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There are systems that we can proof the consistency of just fine. See eg https://en.wikipedia.org/wiki/Presburger_arithmetic https://en.wikipedia.org/wiki/Pres
by eru 1y ago
There are systems that we can proof the consistency of just fine. See eg https://en.wikipedia.org/wiki/Presburger_arithmetic https://en.wikipedia.org/wiki/Presburger_arithmetic
Presburger Arithmetic cannot prove its own consistency inside of itself, but that doesn't mean we can't prove its consistency 'at all'.
- mathgradthrow 1y agoWhat on earth do you mean by prove, If not within a system of proof? You can prove the consistency of PBA, But you cannot prove that you cannot prove the inconsistency of PBA, because The inability to do both is the definition of consistency in the larger system.
- Scarblac 1y agoBut it's not really relevant for anything to be able to prove that you cannot prove the inconsistency.