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The nature or the universe where we live in has a rule controlling how things work (if not, then the world surely is agnostic). Take it as our model, then the model allows the arithmetic.

No matter how we expand our language or theory, Godel's incompleteness theorem tells that our theory can't sort all truths out.

So, does Godel's incompleteness theorem actually support agnosticism?

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    No. No connection. Sep 30, 2022 at 13:00
  • It merely implies that we cannot use mathematical axioms and deductive logic to find all truth. It says nothing about other ways of finding truth, such as intuition, faith, etc. Sep 30, 2022 at 15:48
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    No. Godel's theorem does not stop us from learning some truths and sorting them out, that we cannot learn all truths is not agnosticism, it is a trivial consequence of our finite abilities. Godel's theorem only tells that no matter how we expand our (formal first order) theory we cannot deduce all truths from its axioms. But we'd have to get to the axioms by some other means anyway. And if we can do that then what difference does it make if we can deduce them from those already at hand or need to add them as new axioms. So it really tells us nothing about the limits of our knowledge.
    – Conifold
    Sep 30, 2022 at 19:22
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    If Godel's incompleteness theorem supports agnosticism then why he had a modal ontological argument proof?... Sep 30, 2022 at 19:40

2 Answers 2

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Goedel's incompleteness theorem is a very specific statement about the nature of mathematics. As such, it is silent on the issue of religious faith and has no applications in that field.

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Framge challenge: You say Goedel's theorem tells us our theory can't sort out all truth.

Consider a statement A that is an example of G's theorem. Within the system of logic at hand the statement A cannot be proved true or false.

How do you know it is a true statement? How do you know it needs to be "sorted out?"

There have been some examples of statements of this kind in logic. People found a statement they could not prove true or false. They attempted to use such tactics as assuming it true and looking for contradictions. Or assuming it false and looking for contradictions. And they have found that fortifying the original system of logic with a new hypothesis resulted in a new system of logic that was still self consistent, but larger. And, quite charmingly, is still potentially "mineable" for new hypothesis that cannot be proved true or false within the new system.

One fairly wonderful example is non-Euclidean geometry. One inroad into non-Euclidean is to assume that parallel lines can meet.

The kicker in this is, this process provides "job security" for those who study logic. G's theorem tells us there will always be more things to discover.

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