[DonbunEf7]

You seem intelligent, so I'm going to drop you into the deep end. In category theory, a topos [0][1] (plural topoi) is a structure-place where logic can be done. Boolean logic corresponds to a particular topos. Actually, there are at least two topoi which do Boolean logic; one of them has the law of excluded middle, and another has the axiom of choice. [2]

And there's an infinite other number of topoi to choose from! Topoi can be custom-made to categorical specifications. We can insist that there are three truth values, and then we can use a topos construction to determine what the resulting logical connectives look like. [3]

Finally, there are logical systems which are too weak to have topoi. These are the fragments, things like regular logic [4] or Presburger arithmetic.

To address your second argument, why do we work in a world with Boolean logic? Well, classical computers are Boolean. Why? Because we invented classical computing in a time where Boolean logic was the dominant logic, and it fits together well with information and signal theory, and most importantly because we discovered a not-quite-magical method for cooking rocks in a specific way which creates a highly-compact semiconductor-powered transistor-laden computer.

Computers could be non-Boolean. If you think that the brain is a creative computer, then the brain's model of computation is undeniably physical and non-classical. It's possible, just different.

Oh, and even if Boolean logic is the way of the world, does that really mean that all propositions are true or false? Gödel, Turing, Quine, etc. would have a word with you!

[0] https://en.wikipedia.org/wiki/Topos#Elementary_topoi_(topoi_...

[1] https://ncatlab.org/nlab/show/topos

[2] https://ncatlab.org/nlab/show/two-valued+logic

[3] https://toposblog.org/2018/01/15/some-simple-examples/

[4] https://arxiv.org/abs/1706.00526