Comments Elsewhere

Well, this argument:

“If God exists, then the sky is orange. The sky is not orange. Therefore, God exists.”

… is invalid. Did you mean for the first premise to be “If God does not exist, then the sky is orange”?

In any case, I think there’s an important difference here. Scott’s argument seems plausible at first glance; the reason why is that premise 4 expresses something that seems like it ought to be true: “If God does not exist, then it’s not the case that if I pray to God my prayers will be answered.” Of course; after all, if there is no God then He can’t be answering prayers. What I suggested to be the problem is that what is meant by the if-then nested in the consequent of the premise can’t be captured by truth-functional material implication, because you can’t deny a material implication except where you’re willing to affirm that the hypothesis is true (~(p—>q) <-> (p & ~q)).