The cosmological Ideas with regard to time and space, thus of the limits of the world in both, are boldly regarded as determined through the category of quantity, with which they clearly have nothing in common, except the accidental denotation in logic of the extent of the concept of the subject in the judgment by the word quantity, a pictorial expression instead of which some other might just as well have been chosen. But for Kant's love of symmetry this is enough. He takes advantage of the fortunate accident of this nomenclature, and links to it the transcendent dogmas of the world's extension.
(2.) Yet more boldly does Kant link to quality, i. e., the affirmation or negation in a judgment, the transcendent Ideas concerning matter; a procedure which has not even an accidental similarity of words as a basis. For it is just to the quantity, and not to the quality of matter that its mechanical (not chemical) divisibility is related. But, what is more, this whole idea of divisibility by no means belongs to those inferences according to the principle of sufficient reason, from which, however, as the content of the hypothetical form, all cosmological Ideas ought to flow. For the assertion upon which Kant there relies, that the relation of the parts to the whole is that of the condition to the conditioned, thus a relation according to the principle of sufficient reason, is certainly an ingenious but yet a groundless sophism. That relation is rather based upon the principle of contradiction; for the whole is not through the part, nor the parts through the whole, but both are necessarily together because they are one, and their separation is only an arbitrary act. It depends upon this, according to the principle of contradiction, that if the parts are thought away, the whole is also thought away, and conversely; and by no means upon the fact that the parts as the reason conditioned the whole as the consequent, and that therefore, in accordance with the principle of sufficient reason, we were necessarily led to seek the ultimate parts, in order, as its reason, to understand from them the whole. Such great difficulties are here overcome by the love of symmetry.
(3.) The Idea of the first cause of the world would now quite properly come under the title of relation; but Kant must reserve this for the fourth title, that of modality, for which otherwise nothing would remain, and under which he forces this idea to come by saying that the contingent (i. e., according to his explanation, which is diametrically opposed to the truth, every consequent of its reason) becomes the necessary through the first cause. Therefore, for the sake of symmetry, the conception of freedom appears here as the third Idea. By this conception, however, as is distinctly stated in the observations on the thesis of the third conflict, what is really meant is only that Idea of the cause of the world which alone is admissible here. The third and fourth conflicts are at bottom tautological.
About all this, however, I find and assert that the whole antinomy is a mere delusion, a sham fight. Only the assertions of the antitheses really rest upon the forms of our faculty of knowledge, i. e., if we express it objectively, on the necessary, a priori certain, most universal laws of nature. Their proofs alone are therefore drawn from objective grounds. On the other hand, the assertions and proofs of the theses have no other than a subjective ground, rest solely on the weakness of the reasoning individual; for his imagination becomes tired with an endless regression, and therefore he puts an end to it by arbitrary assumptions, which he tries to smooth over as well as he can; and his judgment, moreover, is in this case paralysed by early and deeply imprinted prejudices. On this account the proof of the thesis in all the four conflicts is throughout a mere sophism, while that of the antithesis is a necessary inference of the reason from the laws of the world as idea known to us a priori. It is, moreover, only with great pains and skill that Kant is able to sustain the thesis, and make it appear to attack its opponent, which is endowed with native power. Now in this regard his first and constant artifice is, that he does not render prominent the nervus argumentationis, and thus present it in as isolated, naked, and distinct a manner as he possibly can; but rather introduces the same argument on both sides, concealed under and mixed up with a mass of superfluous and prolix sentences.
The theses and antitheses which here appear in such conflict remind one of the δικαιος and αδικος λογος which Socrates, in the “Clouds” of Aristophanes, brings forward as contending. Yet this resemblance extends only to the form and not to the content, though this would gladly be asserted by those who ascribe to these most speculative of all questions of theoretical philosophy an influence upon morality, and therefore seriously regard the thesis as the δικαιος, and the antithesis as the αδικος λογος. I shall not, however, accommodate myself here with reference to such small, narrow, and perverse minds; and, giving honour not to them, but to the truth, I shall show that the proofs which Kant adduced of the individual theses are sophisms, while those of the antitheses are quite fairly and correctly drawn from objective grounds. I assume that in this examination the reader has always before him the Kantian antinomy itself.
If the proof of the thesis in the first conflict is to be held as valid, then it proves too much, for it would be just as applicable to time itself as to change in time, and would therefore prove that time itself must have had a beginning, which is absurd. Besides, the sophism consists in this, that instead of the beginninglessness of the series of states, which was at first the question, suddenly the endlessness (infinity) of the series is substituted; and now it is proved that this is logically contradicted by completeness, and yet every present is the end of the past, which no one doubted. The end of a beginningless series can, however, always be thought, without prejudice to the fact that it has no beginning; just as, conversely, the beginning of an endless series can also be thought. But against the real, true argument of the antithesis, that the changes of the world necessarily presuppose an infinite series of changes backwards, absolutely nothing is advanced. We can think the possibility that the causal chain will some day end in an absolute standstill, but we can by no means think the possibility of an absolute beginning.8
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.
That the assumption of a limit of the world in time is certainly not a necessary thought of the reason may be also proved historically, for the Hindus teach nothing of the kind, even in the religion of the people, much less in the Vedas, but try to express mythologically by means of monstrous chronology the infinity of this phenomenal world, this fleeting and baseless web of Mâyâ, for they at once bring out very ingeniously the relativity of all periods of time in the following mythus (Polier,
