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Isn't this like saying if X is an axiom and you can prove Y via X, you shouldn't trust Y is true because you can't prove X is true? What systems for determinin
by seanwilson 6y ago
Isn't this like saying if X is an axiom and you can prove Y via X, you shouldn't trust Y is true because you can't prove X is true?
What systems for determining the truth exist that aren't built on top of some fundamental axioms?
- hprotagonist 6y agonone; you have to at least claim as an axiom "axioms are things that can be claimed" -- but that's not what's under discussion here: logic and math are neither of them empirical sciences, after all. my point is that "we define science as empirical falsificationism" is itself nonscientific by its own definition, and that that's OK, still capable of being true, and is a handy way to get stuff done.
- andreskytt 6y agoThat’s where Gödel’s theorem comes in. There’s always axioms unprovable without expanding the system
- wurp 6y agoGoedel's completeness and incompleteness only apply if the initial set of axioms is powerful enough to express addition over all the integers.