It is already a doctrine of Aristotle’s that an infinity can never be _actu_, _i.e._, actual and given, but only _potentiâ_. Ουκ εστιν ενεργειᾳ ειναι το απειρον ... αλλ᾽ αδυνατον το εντελεχειᾳ ον απειρον (_infinitum non potest esse actu: ... sed impossibile, actu esse infinitum_), Metaph. K. 10. Further: κατ᾽ ενεργειαν μεν γαρ ουδεν εστιν απειρον, δυναμει δε επι την διαιρεσιν (_nihil enim actu infinitum est, sed potentia tantum, nempe divisione ipsa_). _De generat. et corrupt._, i., 3. He develops this fully in the “Physics,” iii. 5 and 6, where to a certain extent he gives the perfectly correct solution of the whole of the antinomies. He expounds the antinomies in his short way, and then says, “A mediator (διαιτητου) is required;” upon which he gives the solution that the infinite, both of the world in space and in time and in division, is never _before_ the regressus, or progressus, but in it. This truth lies then in the rightly apprehended conception of the infinite. Thus one misunderstands himself if he imagines that he can think the infinite, of whatever kind it may be, as something objectively present and complete, and independent of the regressus. Indeed if, reversing the procedure, we take as the starting-point what Kant gives as the solution of the conflict, the assertion of the antithesis follows exactly from it. Thus: if the world is not an unconditioned whole and does not exist absolutely but only in the idea, and if its series of reasons and consequents do not exist _before_ the regressus of the ideas of them but only _through_ this regressus, then the world cannot contain determined and finite series, because their determination and limitation would necessarily be independent of the idea, which would then only come afterwards; but all its series must be infinite, _i.e._, inexhaustible by any idea. On p. 506; V. 534, Kant tries to prove from the falseness of both sides the transcendental ideality of the phenomenon, and begins, “If the world is a whole existing by itself, it is either finite or infinite.” But this is false; a whole existing of itself cannot possibly be infinite. That ideality may rather be concluded from the infinity of the series in the world in the following manner:—If the series of reasons and consequents in the world are absolutely without end, the world cannot be a given whole independent of the idea; for such a world always presupposes definite limits, just as on the contrary infinite series presuppose an infinite regressus. Therefore, the presupposed infinity of the series must be determined through the form of reason and consequent, and this again through the form of knowledge of the subject; thus the world as it is known must exist only in the idea of the subject.