That is actually one of my favorite arguments for God, “The inteligibility of the universe”. Well, I do think we can use logic to establish an efficient “algorithm” for reaching a specific goal. Let’s say your goal is “I wish that as many people as possible can be happy and live fullfiling lifes”, then sure, we can develop a set of rules and “morals” for that. But why do we value those things as positive (have empathy, in your words) in the first place? That is not something that just spontaneously pop out of logic and reason alone.
Yeah, that’s my point, empathy don’t just “pop out” as a natural, inevitable consequence of being able to use logic and reason properly, if it did, psychopaths wouldn’t be able to lack it without lacking logic and reason as well.
Well, I’ve always had these innate morals inside me, even as an atheist, and I also believed that they were “good for the sake of good”, it just felt contradictory to me to hold such belief without believing in anything transcendent, like I said before, I think they are either arbitrary or transcendent, which by no means mean that I would give them up if I didn’t believe in God, and I also don’t discard the possibility that they are in fact arbitrary, since I’m not 100% certain of God. All I’m saying it that I don’t believe you can both have the cake and eat it (believing morals are not arbitrary and at the same time believing there is not anything transcedent, be it God or whatever), and that was one of the many arguments that convinced me that the existence of God is more likely than not.
EDIT: If we accept “empathy” as some kind of axiom of morality, then yeah, we can build morality on top of it by using logic and reason. But empathy itself would still be an arbitrary value.