>Every technical branch of engineering/physics has a strong basis in logic.
Doesn't mean that logic specifically made them what they are
>Science simply wouldn't be possible without a logical system to advance it.
Implying Science is a necessarily (as a matter of fact) a method that discern truths and falsities
>It's fundamentally the same exercise. See: Axioms
>Axioms are things that we assume true not because of faith, but because we can draw conclusions out of them that prove out to be true.
Who told you that? They are by definition undemonstrable
Regardless of that conclusions they (by definition btw) yield to be true
>The fundamental axioms of geometry can't be proven by our logic system either because it's imperfect or because they're above it, however, by assuming them true, we can make logical chains of propositions that ends in conclusions that are proven true by the natural world.
See the response right above
What you're doing here is 100% circular reasoning
>We believe in them because they've been proven useful for hundreds of years, not because we have blind faith.
"Proven" by your definitions
>If at some moment in the future a time comes in which we can logically prove how they're all somehow false, then we'll simply ditch them.
It depends on what logical rules you use
See Quantum Physics for a complete redefinition of them in Physics
>Thinking that you "believe" in logic is literally missing the point of it, logic is a tool, a mean so you don't have to blindly believe in things, not a superior metaphysical concept that rules everything.
Doesn't mean that it's a demonstrably useful tool
And circular reasoning ain't gonna cut it