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Bulgakov, Sergei Church. Personalities Padre Pio

Fr. Pavel Florensky

Born: 9 (21) January 1882; Yevlakh, Elisabethpol Governorate
Died: 8 December 1937; near St. Petersburg

Pavel Florensky was a Russian Orthodox theologian, priest, philosopher, mathematician, physicist, electrical engineer, inventor, polymath and neomartyr.

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

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