Let us now examine the other kind of infinity:
… A certain constant can be such that it is … not in a series of other constants because it is greater than
finite constant, however greater we take it to be. Then we will say that our
is an actual infinity, infinity
in actu, actualiter,
and not only
Thus, in his dialog
Schelling briliantly shows that every concept is an infinity, because it unites in itself a diversity of representations, which is not finite;
but since the scope of a concept is, in essence, fully determinate and given, this infinity can be nothing else but
an actual infinity.
Every judgment and every theorem bear in themselves actual infinity, and in this lies the whole power of logical thinking, as Socratos indicated.
Let us take examples that are more concrete. Turning to space, we can afferm that all points inside a certain closed surface form an actually infinite set. In fact, each of these points is fully determinate, which means that all of them are also fully determinate;
but their number exceeds each of the numbers of the series 1,2,3…,n… and is greater then each of these numbers. In the same sence we can say that the powerfulness of God is actually infinite, because it, being determinate (in God there is no change), at the same time is greater than all finite powerfulness.
Potential infinity already presupposes the existence of an actual infinity as its super-finite limit.
already presupposes the existence of an
all infinite progress already presupposes the existence of an
infinite goal of the progress;
all infinite perfecting requires a recognition of
Con. Gutberlet, “Das Problem d. Unendlichen” («Zeitschr. f. Philos. u. philos. Kr.», Bd. 88, 1886. S. 215).