If we are already assuming infinite resources, then do we really need anything stronger than PA?
And even if this is not the case, consistent/inconsistent doesn’t depend on resources, only on the axioms and rules for deduction.
A formal system may be inconsistent, but a resource-bounded theorem prover working on it might never be able to prove any contradiction for a given resource bound. If you increase the resource bound, contradictions may become provable.
If we are already assuming infinite resources, then do we really need anything stronger than PA?
A formal system may be inconsistent, but a resource-bounded theorem prover working on it might never be able to prove any contradiction for a given resource bound. If you increase the resource bound, contradictions may become provable.