In a recent post I said I affirm a strong doctrine of divine impassibility according to which God is not really affected, emotionally or otherwise, by anything that happens in the creation. Of course I think that when he incarnates as human, God feels pain, hunger, etc., and all the rest. But it is not as God unincarnate but as God incarnate. In his divinity God cannot suffer nor be affected at all.
It seems to me that many discussions of divine impassibility here and there on the web address this doctrine and attempt to make conceptual room for an attenuated form of impassibility -- e.g., God's character cannot be changed by the world, or something of that sort. This won't do, however, because the doctrine ultimately is motivated by heavy-duty philosophical arguments from nigh undeniable principles of classical metaphysics, arguments which at the end of the day warrant a much stronger doctrine than these attenuated forms. My goal in what follows is to present some argument which might motivate a person to hold to a stronger form.
Thomas Aquinas, for instance, and Aristotelians more generally posit that there are at least two modes or ways of being: being in act and being in potency; actuality and potentiality; the ways a thing is, and the ways a thing could be. Making this distinction is ultimately necessary if we are to make sense of the phenomenon of change in the world; for more details, consult Edward Feser, Scholastic Metaphysics. On this view of things, change is what happens what a thing's potentiality is made actual, or in more Scholastic terms, when a thing's potency is reduced to act. For instance, a change in shape which takes place in an ice cube when it melts is an actualization of its potentiality to take on a different from.
Now a further principle of Aquinas' philosophy is that whatever is changed must be changed by something else, and it must be changed by something actual. Of course merely the potential to be such-and-such cannot change anything, since it is merely a potential. If one thing changes another -- e.g., if the warmth of the sun melts an ice cube -- it is because of the former's actual qualities, not its potential qualities. And it must always be one thing changing another: ice can't melt itself, since it is only in potential with regards to its adopting a different shape; it must be something actual which changes it.
This is where Aquinas argues that there must be something which is purely actual, which is ultimately the cause of the changing of everything else but is not and could not be changed itself by anything else. This purely actual thing is just actuality, no potentiality at all, and so it effects things and makes changes entirely of itself without any mediation or actualization on the part of another. The argument goes like this.
(1) If A is changed, then A is changed by B. (2) Now B is either purely actual as we've defined or it isn't. (3) If it is, then the conclusion of the argument is granted. (4) But if it isn't, then B is actualized by some third thing C. (4) Now this chain cannot go on infinitely, since then there wouldn't be any change at all. (5) Therefore there must something that is purely actual, quod omnes dicunt deum -- which all people call 'God.'
The critical premise is (4), the defense of which goes like this.
The Scholastics like Aquinas distinguished between two kinds of causal chains. In an accidentally ordered causal series, one thing brings about an effect, which then brings about another effect, but the later members of the series do not depend on the earlier ones for their causal activity. For example, Paul has a son Peter, who when he grows older has a son James. In this case Peter does not depend on Paul for bringing James into the world; indeed Paul could have been dead for a while by the time James comes into the world. In an accidentally ordered series, then, causal agents bring about effects independently of one another.
In an essentially ordered series, however, one thing brings about an effect only because of the continued activity of another, by virtue of which it is enabled to realize an effect in the first place. For instance, suppose you use a stick to move a rock, and the rock leaves grooves in the sand as you drag it from here to there. In this place, the rock leaves a mark upon the sand only because of the activity of the stick, pushing it; and the stick only pushes the rock because of the activity of your hand, grabbing and moving it; and your hand only moves the stick because you will to do so; etc. In this case a later member of the causal series (e.g. the rock) can only bring about an effect (viz. the grooves in the sand) because of the continued causal empowerment and enabling of a previous member (viz. the stick and ultimately you).
Aquinas argues that in the case of essentially ordered causal series, there must be a purely actual first cause. The reasoning is like this. Because in such series the ability to bring about an effect is derived from one member to another, if there weren't ultimately a first member in the series which had the power of itself, the series wouldn't exist in the first place. In other words, the power to bring about an effect is a critical presupposition of any such causal series, and so unless the power to bring about an effect existed 'on its own' in some agent, underived from anything else, then there couldn't be the series in the first place. Consider the following analogy: if you borrow a book from me, and I borrowed it from Joe, and Joe from Jack, and so on, there couldn't be an infinitely long series of borrowings and lendings; someone had to have had the book to begin with, to have produced it or whatever, or else it couldn't have been lent in the first place. Likewise, if actuality is derived from A to B to C and so on, eventually there has to be something which just is actual and does not get it from anything else.
There are such causal series as these; I've already given an example. Moreover, John Duns Scotus has also argued that all accidentally ordered causal series presuppose ontologically prior essentially ordered series. See this post, the paragraph beginning "Furthermore, Scotus argues that. . ." So the reality of such causal series cannot be avoided, and consequently neither can the conclusion of Aquinas' argument.
Therefore there is something which is purely actual, which only ever changes other things and is not changed in itself. This thing is impassible, since nothing can possibly change it. Now classical theists such as Aquinas and others identify this thing with God; this is one of many things which they mean by the word "God." Therefore these other attenuated versions of impassibility simply won't do.
You couldn't say, for instance, that part of God is purely actual whereas another part is not and is changeable. This is because God cannot have parts on the classical view; he cannot be composite in any way. As Aquinas says in Summa theologiae Ia, q. 3, a. 7, resp.: "every composite has a cause, for things in themselves different cannot unite unless something causes them to unite. But God is uncaused." There can't be composition in God because his composition would require an outside to unite it. This is something true of all composites -- the parts of a bicycle, for instance, cannot simply unite themselves into a bike but must be united by the person who assembles them. If God were a composite reality, he would need to be actualized by something outside of him. This is impossible because God is supposed to be the first cause, the ultimate ontological rock-bottom, if you will.