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- TL;DR Summary
- What are the implications of Gödel theorem for fundamental science and metaphysics?

What does Gödel’s theorem say about physical reality? Does Gödel’s theorem imply that no finite mathematical model can capture physical reality? Does the nondeterminism found in quantum and chaos physics - it’s impossible to predict (prove) the future from the present and the laws of physics - have something to do with Gödel’s incompleteness?

Many scientists e.g. Stanley Jaki, Freeman Dyson, and recently Stephen Hawking ("According to the positivist philosophy of science, a physical theory is a mathematical model. So if there are mathematical results that can not be proved, there are physical problems that can not be predicted…") have formulated this intuition.

But I'm not aware of any proof (or very strong semi-rigorous argument) that causal openness in physical reality follows from Gödel's theorems (or the related results of Turing, Chaitin etc.).

Can anyone give me links/ideas?

Many scientists e.g. Stanley Jaki, Freeman Dyson, and recently Stephen Hawking ("According to the positivist philosophy of science, a physical theory is a mathematical model. So if there are mathematical results that can not be proved, there are physical problems that can not be predicted…") have formulated this intuition.

But I'm not aware of any proof (or very strong semi-rigorous argument) that causal openness in physical reality follows from Gödel's theorems (or the related results of Turing, Chaitin etc.).

Can anyone give me links/ideas?