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Comment by ninetyninenine | Hacker News Reader

I wonder if there’s any physical phenomena that can be modeled with inconsistent math.

Like we assume everything is consistent but maybe it’s not.

As the article explains (and the title alludes to), if your axioms are inconsistent, so you can prove a contradiction, you can prove anything. Literally any statement that can be formulated can be proven to be true (as can its negation!). So you'd be trying to model the universe with a maths in which 1 = 2. And also 1 = 3. And also 1 =/= 3.

Any useful set of axioms has to be consistent, because any inconsistency is catastrophic. It wrecks the entire thing. Of course that also means, thanks to Godel's theorem, that any useful set of axioms is incomplete, in that there are true statements that cannot be proved from them.

I guess let me rephrase the question. Does there exist system that is inconsistent but the inconsistency is localized and therefore we can actually miss the inconsistency by not knowing or noticing the localized inconsistency? Is there a proof of what you said as well? An inconsistent system with the inconsistency in one spot can have any statement made about the system be both true and false? I’m adjusting the parameters here so we can ask the deeper question of whether one exists in the real world.

“Paraconsistent logic” or “paraconsistent set theory” is what you are searching for.

I didn't think I'd get an answer to this, but awesome.

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