objective grounds, the infinity of the world in space in his “Natural History of the Theory of the Heavens,” part ii. ch. 7. Aristotle also acknowledges the same, “Phys.,” iii. ch. 4, a chapter which, together with the following one, is very well worth reading with reference to this antinomy.
In the second conflict the thesis is at once guilty of a very palpable petitio principii, for it commences, “Every compound substance consists of simple parts.” From the compoundness here arbitrarily assumed, no doubt it afterwards very easily proves the simple parts. But the proposition, “All matter is compound,” which is just the point, remains unproved, because it is simply a groundless assumption. The opposite of simple is not compound, but extended, that which has parts and is divisible. Here, however, it is really tacitly assumed that the parts existed before the whole, and were brought together, whence the whole has arisen; for this is the meaning of the word “compound.” Yet this can just as little be asserted as the opposite. Divisibility means merely the possibility of separating the whole into parts, and not that the whole is compounded out of parts and thus came into being. Divisibility merely asserts the parts a parte post; compoundness asserts them a parte ante. For there is essentially no temporal relation between the parts and the whole; they rather condition each other reciprocally, and thus always exist at the same time, for only so far as both are there is there anything extended in space. Therefore what Kant says in the observations on the thesis, “Space ought not to be called a compositum, but a totum,” &c., holds good absolutely of matter also, which is simply space become perceptible. On the other hand, the infinite divisibility of matter, which the antithesis asserts, follows a priori and incontrovertibly from that of space, which it fills. This proposition has absolutely nothing against it; and therefore Kant also (p. 513; V. 541), when he speaks seriously and in his own person, no longer as the mouthpiece of the αδικος λογος, presents it as objective truth; and also in the “Metaphysical First Principles of Natural Science” (p. 108, first edition), the proposition, “Matter is infinitely divisible,” is placed at the beginning of the proof of the first proposition of mechanics as established truth, having appeared and been proved as the fourth proposition in the Dynamics. But here Kant spoils the proof of the antithesis by the greatest obscurity of style and useless accumulation of words, with the cunning intention that the evidence of the antithesis shall not throw the sophisms of the thesis too much into the shade. Atoms are no necessary thought of the reason, but merely an hypothesis for the explanation of the difference of the specific gravity of bodies. But Kant himself has shown, in the dynamics of his “Metaphysical First Principles of Natural Science,” that this can be otherwise, and indeed better and more simply explained than by atomism. In this, however, he was anticipated by Priestley, “On Matter and Spirit,” sect. i. Indeed, even in Aristotle, “Phys.” iv. 9, the fundamental thought of this is to be found.
The argument for the third thesis is a very fine sophism, and is really Kant's pretended principle of pure reason itself entirely unadulterated and unchanged. It tries to prove the finiteness of the series of causes by saying that, in order to be sufficient, a cause must contain the complete sum of the conditions from which the succeeding state, the effect, proceeds. For the completeness of the determinations present together in the state which is the cause, the argument now substitutes the completeness of the series of causes by which that state itself was brought to actuality; and because completeness presupposes the condition of being rounded off or closed in, and this again presupposes finiteness, the argument infers from this a first cause, closing the series and therefore unconditioned. But the juggling is obvious. In order to conceive the state A. as the sufficient cause of the state B., I assume that it contains the sum of the necessary determinations from the co-existence of which the estate B. inevitably follows. Now by this my demand upon it as a sufficient cause is entirely satisfied, and has no direct connection with the question how the state A. itself came to be; this rather belongs to an entirely different consideration, in which I regard the said state A. no more as cause, but as itself an effect; in which case another state again must be related to it, just as it was related to B. The assumption of the finiteness of the series of causes and effects, and accordingly of a first beginning, appears nowhere in this as necessary, any more than the presentness of the present moment requires us to assume a beginning of time itself. It only comes to be added on account of the laziness of the speculating individual. That this assumption lies in the acceptance of a cause as a sufficient reason is thus unfairly arrived at and false, as I have shown at length above when considering the Kantian principle of pure reason which coincides with this thesis. In illustration of the assertion of this false thesis, Kant is bold enough in his observations upon it to give as an example of an unconditioned beginning his rising from his chair; as if it were not just as impossible for him to rise without a motive as for a ball to roll without a cause. I certainly do not need to prove the baselessness of the appeal which, induced by a sense of weakness, he makes to the philosophers of antiquity, by quoting from Ocellus Lucanus, the Eleatics, &c., not to speak of the Hindus. Against the proof of this antithesis, as in the case of the previous ones, there is nothing to advance.
The fourth conflict is, as I have already remarked, really tautological with the third; and the proof of the thesis is also essentially the same as that of the preceding one. His assertion that every conditioned presupposes a complete series of conditions, and therefore a series which ends with an unconditioned, is a petitio principii, which must simply be denied. Everything conditioned presupposes nothing but its condition; that this is again conditioned raises a new consideration which is not directly contained in the first.
A certain appearance of probability cannot be denied to the antinomy; yet it is remarkable that no part of the Kantian philosophy has met so little contradiction, indeed has found so much acceptance, as this exceedingly paradoxical doctrine. Almost all philosophical parties and text-books have regarded it as valid, and have also repeatedly reconstructed it; while nearly all Kant's other doctrines have been contested, and indeed there have never been wanting some perverse minds which rejected even the transcendental æsthetic. The undivided assent which the antinomy, on the other hand, has met with may ultimately arise from the fact that certain persons regard with inward satisfaction the point at which the understanding is so thoroughly brought to a standstill, having hit upon something which at once is and is not, so that they actually have before them here the sixth trick of Philadelphia in Lichtenberg's broadsheet.
If we examine the real meaning of Kant's Critical Solution of the cosmological problem which now follows, we find that it is not what he gives it out to be, the solution of the problem by the disclosure that both sides, starting from false assumptions, are wrong in the first and second conflicts, and that in the third and fourth both are right. It is really the confirmation of the antitheses by the explanation of their assertions.
First Kant asserts, in this solution, obviously wrongly, that both sides started from the assumption, as their first principle, that with the conditioned the completed (thus rounded off) series of its conditions is given. Only the thesis laid down this proposition, Kant's principle of pure reason, as the ground of its assertions; the antithesis, on the other hand, expressly denied it throughout, and asserted the contrary. Further, Kant charges both sides with this assumption, that the world exists in itself, i. e., independently of being known and of the forms of this knowledge, but this assumption also is only made by the thesis; indeed, it is so far from forming the ground of the assertions of the antithesis that it is absolutely inconsistent with them. For that it should all be given is absolutely contradictory of the conception of an infinite series. It is therefore essential to it that it should always exist only with reference to the process of going through it, and not independently of this. On the other hand, in the assumption of definite limits also lies that of a whole which exists absolutely and independently of the process of completely measuring it. Thus it is only the thesis that makes the false assumption of a self-existent universe, i. e., a universe given prior to all knowledge, and to which knowledge came as to something external to itself. The antithesis from the outset combats this assumption absolutely; for the infinity of the series which it asserts merely under the guidance of the principle of sufficient reason can only exist if the regressus is fully carried out, but not independently of it. As the object in general
