From Wikipedia:
[Nihilism]... rejects general or fundamental aspects of human existence, such as objective truth, knowledge [...]
Rejecting something means to me, claiming that something is not true (here we could go into a long discussion about whether this interpretation of rejection is true). Saying that the existence of truth is not true however requires the existence of truth. Further I would say that reasoning about something is basically just assigning truth values. So reasoning about anything would require the belief in the existence of truth. Therefore reasoning about nihilism would require the existence of truth. A nihilist would claim the idea of nihilism to be true. But the fact that the nihilist is reasoning would be a contradiction. So being a nihilist is paradoxical - no one can be a nihilist, right?
Also a nihilist would not be able to discuss the idea of nihilism, since there is no truth and thus any statement about nihilism would be meaningless in the sense that it has no truth. Actually a nihilist would not be able to argue about anything.
I have read this similar question, but I am not satisfied with any of the answers and the question is not exactly the same. So back to my question; can there be any nihilists?