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What happens if our mathematical system is proven to be inconsistent? (lemmy.ml)
submitted 9 months ago by to c/asklemmy@lemmy.ml
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From my "watched a YouTube video" understanding of Gödel's Incompleteness Theorem, a consistent mathematical system cannot prove its own consistency, and any seemingly consistent system could always have a fatal contradiction that invalidates the whole system, and the only way to know would be to find the contradiction.

So if at some point our current system of math gets proven inconsistent, what happens next? Can we tweak just the inconsistent part and have everything else still be valid or would we be forced to rebuild all of math from basic logic?

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[–] 4 points 9 months ago* (last edited 9 months ago) (2 children)

It's a good point. ZFC is a kind of de facto standard, though.

Some branches are simple enough that we can prove consistency.

Using the tools of a different, more complex one. Which might itself be inconsistent.

That's not really a problem, though. There was never a guarantee we can rigorously prove everything.

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