What is the explanation for the fact that Scripture says in many places that God changes His mind?
It's an anthropomorphism, we are told. It's similar to how the Bible speaks of "the arm of the Lord" as if God has arms.
But the more I think about it, the more this explanation just doesn't do justice to the text. For one thing, we use anthropomorphisms as a metaphorical way of expressing something true. In the case of "the arm of the Lord", the expression is a metaphor for the ability of the Lord to get things done. If "changing His mind" is an anthropomorphism, then what is it a metaphor for? The disconnect here is that whereas arms are a physical feature, the mind is not. It's easier for us to see arms as a metaphor when it comes to God because even though God has no form, we know that arms represent the ability to get things done. But even if God does not have literal arms, are we to believe that He doesn't have a literal mind?
Secondly, is it even true that God has no physical form? The Bible speaks of God walking in the garden, of allowing Moses to see His back (for if he saw the Lord's face, he would die), of of course manifesting Himself in the flesh in the person of Jesus Christ. We are said to be made in the image of God, which surely signifies that our physical form corresponds to God's own form. What else is an image?
It seems to me that the anthropomorphism argument falls short of explaining the logical problems entailed by taking the text at face value.