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Gödel also formally proved the existence of God. As in it can be checked by computerized theorem provers.[1]

[1] https://en.m.wikipedia.org/wiki/Gödel%27s_ontological_proof

Well, he proved a theorem. He chose to define a “godlike object” and showed in every carefully-defined “world” such an object exists. Saying that this “proves the existence of god” is … a bit of an overreach, don’t you think?

No, I don’t. Also that’s how we prove literally anything. There is always a model, because we don’t have direct access to reality. So if your bar is that high you’re going to have to call climate change and relativity a bit of an overreach too.

Gödel's proof is an example of deductive reasoning. It falls apart if you don't accept its axioms.

The case for climate change, or for relativity, is made inductively, by empirical observation.

The two cases are not remotely comparable.

Funny you should say that on account of it’s well known that deduction is never wrong and induction sometimes is.

A proper deductive argument that contains no errors will be valid, but it won't necessarily be sound if the premises are incorrect. In that sense deduction can most certainly be "wrong".

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