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Premise 6: Since logical absolutes are transcendent and conceptual they must exist in a transcendent mind.
Premise 5 seems faulty: logical absolutes MIGHT be transcendent, because Premise 4 didn't deny that they MIGHT be seen by our minds, too. Therefore, possible for every thinking brain.
No, I am arguing that a necessary truth CAN be non-conceptual. It may simply "be the case".
For example, the laws of gravity would still be true whether a mind was containing them or not.
What if logic is something only the human brain can conceptualize?
It is not necessary for a transcendental mind to exist. The logical absolutes can be thought of by every thinking brain.
IF there is no more thinking brain, does there have to be logical absolutes?
Your "logical absolutes" are hypothetical at best because at this time, there is no way to test the absolute nature of such logic. Being confined to one planet and one reality and all that good stuff.
But that's because you can only think within the framework of how our brains work. We don't have evidence of how a brain developed throughout a different course of evolution on a different planet would behave. So we don't know if there are other ways intelligent minds could function in the universe