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.