Can you explain the 'overestimation'? Utilizing the bible is a bit of a strawman, IMO, in that it can be attacked as inconsistent without appeal to Kurt Godel. The same applies to evolutionary biology. However, in a discussion of, let's say, positivist claims about Popper's notion of falsifiability in terms of what counts as a 'theory', Godel's incompleteness theorem is extremely relevant especially when dealing with sciences that rely on mathematical apparatuses for their expression and interpretation.
I know you're using falsifiability as any old example of a dispute, but I'm afraid I don't see how Popper is relevant. Falsifiability is a statement about empiricism and hypothetical worldly evidence. Gödel's theorems are statements about the properties of strictly deductive axiomatic systems and have nothing to do with empirical facts.
If what you're suggesting is that the incompleteness of consistent arithmetics calls into question the deductive apparatus that gets us from evidence/counter-evidence to supporting/falsifying theories, I'd say that it doesn't much matter if said arithmetics have unprovable theorems laying about. They just sit in their own little corner, no?
Paraphrasing the paper: the idea that one can question the validity of a set of axioms not something new brought by Gödel. It was so since the antiquity.
I feel obliged to post this given the popularity of the video concerning Gödel's stuff.
TLDR: The reach of Gödel's incompleteness theorems is vastly overestimated.
Can you explain the 'overestimation'? Utilizing the bible is a bit of a strawman, IMO, in that it can be attacked as inconsistent without appeal to Kurt Godel. The same applies to evolutionary biology. However, in a discussion of, let's say, positivist claims about Popper's notion of falsifiability in terms of what counts as a 'theory', Godel's incompleteness theorem is extremely relevant especially when dealing with sciences that rely on mathematical apparatuses for their expression and interpretation.
I know you're using falsifiability as any old example of a dispute, but I'm afraid I don't see how Popper is relevant. Falsifiability is a statement about empiricism and hypothetical worldly evidence. Gödel's theorems are statements about the properties of strictly deductive axiomatic systems and have nothing to do with empirical facts.
If what you're suggesting is that the incompleteness of consistent arithmetics calls into question the deductive apparatus that gets us from evidence/counter-evidence to supporting/falsifying theories, I'd say that it doesn't much matter if said arithmetics have unprovable theorems laying about. They just sit in their own little corner, no?
Paraphrasing the paper: the idea that one can question the validity of a set of axioms not something new brought by Gödel. It was so since the antiquity.