(Doctrine of Eternal Recurrence — Preface, aph. 4)

Enlightened by an insight into the ultimate eschatological possibilities of the world in which we live — that it is finite rather than infinite in its possibilities — the author of this book came to realize that the very notion of the infinite, alongside the notion of God the Creator, is one of our greatest inventions, born out of the need to survive.
Infinity may exist only in our experience of space and time — as Kant taught us with merciless clarity — yet the question remains open whether it exists in the reality that surrounds us. And since our mathematics, too, rests upon that same experience of space and time, we find infinity also in mathematics, at its present stage of development.

On the other hand — and at the same time — we shall attempt to show that science, as such, cannot answer the question of what the world, the universe, or the multiverse is — if it is at work at all — but that it can reveal how it functions. Science cannot tell us what things are in themselves, nor what we ourselves are in ourselves; it cannot determine where we and things begin, or where we end — quantum mechanics has only vague intimations of this — but it can show us how we function and how this world, this universe (or multiverse), functions. It is precisely in this ability to uncover the mode of functioning of all that is that the ultimate possibility of science itself lies: that one day it might discover that this world functions as an Eternal Recurrence. That is the boundary to which science may one day arrive — the limit of its power and its knowledge.

The Eternal Return is therefore, in principle, a scientifically testable hypothesis.
And although it may not seem to be at work at this moment — whether because of the entropic principle of the Second Law of Thermodynamics, the provisional theory of the Big Bang, or the metaphysical presupposition of God’s existence — this does not mean that it will not one day come to be. And even though this thought may, for a long time to come, remain merely a hypothesis, we believe that one day it will become possible to confirm it scientifically. After all, did not our Teacher himself call the Doctrine of Eternal Recurrence “the most scientific of all possible hypotheses” (Nachlass, 1881)?!

“It is the most scientific of all possible hypotheses. We deny final purposes: if existence had one, it would have been reached already. One then understands that the circle of recurrence has no “goal,” nor anything resembling one; rather, in its entirety, it is the highest state one can conceive.” (The Will to Power, ed. W. Kaufmann & R.J. Hollingdale, Vintage 1989)