I've been told that Wolterstorff attributes the prominence of divine simplicity in the Christian tradition to the influence of Aristotelian metaphysics. Whatever the history of the issue may be, it seems that there is a perfectly good argument for divine simplicity that makes no reference to Aristotelian metaphysics, and whose only really controversial premise—the first one—is something that most theists should immediately accept (though Wolterstorff himself denies it). Let a "proper part" of X be a part of X that is not identical with X.
- (Premise) Everything other than God himself is created by God.
- (Premise) If God has proper parts, then at least one proper part of God is not created by God.
- No proper part of God is identical with God. (By definition of "proper part".)
- If God has proper parts, then there is something that is neither identical with God nor created by God. (By 2 and 3)
- God has no proper parts. (By 1 and 4)
One might quibble about (3). One might think that all of God's current parts are created by God, because at some point created new parts for himself, and then destroyed the old, non-created ones. However, (1) is not only true now, but it was always true. So there couldn't have ever been any non-created divine proper parts. I guess one could have a super-weird view on which God from eternity has been replacing his parts, and never had any parts that were not created by him at an earlier time. But that constantly changing view of God is surely incompatible with any reasonable take on divine immutability. (Take it as a criterion of adequacy on a theory of immutability that it rejects this!)
The real controversy will be about (1). But here I just want to make one point. The deep plausibility of (1) to theists does not come from Aristotelian metaphysics: it comes, rather, from a commitment to God as creator that appears at the heart of Judaism and Christianity. In fact, it may be that the direction of justification between (1) and Aristotelian metaphysics goes the other way: it is (1) that pushes the theist to more immanent views of universals.