In rereading Nietzsche, I had a question: Is Nietzsche a determinist? As far as I understand from reading Beyond Good and Evil, it follows that it does not, for Nietzsche himself, as I understand it, suggested that the only real thing about will is whether it is strong or weak, while “cause” and “effect” are just some kind of internal mental models, contents of out minds. But how come everything returns eternally, why is the concept of eternal reccurence true then? Doesn’t it imply the absence of free will?
Nietzche did not believe in what we would now call "libertarian free will", his assessment of Spinoza's work, Spinoza being one of the most prominent deniers of free will, being probably the most direct hint about it:
[Spinoza] is closest to me precisely in these matters: he denies the freedom of the will, teleology, the moral world-order, the unegoistic, and evil.
There is on the other hand not much evidence that Nietzche believed in the physical reality of the eternal return. Although he untertains the possibility in private notes, his main published works use it as an allegory to illustrate his thoughts about the will, what constitutes the strength of the will, and ethics (how one should live their own life).
In the Gay Science, he portrays a demon who taunts a man with the idea that he will have to go again through his life endlessly, redoing the same choices and taking the same actions (or lack thereof), implying that feeble people would be crushed at the idea of re-living their crappy life while strong people can conceive of no better news. In the same way in Thus Spoke Zarathoustra it's part of the title character's journey toward wisdom to evolve from being afraid of the idea to embracing it.
For Nietzche, eternal return illustrates a life with no regrets, and ultimately the strength of one's will. We are all making choices every day, but are we doing them in a mindful way? Should the same circumstances present themselves again and again a thousand times, would we be confident to do the same choice a thousand times?
For example most of us are going to work every day, but is there nothing we'd rather do? Or if there is something we'd rather do at this very moment, is there a larger goal that we want to fulfill by doing this momentary sacrifice? The idea is to not go through life haphazardly, but fully and confidently knowing why we do what we do, which consitutes having a strong will. Such a person lives with no regret, not because of carelessness or callousness, but because they know that at each moment they made choices according to their values.
Notice how it connects with Nietzche's view on morality and the Ubermensch: no one can impose their own moral values or shame a person who embraces the idea of eternal return.
Notice also this has nothing to do with kitchen philosophy concepts often trying to associate themselves with Nietzcheism, like "being an alpha". One can experiment major failures in the face of overwhelming adversity and still embrace the idea of eternal return, still be an Ubermensch. An example of this being Socrates, who submitted to the will of men less wise than him but did it according to his own values and a full understanding of his own reasons to do so.
Nietzsche describex 'unfreedom of will' as nonsense. See Friedrich Nietzsche and free will.
This answer gives the full quote of Nietzsche laying out his Eternal Recurrence, with discussion of it: What if I get born again as the same person for ever? He was not stating a doctrine, asserting a truth, or demanding we accept something self-evident. Read more closely.
I argue free-will emerged as a special concept and topic in Western thought, in relation to theodicies, solutions to the problem of evil: Does philosophy have a dark side?
Freedom does not need to be absolute, indeed it's obvious we are always bound by the laws of physics, yet still feel we can make decisions. Decisions involve us not having complete information, and doing our best in the face of that. Knowing that total information exists that could determine all possible or the inevitable outcomes, cannot ease our facing subjective dilemmas, which are not located in the world but in our incomplete experiences of it. I relate wisdom to the skill of good decision making, and frame it as the skill allowing us to becoming 'more' free, here: Wisdom and John Vervaeke's awakening from the meaning crises? That is, escape conditioning, habit, coercion, and inconsistency.
I would say Nietzsche is pointing towards a spiritual lesson with Eternal Recurrence, towards what might mean to be able to live a life without regrets, where at the end of it you'd wish to change nothing. That is about living with integrity.
Perhaps some examples of such, can help elucidate:
"I thought at the time that I ought not to do anything common or mean when in danger: nor do I now repent of the style of my defence; I would rather die having spoken after my manner, than speak in your manner and live.
The difficulty, my friends, is not to avoid death, but to avoid unrighteousness; for that runs faster than death."
-from the closing remarks of Socrates in Plato's 'Apology'
"I have done every thing of consequence which I ever meant to do; and I could at no time expect to leave my relations and friends in a better situation than that in which I am now likely to leave them. I therefore have all reason to die contented."
-from Hume's letter to William Strahan composed as he lay dying, dictated to Adam Smith
"Tell them I've had a wonderful life."
-final words of Wittgenstein
Nietzsche harshly criticised Socrates, but also said "Socrates, to confess it frankly, is so close to me that almost always I fight a fight against him". He sneered at Hume as advocating 'English-mechanistic world-stupification'. And, he would have scorned the Tractatus no doubt.
But in living with integrity, conviction, and going to their deaths reconciled, I think he would have accepted as three as ready for the 'intimations of eternally repeating' their lives.