In regards to basic mathematical truths, like 2 plus 2 make 4, we perceive logically that it must be so.
There you use "perceive logically." In
Message 1, you wrote, of moral rules, that "they have no logical grounds." In
Message 16, you wrote "but I see no logical justification for this belief, if one is an atheist."
I'm not sure what you mean by "logical" in any of those statements. It "logical" merely some adornment you are adding to your sentences, with no apparent reason for adding it?
Logic is the application of rules of inference to assumed premises. The grounding is provided by the premises, not by the logic. To say something is grounded in logic, would seem to say that it has no grounding whatsoever.
Mathematics is grounded in the assumed axioms, not in logic. We use logic as a tool for doing mathematics, but we don't expect it to provide grounding. Morality is grounded in the shared assumptions of a society. We may use logic, applied to moral rules, to deduce implications. But the moral rules are not grounded in anything other than the shared assumptions of the society.