and before that revolution another, and so on without end, occurring successively in one and the same substrate, just as in the future. For we say that after this revolution there will be infinitely many revolutions. It would then follow that, ten thousand years after this revolution, there will be infinitely many revolutions, while after this revolution there will also be infinitely many revolutions. Thus one infinity would be greater than another, which is impossible.”

The infinity whose consequence he deemed impossible therefore means that which admits of no addition: that which has neither beginning nor end.

But if it is said, “Before this revolution there existed another revolution, and before it another, and so on without end,” then an endpoint is denied only in the past direction, not in the future direction. The totality cannot therefore be called infinite, since it has reached an endpoint in one direction, even though it is infinite in the other.

He thus concedes that the existence of an infinity in the past cannot have come to an end, if what is meant is something infinite in both directions.

As for what is posited as finite in one direction, he does not concede that its coming to an end is impossible, nor does he call it infinite. Rather, in his view, it has reached an endpoint because it has come to an end; and reaching an endpoint