It looks like Greg Boyd will be starting a series of posts on the immutability of God. I find that more often than not, these discussions suffer at least the following major deficiency: they don't address the very compelling philosophical arguments proffered in defense of divine immutability by the most able defenders of the doctrine. I've written on this before, but perhaps it would be well to pick it up again.
Thomas Aquinas spills a lot of ink in defense of the doctrine of divine immutability in his Summa theologica and elsewhere, such as Summa contra gentiles I. The most compelling argument in favor of divine immutability draws from his most compelling argument for the existence of God: the argument from motion, by which he means change.
The argument goes like this. For a thing to change is for it to gain in actuality what it previously had only in potentiality. For instance, for a match to become lit is for it to gain the actual property of being lit which it previously had only potentially. (If a thing does not potentially have some quality, just as my body does not have the potential to breath underwater, then I cannot gain that quality in actuality.)
Now insofar as a thing undergoes change, it must be changed by something else. Let's take the example of a match being lit. Prior to being lit, the match only has the potential to be on fire, and consequently it cannot bring itself to catch fire. It is in a state of potential, whereas only what is actual can cause any changes in the world. Now it is not as if some other part of the match can bring it to catch fire, either; it is not as if, for instance, the match head can cause itself to catch fire, since it would already be on fire seeing that the match head was already present. What is needed is something outside of the match. Importantly, too, the cause must be something outside the match which is actual and not merely potential. This would be the actual motion of your hand as you strike it against an appropriate surface (e.g., the side of the matchbox).
Now Thomas insists this is true for every instance of change whatsoever in the whole world: whatever undergoes change must be changed by something else which is actual. Now the list of causes of change cannot be infinite. There is a long and sophisticated but intuitive reason why this is so, and I've written on it before (e.g., here and here). Just trust me. Consequently there has to be something at the end of that long list of causes.
Since it is the cause of the change of everything else, this thing cannot change other things by undergoing change itself. In that case it would not be the end of the chain of causes but just one more link, and it would need something to explain its change. No, it has to be purely actual entirely of itself, something that is the cause of the change of everything else but is not made actual by anything else. That is the only way it can put an end to the long chain of causes of change -- by not being subject to change itself.
Now according to Thomas, this ultimate cause of all change is quod omnes dicunt deum, "that which everyone calls God." By definition God cannot be changed or affected by anything, since he is the ultimate explanation of why everything else changes to begin with. Therefore he is immutable and is not actually affected by anything that happens in the world.
I've presented the argument in a very short-hand way; others have developed it in excruciating detail. My point in all this is that it makes no sense to talk about divine immutability and to argue against it apart from dealing with arguments like those of Thomas. Why is that? Because the arguments are damn-nigh irresistible. The point that change is the actualization of a thing's potentials makes a lot of sense, and is a lot better than other proposals; the suggestion that this actualization must take place by something already actualized, and thus something outside of the thing being changed is intuitively obvious; the impossibility of an infinite chain is a clear enough point once you grant the essential points to be made about causal series; and the pure and immutable actuality of the source of all change follows obviously and logically from all these premises.
Whatever we say about the biblical language of God's change -- and there is an important discussion to be had about that, by the way -- we cannot have a serious discussion about God's immutability without addressing the sophisticated arguments of Thomas and others in favor of the doctrine. Plato's argument in the Republic to which Boyd makes reference is a start but it is hardly the final word on the topic.