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Florensky. Bad infinity Category: Nature Bulgakov. Bad infinity

Nature. Bad infinity

7 And when the thousand years are expired, Satan shall be loosed out of his prison,
8 And shall go out to deceive the nations which are in the four quarters of the earth, Gog and Magog, to gather them together to battle: the number of whom is as the sand of the sea.

The number of angels is finite

The number of angels is finite, determinate, limited. The fact that the angelic world is internally finished or full in no wise requires bad infinity or unlimitedness.

Enormously important for us is the fact that the angelic world is given as full and finished in the instantaneous creation of this world. The creation of this world does not go beyond this, and we just conclude that the number of angels is finite, determinate, limited. But this finiteness is not connected with any external boundary or limit, beyond which God's omnipotence, wisdom, and love grow weak and are nullified. Clearly, there can be no such weakening. Rather, this boundary expresses the fact that this world is internally finished or full, which in no wise requires bad infinity or unlimitedness. Otherwise, the angelic world would run the risk of lacking fullness or of being unfinished. And if our faith teaches us the contrary this means that not only a negative ("bad") finitude but also an actual, positive finitude is possible, at least in the angelic world.

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

The determinate completeness of the creation

The divine fullness of the creation is combined not with a negative ("bad") infinity that is powerless, but with a determinate completeness. Such completeness is characterized by an inexhaustible depth of eternity and by an eternal life realized in creaturely temporality.

Such a positive, finite infinitude is, in general, revealed to us through the creation of the world, in which the divine all is implanted. But this all is realized in a definite, limited period of time («the six days of creation»), and is implanted in definite, limited forms, or modes, of being. Otherwise, the world could not have been fully created, fully finished. And the divine sabbath could not have come, just as it would not have been said: “Thus the heavens and the earth were finished, and all the host of them. And on the seventh day God ended his work which he had made” (Gen. 2:1-2). The divine fullness is therefore combined not with an infinity that is powerless to exhaust itself and in this sense is genuinely bad, but with a determinate completeness, which is nevertheless characterized by an inexhaustible depth of eternity, by an eternal life realized in creaturely temporality. By virtue of this combination, every atom of being, however small it might be, potentially contains its entire actual infinity, which is manifested not only in the static profile of its being but also in its dynamic, energetic realization.

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