Great comment – hitting the nail squarely on the head!! I had forgotten that logic was not developed in universities to deal with abstractions, but was discovered in the concrete of everyday life (in contrast to, for example, post-modernism, which is contrary to every real experience yet appeals to the abstract intellect.)

Post-modernism, in fact, was the thought behind this post. If, as you say, “somehow it were proven to be false, if some P managed to be both within and outside a given set, logic as we know it would have failed.”". Yet this is exactly the claim post-modernism makes. Indeed, in my view, postmodernism is so logically contradictory you would need to reject logic to hold onto it. Thus, I was wondering how on earth you might argue with someone who has rejected logic.

And so it is encouraging to see that one can simply appeal to the everyday and derive the laws of logic inductively.

(The pedant inside me wants to point out that “Humans didn’t discover … the “laws” of logic.” seems to conflict with the thrust of your post, eg“This was an observation before it came to be known as a rule. “)

Luke, hilarious!!! Good pickup!

One final thought, stolen from Ravi Zacharias:
You cannot consistently deny the law of non-contradiction (but nor can you verify it).

We assume logic works because it always has worked.  If P is in set Q and R is not in set Q then P is not R, and so on.  This was an observation before it came to be known as a rule.  If somehow it were proven to be false, if some P managed to be both within and outside a given set, logic as we know it would have failed.  It takes new evidence to change something that well-supported.

If logic really is poppycock, and we haven’t realised it by now, then what does it matter?  Even assuming our concept of logic is fundamentally flawed, it still allows us to make predictions which turn out to be correct and decisions which benefit people.  We don’t have to sit and wonder about this, though.  Logic can be tested.

It runs through everyday thoughts like, “If my girlfriend’s phone isn’t ringing she’s probably in that dead zone on the road home, so I’ll start dinner now.”  That could be completely wrong, but otherwise I’ll have predicted another person’s whereabouts at a future time (home in half an hour) with great accuracy and prepared for it.  I road-test my logic, and it doesn’t let me down.  If it does let me down, I see where it fell over and adjust accordingly (e.g. “The car charger isn’t working, so maybe her phone died.  I’ll ask her later.”).  More often than not, though, my girlfriend gets a hot dinner.

So I don’t wonder whether logic is reliable.  It’s delivered for me often enough that I just go ahead and use it.  If it fails, I examine it, and to date any apparent logical contradictions have been due to missing information. 

It’s like a car; the driver usually only looks under the hood if something goes clunk.