The apologetic claims the argument is logically valid by modus tollens. The somewhat detailed version is:
Premise 1. If Argument A for God's existence is sound, then God exists.
Premise 2. But God does not exist.
Conclusion. Therefore, Argument A for God's existence is not sound.
Another variant is:
Premise 1. If E is evidence for God's existence, then there is some evidence for God's existence.
Premise 2. But there is no evidence for God's existence.
Conclusion. Therefore, E is not evidence for God's existence.
We know that only two conditions for the existence of God can be true:
- God exists.
- God does not exist.
Is this a logical proof?
Source: http://shenvi.org/Essays/RefutingArgumentsForGod.htm