What do you mean, "not that they don't exist...? If they do not NOT exist then they DO exist. The problem for the autonomous, subjectivist world view (and equally for the autonomous objectivist) is how to account for them.
Yes, the "objective standard" that my counterpart embraces, not necessarily one to which I subscribe. It is you who are bound by those rules, not I. One cannot impose "logical" rules on a universe that creates the kinds of paradoxes of which you speak.
There you go again. You claim not to be bound by them but you can't help using them even in your denial of them. "One cannot impose" is itself a logical inference that contradicts the proposition itself. Your claim that you do not subscribe to the laws of logic is completely undermined by your utter inability to desist from using them.
Have you noticed that neither one of us acts like the of logic are just conventional, like the rules of grammar? But you say you do not subscribe to the laws of logic. Well if that's the case why don't we just agree that instead of A is not non A, we will stipulate that A is non A? Or maybe we could just write to each other in gibberish like monkeys pounding on keyboards. Or maybe we could just write meaningless 1905 page suicide notes about why there is no meaning, full of sound and fury, signifying nothing.
I don't expect you to admit this, but the "paradoxes" to which you refer are themselves evidence of the futility of one's attempt to free oneself from the standard of God's thinking that God has put in every human heart - a Biblical truth that as has already alluded to by others on this thread. The infinite personal God of Christianity is the Author of logic. He is why these immaterial, universal, invariant laws exist. The laws of logic reflect His thinking and His character. You are made in the image of God, which in part means that he has given knowledge of Himself to you, and one of the inescapable evidences of that built-in knowledge is your use of logic, the reflection in your nature of God's thoughts.
So if God didn’t exist, logic wouldn’t exist?