There are several things such a person who makes the claim that there are no absolutes could say:
1. Nothing is provable, because everything assumes postulates, such as (p --> p) or (p v ~p)... 2. We cannot know reality, because A. Our only judge of reality is our senses, which are fallible. B. Say our entire life were a simulation like The Matrix. We cannot say we know reality then!
Now, tell me, if Absolutes do not exist, then why should we believe anything, and what creates objectivity?