Today I attended an interesting guest seminar by the famous metaphysician (metaphysicist?) Ted Sider, on Parthood. The core idea was that there seems to be a special 'intimacy' between a whole and its parts, an idea which we grope towards with such phrases as "the parts exhaust the whole", or "the whole is nothing above and beyond its parts", and so forth. Sider was exploring how best to explicate this intimacy. In particular, he examined (and rejected) the most obvious contender: the principle of "Composition as Identity", according to which the whole just is its parts (understood as a plurality).
I won't discuss Sider's main argument. You can read the paper if you're interested in that. But one thing I liked about Sider's talk was how, during question time, he clarified the often-misinterpreted gestalt motto that "the whole is more than the sum of its parts". As I've said before, the idea behind this principle is entirely compatible with reductionism. It is obviously true that the whole may possess properties which its individual parts, considered in isolation, lack. For example, water is wet, though no individual H2O atom is wet. But this problem only arises when one ignores the relations between the parts, and fails to consider them in their totality. Of course considering each part in isolation will leave out much of importance! For although no individual H2O atom is wet, a bunch of them together can be.
So, the gestalt motto is right in that the whole is more than the sum of its parts considered in isolation. But that is no threat to reductionism, for the reductionist is instead claiming that the whole is nothing above and beyond its parts considered as a totality (which includes the relations between those parts). The parts are considered in context, not in isolation. That's the crucial difference.
That's not to say that I accept Composition as Identity. I think I would prefer to introduce some sort of 'sum' function, to keep identity as a one-one relation. For note that parts are many in number, whereas the sum of the parts is one in number. The whole is also one in number. CaI treats identity as a many-one relation (holding between the *many* parts, on the one hand, and the *one* whole, on the other). Further, if the parts are many in number, and the whole is identical to the parts, then it follows that the whole is many in number too. That doesn't sound very sensible to me. So I would reject CaI - the view that the whole just is the parts - and hold instead that the whole is the sum of its parts. (I hope I've made the distinction there clear enough?)