If by saying that logic "works" you mean that one proposition is closer to some truth standard than another proposition, then you introduce another topic - truth - that does not ultimately exist if it does not exist independently of humankind and in a conscious entity. Truth by any other definition would not truly be truth. Ponder it.Uh oh, now I feel like I'm taking The Final Exam. (See esp. "Epistemology".)
OK. Truth exists whether we're here to observe it or not. Sure, it would be kind of irrelevant if there were no thinking entities around to notice what's true vs. what's false, but truth & falsity just are. Just like light & dark just are regardless whether there are humans around to see them, or high & low, or...???
Me, I'm trying to understand why this seeming retreat into word games & goalpost-moving. Are you trying to avoid having to recant your argument in public, is your Morton's Demon working overtime to prevent an internal crisis of faith, or do you really think that shifting the argument is a valid way of finding the truth?
Either mindless atoms can in principle create a brain that produces a conscious mind or they can't. If they can't, then it can only be because "consciousness" is a quality that derives from the individual components themselves (like mass) and not from their higher-order arrangements (how the neurons are connected together into a working information processor). But I say these collections of atoms we call "each other" exhibit obviously conscious thought as part of our mundane reality because of how our brains are wired together. All the evidence points to this conclusion; there is no evidence you can point to that it isn't.
There is no logical problem whatsoever with conscious beings existing who are made up of non-conscious parts. Thus there is no need for a God in order to explain consciousness.