Premise 1: If God does not exist, objective moral values and duties do not exist. Premise 2: Objective moral values and duties do exist. Conclusion: Therefore, God exists. Can we accept the conclusion above as valid or even fact?

The argument itself is logically valid -- indeed, formally valid. It uses only modus tollens and the rule that "P" and "~ ~ P" are equivalent, both of which are valid rules of inference.

However, I think the argument is unsound -- and therefore I think it fails to establish its conclusion -- because Premise 1 is false, at least if Premise 1 is meant as a strict conditional. (I think it's also false if it's meant as a material conditional, but that's more controversial.) For excellent discussion of Premise 1, I recommend this article and this collection of essays.

Stephen is right. The argument is valid, but it's not sound. It has a false premise. Even if you are a theist like me you can think that if God did not exist, there would be or could be such things as objective moral values and duties. Honesty would still be good, and we would still have a duty to help those in need. Philosophers who share my view find a great ally in Leibniz. For him, God loves the good because it is good. It is not the case that it is good because he loves it. In God reason comes before will.

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