Nietzsche

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The Eternal Recurrence
Nietzsche: The Will to Power, §1066

The world is a certain definite quantity of force and a certain definite number of centers of force.
Therefore, the world must pass through a calculable number of combinations.
Time is infinite.
[Diodorus?principle: If a combination is possible, then in an infinite time it will at some time be actual.]
Therefore, every possible combination is realized at some time or other.
[Determinism: Every combination K1, whenever it occurs, is followed by exactly one combination K2, where K1?K2.]
Therefore, every combination will be realized an infinite number of times.
Therefore, between each occurrence of any combination and its next recurrence, all other possible combinations have to take place.
Therefore, each combination conditions the entire sequence of combinations in the same series.
Therefore, there is a circular movement of absolutely identical series.

Definitions

Abolition of necessity:: No event in the world’s history happens necessarily (Will to Power, §1060).
Fatalism:: Given any event in the world’s history, all else happens as it does necessarily (Portable Nietzsche, p. 270; cf. Will to Power, §1060).
Cosmic recurrence:: There is a circular movement of absolutely identical series of combinations, each series recurring infinitely often in the past and infinitely often in the future.
Personal recurrence:: My life has occurred infinitely often in the past and will occur infinitely often in the future, each time exactly the same down to the smallest detail. (Portable Nietzsche, pp. 101, 270).
Recurring personal identity:: My life consists in a qualitatively describable part of a certain series of possible combinations; whenever that part occurs, I and my life occur.
Hypothetical personal recurrence:: If my life were to recur, it would recur exactly as I am now living it, down to the smallest detail (Portable Nietzsche, p. 435).
Omniessentialism:: Every property of every thing is essential to that thing; every event which occurs in the world is essential to everything that exists. Hence if even the smallest detail of the actual course of things had been different, no actual thing that does exist would have existed (Portable Nietzsche, p. 500).