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After Godel published his landmark incompleteness proof, that a logical system can't be complete and also without any internal inconsistencies, I would have exp
by mihaic 2y ago
After Godel published his landmark incompleteness proof, that a logical system can't be complete and also without any internal inconsistencies, I would have expected this to trickle into philosophical arguments of this type.
I see no practical usefulness in all of these examples, except as instances of the rule that you can get correct results from incorrect reasoning.
- dist-epoch 2y agoPhilosophy is quite far away from pure math for Godel's argument to really matter.
- mihaic 2y agoWhy though? You lose quite a bit of credibility when you say that theorems that apply to any system of logic don't apply to you in any way.
- dist-epoch 2y agoIf philosophy was just about logic, it would be called math, wouldn't it. But it's also about fuzzy stuff which doesn't follow the A or not A logic.
- mjburgess 2y agoGodel's theorem is irrelevant to systems of concepts, conceptual analysis, or theorising in general. It's narrowly about technical issues in logic. It has been "thematically appropriated" by a certain sort of pop-philosophy, but it says nothing relevant. Philosophy isnt the activity of trying to construct logical embeddings in deductive proofs. If any one ever thought so, then there's some thin sort of relevance, but no one ever has.
- rnhmjoj 2y agoNote that Gödel's incompleteness theorems do not apply to just any system of logic: they are about particular formal systems that can prove certain facts about the arithmetics of integers. So, for them to fail, it doesn't even take a non-mathematical formal system, just something that has nothing to do with natural numbers, for example, Euclidean geometry, which happens to be fully decidable.