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Bulgakov. Bad infinity Category: Nature Florensky. Bad infinity

Actual infinity
In the works of Fr. Pavel Florensky

Every concept is an infinity

Fr. Pavel Florensky: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.

Fr. Pavel Florensky: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.

Let us now examine the other kind of infinity: actual infinity. … A certain constant can be such that it is … not in a series of other constants because it is greater than any finite constant, however greater we take it to be. Then we will say that our quantum is an actual infinity, infinity in actu, actualiter, and not only in potentia.

Thus, in his dialog Bruno, 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.

Fr. Pavel Florensky
The Pillar and Ground of the Truth
XV. Certain Concepts from the Theory of Infinity

Potential and actual infinities

Potential infinity already presupposes the existence of an actual infinity as its super-finite limit.

… every potential infinity already presupposes the existence of an actual infinity as its super-finite limit;850) all infinite progress already presupposes the existence of an infinite goal of the progress; all infinite perfecting requires a recognition of infinite perfection.


850 Con. Gutberlet, “Das Problem d. Unendlichen” («Zeitschr. f. Philos. u. philos. Kr.», Bd. 88, 1886. S. 215).

Fr. Pavel Florensky
The Pillar and Ground of the Truth
XV. Certain Concepts from the Theory of Infinity

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