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But if an individual thinks that life is worthwhile only if there is some higher purpose to it, and they come to believe that there is no such purpose, this latter belief will serve as a reason for finding life not worth living. In this case, since the individual’s belief in the purposelessness of life leads to a negative evaluation of life itself – thus serving as a reason to deny life – Nietzsche would designate the belief nihilistic.
https://psyche.co/ideas/for-nietzsche-nihilism-goes-deeper-than-life-is-pointless
https://psyche.co/ideas/for-nietzsche-nihilism-goes-deeper-than-life-is-pointless