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Bulgakov. Bad infinity Category: Nature Asteroid 99942 Apophis

Bad infinity
In the works of Fr. Pavel Florensky

Potential infinity

Potential infinity is only an auxiliary notion.

Let us assume that we have a variable and that it varies not just in any way but in a determinate way — precisely in such a way that it becomes greater or smaller than any constant finite quantum of the same kind. In every state this variable is finite; but in our understanding the combination of these states differs from the combination of any arbitrary chosen states. In this sense we say that our quantum is a potential infinity, since it can become greater than any other quantum. Thus potential infinity does not represent any quantum taken in itself, but only a special way of considering a quantum, namely, in connection with the character of its special variation. Potential infinity, according to Cantor, is not an idea but only an auxiliary notion; it is ens rationis according to Stökl's apt expression. In short, potential infinity is the same thing that the aicients called apeiron, the scholastics called syncategorematice infinitum or indefinitum, and the modern philosophers call bad or, more precisely, simple infinity, schlechte Unendlichkeit.

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

Actual 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.

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, abd 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

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