Is there a problem for atheists to explain, for example, the laws of logic and objective morality. How could we really account for either if the material realm is all that exists?

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Interesting question, but the illusion here is to think that atheists face any special problem. Let's take the issues in turn.

On morality: suppose God exists. How would that make morality objective? Someone might think that if God commands something, that makes it morally right. But it's long been pointed out (at least since Plato's Euthyphro) that this way of thinking about things is problem-ridden. What if God commanded torturing all blue-eyed babies? Would that make it right? Hard to see why anyone should agree.

Someone might say that God would never command any such thing. But why not? Presumably because God, if there is one, doesn't command evil deeds. In fact, if the theist wants to make sense of the idea that God is praiseworthy partly because he is good, there will have to be a standard of good and bad, right and wrong, separate from what God happens to will.

This may still leave it puzzling how there can be objective moral truths. That's too big an issue to tackle here, but it's worth seeing that theism isn't obviously in any better position than atheism when it comes to addressing this question.

Turn to logic. P and not-P can't both be true; that's the Law of Non-Contradiction. Is God responsible for that? If so, then presumably the Law of Non-Contradiction didn't have to be true; God could have made it otherwise. But how could God have made it otherwise? What are we even being asked to imagine if someone tells us that God might have made contradictions true?

The problem is that we can say that God is responsible for the truth of the laws of logic, but it's not at all clear that we have any idea what we mean when we say it If there is a problem about what makes logical principles objectively true, saying that they're true because God somehow dictated them is an "answer" that doesn't seem to provide any insight.

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