I disagree. Logic still exists without man: A rock could not be completely black and completely white.
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.
I argue, as others have done before me, that mathematical concepts and ideas exist objectively, outside of the physical world and outside of the world of consciousness. We mathematicians discover them and are able to connect to this hidden reality through our consciousness. If Leo Tolstoy had not lived we would never have known Anna Karenina. There is no reason to believe that another author would have written that same novel. However, if Pythagoras had not lived, someone else would have discovered exactly the same Pythagoras theorem. Moreover, that theorem means the same to us today as it meant to Pythagoras 2,500 years ago.
- Edward Frenkel