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It wasn't until the 1930s that people realised second order logic with arithmetic will always lead to contradictions without guardrails. Before then all mathematics was done in the object language of whatever the field in question was and only translated to the meta language for succinctness after the fact.

The magic of modern maths is that we can now work only with the meta language and get results free from contradiction. For this we absolutely need a modern notation to do the new type of maths since we are no longer grounded by the reality of the object language.

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Tainnor 3 days ago | parent [-]

None of what you wrote is true.

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llm_trw 3 days ago | parent [-]

Feel free to explain why.

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Tainnor 3 days ago | parent [-]

Your very first sentence is simply wrong, I don't know what more there is to say other than that you clearly don't understand what Gödel's results are about (hint: they're called "incompleteness theorems", not "contradiction theorems"). Maybe read a textbook? I could recommend several good ones.

The other sentences basically fall in the category of "not even wrong", i.e. basically nonsensical.

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llm_trw 3 days ago | parent [-]

Godel starts by the assumption that the system is free from contradictions which makes his papers largely irrelevant here.

Again, feel free to explain how you can have a second order logical system without axiomatic limitations that doesn't contain contradictions.

Hell, go by the more popular version of first order logic + set theory if you're more comfortable with that.

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Tainnor 3 days ago | parent [-]

Nobody has found a contradiction in (first or second order) ZFC in over a hundred years. You're out of your depth.

	▲	llm_trw 3 days ago \| parent [-]
		>Nobody has found a contradiction in (first or second order) ZFC in over a hundred years. Yes, which is exactly why we have guardrails like ZFC in place. We got all sorts of exciting results without them. We of course have to keep adding axioms to ZFC - or replacing them all together - because there is a lot of math out there which is outside it's purview. >You're out of your depth. You're being incredibly abrasive for no reason.