Артур Шопенгауэр - The World as Will and Idea (Vol. 2 of 3)

With reference to the spatial limits of the world, it is proved that, if it is to be regarded as a given whole , it must necessarily have limits. The reasoning is correct, only it was just the first link of it that was to be proved, and that remains unproved. Totality presupposes limits, and limits presuppose totality; but here both together are arbitrarily presupposed. For this second point, however, the antithesis affords no such satisfactory proof as for the first, because the law of causality provides us with necessary determinations only with reference to time, not to space, and affords us a priori the certainty that no occupied time can ever be bounded by a previous empty time, and that no change can be the first change, but not that an occupied space can have no empty space beside it. So far no a priori decision on the latter point would be possible; yet the difficulty of conceiving the world in space as limited lies in the fact that space itself is necessarily infinite, and therefore a limited finite world in space, however large it may be, becomes an infinitely small magnitude; and in this incongruity the imagination finds an insuperable stumbling-block, because there remains for it only the choice of thinking the world either as infinitely large or infinitely small. This was already seen by the ancient philosophers: Μητροδωρος, ὁ καθηγητης Επικουρου, φηδιν ατοπον ειναι εν μεγαλῳ πεδιῳ ἑνα σταχυν γεννηθηναι, και ἑνα κοσμον εν τῳ απειρῳ ( Metrodorus, caput scholæ Epicuri, absurdum ait, in magno campo spicam unam produci, et unum in infinito mundum ) Stob. Ecl., i. c. 23. Therefore many of them taught (as immediately follows), απειρους κοσμους εν τῳ απειρῳ ( infinitos mundos in infinito ). This is also the sense of the Kantian argument for the antithesis, only he has disfigured it by a scholastic and ambiguous expression. The same argument might be used against the limitation of the world in time, only we have a far better one under the guidance of causality. In the case of the assumption of a world limited in space, there arises further the unanswerable question, What advantage has the filled part of space enjoyed over the infinite space that has remained empty? In the fifth dialogue of his book, “ Del Infinito, Universo e Mondi ,” Giordano Bruno gives a full account of the arguments for and against the finiteness of the world, which is very well worth reading. For the rest, Kant himself asserts seriously, and upon 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.