Take (1) God is the good
compare to (2) Everest is the tallest mountain in the world.

(2) obviously is not a necessary truth. There are possible worlds where Everest is not the tallest mountain. By the same token, (1) is not a necessary truth (well, at least it is not obviously one). Thus there are worlds in which the good is not God. This implies that it is possible for the good to exist and yet God not exist. And thus, goodness and God are logically distinct even if, in this world, the Good inheres in God. My point here is that Adams can consistently hold that God is the good and yet also hold that goodness and God are logically distinct, just as being Everest and being the tallest mountain in the world are logically distinct.

Now Craig will deny that there are worlds in which good exists and yet god does not. So he needs a stronger theory than mere identity. His view is that God’s nature provides the ultimate standard of goodness. But this view cannot be right:
Voluntarism about goodness implies that whatever God wills is, by definition good. But this would make God’s goodness a trivial logical necessity. If we think that God is good in a substantive non-trivial sense, then voluntarism cannot be true of axiological properties. I take it you agree with this argument.

But the exact same reasoning applies to a divine character theory of goodness. If God’s character is the standard of goodness, then God’s character is good by definition. And thus God is good only in a trivial sense. Notice also that the divine character account of goodness is not necessarily voluntarist. If God cannot will his own character, then it is not a voluntarist position. Nonetheless, it shares a very relevant similarity to theological voluntarism about obligation: on this view God’s character is prior to goodness just as, on voluntarism, God’s commands are prior to obligations. On Adams’ view, God is not logically prior to goodness; rather the two are identical.

So Craig is committed, whether he likes it or not, to a view of the good that is parallel in the relevant respect to theological voluntarism about obligation.

Maybe that is too strong, Let me put it this way. If Craig believes that God’s character provides the standard for goodness, a natural way to read him is as taking a position on goodness that is parallel to voluntarism. I don’t see how you get the dependency thesis without that. If you think it can be done, I hope you will explain how.

So, ultimately Craig want to say both that God is good (in a substantive sense) and that goodness depends on God. But you can’t have both (at least I don’t see how). Adams wants to say that God is good in substantive sense and you can say this as long as you accept that goodness and God are logically distinct (even if they are factually identical).

Actually the (evil god) objection does not work here for the reasons Jason alludes to. Adam’s argument is that the best account of the nature of moral obligations is that they are the commands of a loving and just God.

Now an evil God’s commands is not a plausible account of the nature of moral obligations because its possible for an evil being to command creul and malicous acts, whereas its impossible to be obligated to commit evil acts. On the other hand a loving and just God cannot command acts which are cruel malicous, so the evil God, hypothesis does not explain the phenomena and a loving and just God does.

Your comments suggest you have a different picture in mind, the existence of an evil God can explain our obligatons to do evil. The problem is we do not have obligations do evil, thats a self contradictory notion, so there is no need to explain obligations to do evil as they don’t exist.

How could we know what possible world is the actual one?

Adams’ view, as I said, is not supposed to account for axiological properties. Craig, on the other hand, does believe that God is the source of all moral value. In the debate with Kurtz that I mentioned earlier, Craig says, “If theism is false, we do not have a sound foundation for morality” and then he explicitly mentions moral value and moral obligation. Again, “God’s own holy and loving nature supplies the absolute standard against which all actions are measured. He is by nature loving, generous, just, faithful, kind, and so forth.” So Craig very clearly indicates that his view is that if God does not exist, there are not axiological properties.

This equivocates, Adam’s divine command theory is not supposed to account axiological properties. So they exist independently of God’s commands. This does not mean they are independent of God per se In Finite and Infinite Goods, however Adam’s identifies axiological properties with God himself, God being a kind of Platonic exemplar of the good. Craig’s view is the same in the Kurtz debate you mention he states that axiological properties depend on God but he does not make them depend on Gods commands, he is clear in the follow up article at the end “This Gruesome of Guests” that he is only identifying obligations with Gods commands. Goodness he thinks of as different to obligations and grounded in God’s nature not his commands. Craig in fact acknowledges Alston as his source, and I believe Adam’s position has a similar trajectory.
Murphy’s article is addressing voluntarism, the claim moral properties depend on Gods will not the claim they depend on God per se. He is correct that Adams does not ground axiological properties in God’s will. But thats different to claiming that Adams does not ground them in God.

Now, one of the important consequences of Adams’ view is that morality is not completely dependent on God. Goodness and badness exist independently of him. This, in itself, undermines many versions of the moral argument (most notably that of Craig and Copan). But I think it also undermines Adams’ own version. If there is a God-independent standard of good and bad, then an Ideal Observer theory of ethical rightness and wrongness can be made more plausible.

Even if this was accurate of Adam’s (which it isn’t) this seems to me mistaken. Adam’s argument is that God’s commands are the best account of moral obligations, so even if goodness is independent of God it does not follow that moral obligations must be. Adam’s argument in particular is that moral obligations are plausibly understood as social requirements, that is demands made by one person on another backed up by certain type of social pressure, so even if goodness is independent of God he thinks moral obligations have features which require that they be based in the demands of some person. His criticisms of an IOT seem to not depend on goodness being dependent on God.

In his article on moral arguments for theism in his book The Vritue of Faith and Other Essays, Adams argues that rightness and wrongness (denotic properties) give us reason to believe in God. So he is using a very different kind of argument from Craig. (Take a look at Mark Murphy’s article on theological voluntarism at the Stanford Encyclopedia of Philosophy for more on Adams’ view).

So, I am not attacking straw men. I am criticizing Craig. And as I said earlier, I am not familiar enough with your own view to know if you tend more toward Adams’ view or Craig’s. Since you mention Adams in your post, you are correct that I should have assumed that you favor his view.

Now, one of the important consequences of Adams’ view is that morality is not completely dependent on God. Goodness and badness exist independently of him. This, in itself, undermines many versions of the moral argument (most notably that of Craig and Copan). But I think it also undermines Adams’ own version. If there is a God-independent standard of good and bad, then an Ideal Observer theory of ethical rightness and wrongness can be made more plausible.

Well, I’m sure we can get into objections to Ideal Observer Theory, but I would prefer to stay on the topic of whether there are any moral properties (axiological or denotic) that must be independent of God.

That after all is what the divine command theorist contends, to respond that “there is no reason for thinking God has these attributes” seems in this context to beg the question.

I’m only familiar with the arguments of medieval philosophers, which as far as I can tell beg the question by defining God as the greatest possible being, whatever being that might be, and the claiming that greatness entails certain attributes. But the statement that greatness entails those attributes rather than others is question begging, of course.

I’m not familiar with modern swings at this particular pinata.