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Material implication and the fact that logic based on it is considered OK. E.g. "if the moon was made of cheese, then P=NP" is considered true. This would have
by bitL 13y ago
Material implication and the fact that logic based on it is considered OK.
E.g. "if the moon was made of cheese, then P=NP" is considered true. This would have been funny if this kind of proofs wasn't used in proofs of basic facts of set theory, e.g. the theorem about empty set being a subset of any set.
I am glad there are people trying to address these issues with a new logic, such as relevance logic, though almost every mathematician I know is fully reconciled with the former type of logic without questioning it.
- scotty79 13y agop => q sort of means, if you assume p, you can get q by flawless reasoning. It is actually true that when you assume someting false you can get from it to any conclusion by correct reasoning. The path between cheese moon and P=NP might be hard to imagine but it probably leads through 1=0 somewhere and you have o properly define what you mean by moon, cheese, and made of.