Boolean algebra, the math of logic, would also fail your proof test.
There is no basis for any proof in your system.
You do not recognize the most precise objective facts and proofs capable by humans.
Sure there is. But it does not necessarily describe, let alone, "prove" the real world.
You do not recognize the most precise objective facts and proofs capable by humans
I do and I also recognize that they must be understood in proper context and scope as theoretical.
If they are to be considered factual, they must correspond to the observable, detectable world.