As Nietzsche is an obvious example, I am focusing on him. I think that there are no nihilist philosophers, because if someone is a nihilist, Why would the nihilist even bother telling us? As a nihilist, he must not care about anything. What is the main argument against the existence of nihilist philosophers?
1) Nihilist philosophers do not exist because they do not believe in any objective meaning or value.
2) Nihilist philosophers do exist, but they do not bother telling others about their beliefs.
3) Nihilist philosophers exist, but they do not care about anything, including philosophy.
4) Nihilist philosophers exist, but their beliefs are misunderstood by others.