I’m not a mathematician. Gödel proves that there are (true) theorems in math that cannot be proven formally from their axioms.
How is this significant? Isn’t it trivial?
Example:
“Axioms are: A,B,C are each true. Theorem is: D is true.”
While the theorem might be true, it obviously can’t be proven from the axioms.
I mean the example is utterly trivial, what is the catch? Does the example fall into those that Gödel addresses?
In: Mathematics
In your example. Gödel’s theorem basically says that no matter how many of the A, B, C etc you take, there will always be D that isn’t provable by any of their combinations. A, B and C aren’t just separate entities, they allow for other theorems to be derived from them. All Euclidean geometry was initially built on 5 axioms (and modern definitions include up to 20 of them) but look how many provable theorems there are in geometry.
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