Comments Elsewhere

This is obviously just material implication run amok.

If “—>” and “if-then” are read as material implication, there’s no reason to believe that premise 4 is true, since what it says is logically equivalent to “If God does not exist, then both (1) I pray to God and (2) God does not answer my prayers,” which hasn’t got any plausibility independent of whether or not I do in fact pray to God.[*] You get the conclusion because whenever p—>q is false, where —> is material implicaiton, p has to be true. But the premise about the answers to your prayers is only plausible if you’re using the nested “if-then” to express some sort of logical or causal entailment (to the effect that if God doesn’t exist, my prayers aren’t efficacious), which material implication doesn’t express. If it is some kind of logical or causal entailment, then inferring 5 from 3 and 4 is just equivocation.

[*] “If both God does not exist and I pray to God, then God does not answer my prayers” is plausible independently of whether or not I pray to God, but that’s logically equivalent to (~G —> (P —> ~A)), not (~G —> ~(P —> A)).