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Why are Gödel's Incompleteness Theorems not applicable to themselves?
That is, why does Logic get to justify everything except itself?
- birriel 5y agoThat is, why does Logic get to judge everything except itself?
- pbak 5y agoAlthough not answering the question, this recent article might indicate the start of a better way to frame your question : https://edwardfeser.blogspot.com/2021/07/the-metaphysical-presuppositions-of.html https://edwardfeser.blogspot.com/2021/07/the-metaphysical-pr... In other terms, first : What is logic ? In what context ? Alternatively, there's the askphilosophy subreddit.
- birriel 5y agoThanks, I appreciate it!
- cblconfederate 5y agoThey are, since they are proven in a formal system, but the theorems are not unprovable statements. The theorem doesnt claim that all theorems are incomplete, but that some of them are unprovable
- birriel 5y agoThanks for your reply! The problem I have is that the probative value of _anything_ seems to me to be based on the Axiom of axioms, which is Logic itself. I just don't understand how the provability, formality, or completeness of _anything_ may be achieved without having an unassailable tool that determines those things. We might say that Logic is that tool, but how does it sustain itself?