Why does 2 + 2 come out the same way each time? Never mind the question of why the laws of physics are stable - why is logic stable? Of course I can't imagine it being any other way, but that's not an explanation.

My short answer is "because we live in a causal universe".

To expand on that:

Logic is a process that has been specifically designed to be stable. Any process that has gone through a design specifically intended to make it stable, and refined for stability over generations, is going to have a higher probability of being stable. Logic, in short, is more likely than anything else in the universe to be stable.

So then the question is not why logic specifically is stable - that is by design - but rather whether it is possible for anything in the universe to be stable. And there is one thing that does appear to be stable; that if you have the same cause, then you will have the same effect. That the universe is (at least mostly) causal. It is that causality that gives logic its stability, as far as I can see.