Does your definition of objective moral truths implicitly postulate the existence of an external moral agent? Dr. Sam Harris has said the fundamental moral fact is that the maximizing of human flourishing is good. The objection is, “Why is the maximizing of human flourishing good?” Couldn’t someone ask you, “Why is obeying God objectively moral?” It’s not obvious to me why this problem is different from the issue with Harris’s view.
The concept of an “objective” moral value or duty is simply a moral value or duty that is not dependent on the subject. Objective moral values are object-relative (true of the object), whereas subjective moral values would be subject-relative (true of the subject.
Consider a man viewing a painting. The man may say two things about the picture. He may say that the artwork is beautiful, and he may say that the artwork is on canvas. His first statement isn’t about the painting. The claim is about the man. He is saying that he finds the artwork to be beautiful. The second statement, however, is about the painting and is thus objective.
Sam Harris’s moral axiom is something like, “That which is conducive to human flourishing is good.” Presumably, he takes this to be a brute fact. If correct, then this would count as an objective moral value. It wouldn’t be merely a statement about what Harris thinks about human flourishing; he means it as a statement about human flourishing. He says that it is good.
The challenge is that, as a brute fact, this axiom would be true without any explanation. Theism is a better worldview because it can explain more. Theism can furnish an account for the truth of moral facts.
Theism ground moral values in God’s moral character. God is “the good.” Moral duties are rooted in God’s commands. You bring up an important question, “Why are we obligated to obey God?” We are obligated to obey God because he is our creator. The type of union we have with someone gives rise to our moral duties (consider how a child develops the duty to obey his parents). In creating us, God became our creator. God’s authority to issue us commands is not a moral axiom taken as a brute fact but is grounded in God’s historic act of creating us.