LECTURE 13 (208 a 5-24)

HE ANSWERS THE ARGUMENTS WHICH WERE BROUGHT FORTH IN LECTURE 7 TO SHOW THAT THE INFINITE EXISTS NOT ONLY IN POTENCY BUT ALSO IN ACT

             400. After the Philosopher has by means of the definition of the infinite explained the meaning [ratio] of things which are said about the infinite, he here answers the arguments which were set forth above to show that the infinite exists.

             First he states his intention. Secondly, where he says, 'In order that coming to be . . .' (208 a 8), he develops his position.

             He says, therefore, first that after what has been said about the infinite, it remains to answer the arguments according to which it seemed to be shown that the infinite exists not only in potency, as we have established above, but that it exists in act, as do things which are finite and determinate. For some of these arguments do not conclude of necessity, but are totally false, whereas others partially draw a true conclusion.

             401. Next where he says, 'In order that coming to be . . .' (208 a 8), he answers the five arguments which were set forth above to show that the infinite exists.

             First he answers the argument which dealt with generation. For it was concluded that, if generation does not cease, then an infinite must exist.

             This argument draws a true conclusion with reference to the point that the infinite is in a potency which is successively reduced to act, as was said above. But in order that generation does not cease, it is not necessary for there to be an infinite sensible body in act, as the ancients thought. They held that generation is preserved to infinity as if generation were to occur by extraction from some body. And this could not go on to infinity unless that body were infinite.

             But this is not necessary. For in the whole existing finite sensible body generation can endure to infinity by reason of the fact that the corruption of one thing is the generation of another.

             402. Next where he says, 'There is a difference . . .' (208 a 11), he answers the argument which dealt with contact. This argument says that it is necessary for every finite body to touch another, and thus it would be necessary to proceed to infinity.

             He answers this by saying that 'to be touched' and 'to be limited' are different. For 'to be touched' and 'to be included' are predicated in reference to another. For everything which touches touches something. But 'limited' is predicated absolutely, and not in reference to another, insofar as a thing is limited in itself by its proper boundaries. Now some finite things touch. But it is not necessary for everything which is touched by one thing to touch another, so that we should proceed in this manner to infinity. Hence it is clear that this argument concludes in no way from necessity.

             403. Next where he says, 'To rely on mere thinking . . .' (208 a 15), he answers the argument which dealt with the intellect and the imagination, which the ancients did not distinguish from the intellect.

             Through this argument it was shown above that there would be an infinite space outside of the heavens, and consequently an infinite place and an infinite body. But he says that it is absurd to have faith in the understanding in such a way that whatever is apprehended by the intellect or the imagination is true, as some of the ancients thought, whose opinions were disproved in Metaphysics, IV. For if I apprehend that something is larger or smaller than it is, it does not follow that there is some surplus or defect in that thing. Rather this is only in the apprehension of the intellect or the imagination.

             For one can think of any man as a multiple of what he is, i.e., twice or triple or increasing in any way to infinity. Yet because of this a quantity of this sort will not be multiplied outside the intellect or beyond a determinate quantity or magnitude. Rather the thing exists in one way, and one understands it in another way.

             404. Next where he says, 'Time indeed and movement . . .' (208 a 20), he answers the argument taken from time and motion. He says that time and motion are not infinite in act, because nothing of time is in act except the now. Nor is there anything of motion in act except a certain indivisible. But the intellect apprehends the continuity of time and motion by taking the order of before and after, such that that which was first taken of time or motion does not remain as such. Hence it is not necessary to say that the whole of motion is infinite in act or that the whole of time is infinite in act.

             405. Next where he says, 'Magnitude is not infinite . . .' (208 a 23), he answers the argument taken from magnitude. He says that magnitude is not infinite in act either by division or by intelligible increase, as is clear from what was said above.

             Lastly, he concludes that he has now treated the infinite.