Thatâs not a gotcha. Itâs literally the point of stating axioms.
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luciole@beehaw.org âš2â© âšmonthsâ© agoIâd say if your axioms donât hold you would go far in your quest for truth.
lolcatnip@reddthat.com âš2â© âšmonthsâ© ago
Malgas@beehaw.org âš2â© âšmonthsâ© ago
The thing that is absolute is a predicate of the form âif [axioms] then [theorems]â.
And the fun thing about if statements is that they can be true even when the premise is false.
luciole@beehaw.org âš2â© âšmonthsâ© ago
Of course in boolean algebra âif [false] then pâ is always true no matter âpâ, but itâs not telling us much.