/sci/ - Science & Math

It's also important to note that it may very well be that ZFC is consistent, but it could still be schizophrenic nonsense that proves false things in arithmetic. In fact, there is no reason to think that it doesn't prove false things in arithmetic.
The question of consistency is only relevant as long as you want to prove correct statements in the first level of arithmetic hierarchy. If you want to be correct about more complicated arithmetic statements, you need much more than consistency: you need arithmetic soundness.