The traditional axiological argument, also known as the moral argument, has been ably defended by many theistic philosophers. Geisler's version goes like this:
1. Every law has a law-giver.
2. There is an objective moral law.
3. Therefore, there is an objective moral law-giver.
When we consider (1), it becomes clear that laws are prescriptive rather than merely descriptive. In other words, they tell us what we ought to do, instead of merely detailing an action that is done. This suggests to us that the moral law-giver of (3) is personal, since prescriptions have their source in persons. Imagine going to a pharmacy and handing one of the staff a piece of paper without a doctor's signature. If they ask you, "who prescribed this?" and you answer, "nobody; it's just a prescription," then you would get a puzzled look at the least, and an appointment at the nearest psychiatric ward at the worst.
For Geisler, and any moral realist, (2) is supported best by our own moral experience. Indeed, the idea that rape, torture, child abuse, or murder are morally ambivalent is rejected by everyone in practice. Even those who commit these crimes would object if someone did the same to them, which is indicative of the reality of their own moral compass.
Craig's moral argument is summarized as follows:
4. If God does not exist, then objective moral values do not exist.
5. Objective moral values exist.
6. Therefore, God exists.
Craig's version is a reductio ad absurdum, which makes use of modus tollens. The argument is essentially the same, except that Craig's treatment has been more in depth. Not only do we have the reason that Geisler gives for attaching objective moral values (or an objective moral law) to a personal law-giver (God), but there are additional reason for thinking so, as well. One of my favorite reasons makes use of Kant's practical axiological argument, which Craig defended in his debate with Louise Antony:
7. Moral behavior is rational.
8. Moral behavior is rational if and only if justice will be done.
9. Justice will be done if and only if God exists.
10. Therefore, God exists.
The defense of (7) is much the same as the defense of (2) and (5). We have a perception of the rationality of moral behavior. In fact, it would be quite irrational to reject such behavior in practice. Think of the devastation that would result if everyone treated child abuse as morally neutral. The truth is, we have no reason for rejecting the rationality of moral behavior, and every reason to accept that moral behavior is rational.
I would defend (8) by simply pointing out that if justice is not done, then there is no incentive to behave morally. If we benefit the most by being greedy and hateful, and so forth, then why not embrace these vices? Only if justice will be done do we have any reason for striving for virtue as opposed to vice.
Yet, this brings us to premise (9). Upon just a brief reflection, we realize that there is much injustice in the world. If this life is all there is, then justice will not be done and there is no reason, practically speaking, to accept (7). Only if there is a life beyond this can we salvage the rationality of moral behavior. In addition, only if God exists is there any hope that there will be a judgment in which we are reckoned according to our deeds (Psalm 62:12; Prov. 24:12; Rom. 2:6). So, we find that God's existence can be inferred by the practicality of morality.
A number of objections have been made to the moral argument, but I don't find any of these at all compelling. One of these objections is that since we have developed morality through the process of evolution, then we cannot say that the moral law is objective; we could have evolved in another way. A similar objection is that morality is culturally relative, and that we learn our moral behavior by our particular society. The flaw in both of these arguments is that they both commit a very basic genetic fallacy. The manner in which something is learned has no effect upon the verisimilitude (truth-value) of a given proposition. I learned the multiplication tables from my second-grade teacher, but that doesn't mean that multiplication is anything short of objective.
Moreover, the relativity of moral values isn't nearly as great as some purport. And even if it were great, it doesn't make any difference to the argument at hand. The reason why is simply that some cultures can be wrong. Any culture that believes the earth is flat, for example, is not engaging in just another relative speculation. Such a culture is objectively incorrect in that assessment. Likewise, if a culture accepts the practice of, say, genocide, then they are wrong in doing so. I don't believe this to be an arrogant presumption by any means. After all, the relativist who claims this is arrogant is presupposing the objectivity of arrogance being a vice, so the objection actually undermines itself.
Another objection is that we should behave morally, not for the sake of an afterlife, but for the sake of future generations. The immediate difficulty with this is that all future generations will eventually die, as well. Hence, unless there is a God who will judge our works, there remains no incentive to behave morally.
A third objection to consider is that atheists, and non-theists in general, are capable of living morally. I fully acknowledge this. The claim, however, is not that atheists cannot behave morally, but that their atheism cannot make sense out of living morally. To put it another way, atheists can be moral, but only in spite of, and not because of, their respective worldview.
One final objection is the Euthyphro Dilemma: is something good because God wills it, or does God will it because it is good? What the dilemma assumes is that goodness is either due to the arbitrary will of God, in which case God can change it at a whim; or else, goodness exists independently of God, and so we don't have to invoke God in order to make sense out of morality. The problem with this is at least twofold.
First, let's assume that the Euthyphro Dilemma's conclusion is correct and that goodness exists independently of God. Even if this were the case, there is still no assurance that justice will be done. This is why I like Kant's argument so much. It requires the skeptic not only to make sense out of what morality is, but it also requires him to make sense out of moral accountability. On atheism, there simply is no such accountability, so the question remains: why should one engage in moral behavior?
Secondly, what we find is that the Euthyphro Dilemma is actually a false dilemma. A true dilemma states that either A or ~A. What the Euthyphro Dilemma states, on the other hand, is A or B. Since the two are not contradictory, we can accept both. God's willing something is due neither to a mere whim, nor to its being good independently of Him. Instead, something is good because it reflects God's own nature. God is the summum bonum, the "greatest good" itself, and so He is the very standard of goodness.
Overall, then, I believe there is much to be gained by contemplating the inference from morality to God. The challenge for atheists to make sense of axiology, in my estimation, remains.