When reading about Gödel's incompleteness theorem(s) a few years back, I vaguely remember reading the statement that one of their implications was that mathematics can not really be seen as "merely" logic. I think the reasoning was something like: since we have sentences "this cannot be proven within our logical system" and we know they are true, and knowing they are true is conceptually a proof yet on a more meta-level (since you can't strictly prove it in the logical system), the situation is in shorthand: we have statements that can be proven in mathematics, but that can't be proven in logic.(adsbygoogle = window.adsbygoogle || []).push({});

I know that sounds wishy-washy, and don't misunderstand me: I'm not trying to present that as an argument and starting a debate. Rather I'm just trying to remember what I had read and I was wondering whether this sounds familiar to someone? I was trying to find a discussion of this online but couldn't find anything. (It might be that Penrose makes such a claim(?))

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# Does Godel's theorem imply mathematics is more than logic?

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