We always start with an axiom or a premise and infer its consequences. It's great technique to use those inferences to determine whether the axiom is true. In the more complicated questions, the logic can be quite convoluted. Not everything is just a matter of "David is unmarried. Is he also a bachelor?" When it comes to questions of God, both theists and atheists have appealed to nature to support their arguments, and in both cases there is an interpretative element to the logic that's based around some axiom. Ultimately, I think axioms are inescapable. We need to postulate them in order to understand the world, and we need to test them to make sure we aren't being deceived, but we can't do without them.
I'm also interested in the consequences for another reason. If we have an axiom that holds reasonably true (albeit beyond proof either way) then we should take time to figure out what that means for our daily lives and then do it. I don't think there's enough of this going on, and I think that's because we're happy not to have to do that work. And that, I think, is the point of any philosophy that matters.
"The philosophers have only interpreted the world, in various ways; the point is to change it."
Marx, Theses on Feuerbach