Truth exists without man. Logic is the thought process by which we derive non-imperical truth. Thought process doesn’t exist without a thinking being.
IMO: Logic is not the thing, it’s the way to get to the thing. Truth is the thing. And, yes, truth exists without anyone to observe it, which is another way of saying God exists without anyone (else) to observe Him.
“...which is another way of saying God exists without anyone (else) to observe Him.”
Exactly right: science, in using logic (which it must), proves the existence of God! In fact, science itself is impossible without God, for this reason.