1. What does someone need to believe in order to daven for the amud?
2. Is someone who has doubts about certain of those things better or worse than someone who is not smart enough to have those doubts?
3. If someone thinks that all of the facts in the Torah are empirically provable, but thinks that if they weren’t he wouldn’t believe them, can he daven for the amud?
4. If someone believes that none of the facts in the Torah are empirically provable, but thinks they happened anyway, can he daven for the amud?
5. If someone believes that nothing in the Torah is true, but keeps the mitzvos anyway for social and family reasons, and also believes that the people around him are in the same situation, can he daven for the amud? What if he believes that the people around him conform to scenario 3 or 4? May he daven in that scenario?
6. If someone believes that nothing in the Torah is empirically true, but believes it anyway because he thinks that that’s what Hashem wants, may he daven for the amud?