What does "statistically and empirically" mean to you, because it seems a lot like you are using it to mean logic is optional.
Logic is obviously necessary, but as today we know that our universe is not a logical tautology, just one of many possible-Kripke-worlds, different models for the logic can lead to different results, so opening the window from time to time to see which of the possible worlds we actually live in is a good idea.