Here are some thoughts on "emergence". Nothing definitive, but an attempt to get at the psychological core (or cores) of the notion. Thanks are due to others for providing a stimulating discussion.
Emergence is a tricky concept. It's easy to slide it down a slippery slope, and turn it into something implausible and easily dismissable. But it's not easy to delineate the interesting middle ground in between. Two unsatisfactory definitions of emergence, at either end of the spectrum:
(1) Emergence as "inexplicable" and "magical". This would cover high-level properties of a system that are simply not deducible from its low-level properties, no matter how sophisticated the deduction. This view leads easily into mysticism, and there is not the slightest evidence for it (except, perhaps, in the difficult case of consciousness, but let's leave that aside for now). All material properties seem to follow from low-level physical properties. Very few sophisticated people since the 19th century have actually believed in this kind of "emergence", and it's rarely what is referred to by those who invoke the term favourably. But if you mention "emergence", someone inevitably interprets you as meaning this, causing no end of confusion.
(2) Emergence as the existence of properties of a system that are not possessed by any of its parts. This, of course, is so ubiquitous a phenomenon that it's not deeply interesting. Under this definition, file cabinets and decks of cards (not to mention XOR gates) have plenty of emergent properties - so this is surely not what we mean.
The challenge, then, is to delineate a concept of emergence that falls between the deeply implausible (1) and the overly general (2). After all, serious people do like do use the term, and they think they mean something interesting by it. It probably will help to focus on a few core examples of "emergence":
- (A) The game of Life: High-level patterns and structure emerge from simple low-level rules.
- (B) Connectionist networks: High-level "cognitive" behaviour emerges from simple interactions between dumb threshold logic units.
- (C) The operating system (Hofstadter's example): The fact that overloading occurs just around when there are 35 users on the system seems to be an emergent property of the system.
- (D) Evolution: Intelligence and many other interesting properties emerge over the course of evolution by genetic recombination, mutation and natural selection.