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Once I had a similar conversation with Scott Aaronson about this. I said the theorem shows the limits of logic; he said it shows the POWER of logic. My reply wa
by jeromebaek 8y ago
Once I had a similar conversation with Scott Aaronson about this. I said the theorem shows the limits of logic; he said it shows the POWER of logic. My reply was: what does it matter? It just depends on perspective. As in: "logic is so powerful, it can even demonstrate its own limitations!" or: "logic is limited, and we know this for eternity, because logic proved it!"
- empath75 8y agoIt’s not really a limitation of logic, because logic is not constrained to a particular set of axioms.
- googlemike 8y agoBut logic is composed of a particular set of axioms and rules - so is not any thing composed of a set of such things itself constrained by the very nature of its parts?
- empath75 8y agoGodels theorem has nothing to say about first order logic.