this post was submitted on 27 Aug 2024
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I’d say if your axioms don’t hold you wouldn’t go far in your quest for truth.
The thing that is absolute is a predicate of the form "if [axioms] then [theorems]".
And the fun thing about if statements is that they can be true even when the premise is false.
Of course in boolean algebra "if [false] then p" is always true no matter "p", but it’s not telling us much.
That's not a gotcha. It's basically just the definition of an axiom.