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Our new "infinite." - How far the perspective character of existence extends or indeed whether existence has any other character than this; whether existence without interpretation, without "sense," does not become "nonsense"; whether, on the other hand, all existence is not essentially actively engaged in interpretation . . . Rather has the world become "infinite" for us all over again, inasmuch as we cannot reject the possibility that it may include infinite interpretations.

F. Nietzsche, The Gay Science, 374

Is this "perspective character of existence" a statement about value, that nothing exists for us without a value? I just like the idea that it is, haven't read much Nietzsche etc..

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Understanding what Nietzsche means here takes a bit of background:

Nietzsche thought that, starting really with Socrates, a harmful threat had run throughout humanity, especially in Wissenschaft (this term means 'science' in German but really is general to mean any sort of study). The core of this threat is what Nietzsche calls the 'will to truth', which is precisely what it sounds like it is--an insatiable pursuit of the ultimate truth. Science, Nietzsche thought, rested on a kind of faith, namely the conviction that objective truth was both desirable and achievable.

The problem here is that Nietzsche saw a crisis awaiting the 'will to truth'. Eventually, he thought, the will to truth would come around to bite itself in the tail, so to speak. The insatiable pursuit of truth would lead us to realize that in fact there was no objective truth. Since our values are systematized around 'ultimate truth' (a remnant of Christianity, where ultimate truth = God), then the realization that no such ultimate truth exists would lead to a widespread 'suicidal nihilism', where people would no longer believe anything was valuable, and thus life would not be worth living.

Now, coming to your question: Nietzsche's way of combating suicidal nihilism is to give up on objective, innate values. Instead, humans must 'interpret' life and willingly give things the value they otherwise wouldn't have. There are infinite interpretations, each rooted in different individuals' perspectives. Existence has no value other than this interpretation according to perspective, as your passage points out. It is our job to interpret these values in order to make life worth living.

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