that is, the assumption that the substances are absolute Ones. Thus the whole antinomy reduces itself to the separation and direct assertion of the two moments of Quantity as being absolutely separate. Looked at from the point of view of mere discreteness, substance, matter, space and time, and so on, are absolutely divided, and the One is their principle. From the point of view of continuity, this One is merely suspended: division remains divisibility, the possibility of dividing remains as possibility, without ever actually reaching the atom. Now even if we do not move beyond the determination implied in what has been said about these contradictions, still continuity itself contains the moment of the atom, since continuity exists simply as the possibility of division ; just as accomplished division, or discreteness, cancels all distinction between the Ones — for each simple One is what every other is, — and for that very reason contains their equality and therefore their continuity. Each of the two opposed sides contains its other in itself, and neither can be thought of with¬ out the other; and thus it follows that, taken alone, neither determination has truth, but only their unity. This is the true dialectic consideration of them, and the true result.
The dialectic examples of the old Eleatic school, especially those which deal with motion, are incomparably deeper and richer in meaning than the antinomy of Kant which we have considered. They, too, are based on the concept of Quantity, and in it have their solution. To consider them here would lead too far ; they concern the concepts of Space and Time, and can be dealt with in connexion with these subjects and with the history of philosophy. — They do the highest honour to the reason of their inventors; their result is the pure Being of Parmenides, since they demonstrate the solution into itself of all determinate being : in themselves, therefore, they are the Flux of Herakleitos. They therefore deserve a fuller considera¬ tion than the ordinary explanation that they are just sophisms ; — an assertion which clings to empirical perception, following that method of Diogenes (so convincing to common sense), who, when a dialectician demonstrated the contradiction con¬ tained in motion, is said to have put no further strain on his reason, but, by mutely walking up and down, to have referred to the evidence of the eyes; — an assertion and a refutation which of course it is easier to make than to enter upon thought, to seize the confusions into which thought, quite unforced, leads when it formulates itself in ordinary consciousness, and to solve them by means of thought.
The solution of these dialectic formations which Aristotle effects is highly to be praised : it is implied in his truly specu¬ lative concepts of Space, Time, and Motion. Infinite divisibility (which, being imagined as actually completed, is equivalent to infinite division, or the atoms), as being the principle on which are based the most famous of these proofs, is by him opposed to Continuity (of Time as well as of Space), in such a manner that infinite — that is, abstract — plurality is contained in continuity only in itself, or potentially. The actual, as opposed to abstract plurality (or to abstract continuity), is their concrete form, it is* Time and Space itself; and these in turn are opposed to Motion and Matter. The abstract exists only in itself, or potentially ; it exists only as a moment of the Real. Bayle in his Dictionnaire (Article, Zenon) considers Aristotle’s solution of Zeno’s dialectic “ pitoyable ” : he does not understand the meaning of the potentially infinite divisibility of matter. He replies that if matter is infinitely divisible, it actually contains