So I was up late thinking again...
Can there be any objective standards? I think so, given that we possess a faculty that I will call the nous. The nous is responsible for ensuring that the times when we have a certain sort of conviction of the objective truth of a belief actually correspond to the times when we have reached an objective truth. If I have a certain sort of conviction that A, the nous will ensure that A is an objective truth.
The relationship here might run either way. Maybe the nous causes me to have a certain sort of conviction because the world is a certain way; or, maybe the nous changes the world to fit my convictions.
I can't prove that the nous exists, but you can't prove that it doesn't. So, the way I see it, it's logically possible that we have some objective truths and objective standards.