I suspect it may be just an epistemological phenomenon, but I do wonder if there might be some literal truth to the idea that the “whole is greater than the sum of the parts.” Complex systems, we presume, are perfectly predictable with a perfect understanding of the relevant variables, though in practice most are not actually predictable since we can’t hope to manage the volume of information and calculation involved. But I wonder if ideas like chaos theory or QM might hint at some real difference between components in isolation and systems. I don’t have any real evidence this is true, and so I remain skeptical of my intuitive sense that it might be, but I don’t know that it is a closed case. And I’m not sure how one would prove it wither way, beyond developing the ability to accurately predict the behavior of any system, such as the brain, perfectly, which seems unlikely. This is the core of my position in the free will debates—Hard determinism (provisionally) but with a recognition that in practice the heuristic models we use may be as or more useful than the formal analysis of something as complicated as the brain because we can’t yet (or can’t?) apply the formal models well enough to get detailed, reliable predictions.
Well, what we do know from chaos theory and QM makes predictions literally impossible beyond a relatively short timeframe. Let’s take a schematic example. Say we’re talking about a chaotic system of planets, and we’re trying to predict their orbits arbitrarily into the future. In order to do this we have to measure their present positions and momentums with some precision. And the farther into the future we want to predict, the more accurate our measurements have to be. If the system is particularly chaotic, we need to be extremely fine with our measurements, because the chaotic complexity simply explodes the options into the future, and very small mistakes in our initial measurements may well produce predictions that are dramatically wrong.
Knowing about quantum mechanics, and in particular the Heisenberg Uncertainty Principle we can both see where this is going. It is in principle physically impossible to know the position and momentum of a particle to beyond a certain level of accuracy. Speaking metaphysically, one might argue that there simply is no fact to the matter about these measurements beyond a certain level of accuracy, IIRC that level, relevant both to distance and time, is given by the Planck constant, which is an extremely small number.
So yes, chaotic systems are in principle unpredictable beyond a certain time frame or accuracy level. (In fact, any physical systems are unpredictable far enough into the future; it’s simply that chaotic systems become unpredictable a lot quicker).
But that said, I’m not sure it’s the same thing to predict the future behavior of a system, and to know what its emergent properties would be. A chemist can tell us why it is that H2O at ordinary temperatures flows, is transparent to visible light, cools us off when we splash it on us, increases in size when frozen, etc., etc. These are all quite complex, in some sense “emergent”, properties of H2O molecules, and they are all “predictable” (that is, knowable; one doesn’t literally need to do any predicting into the future) from the chemical properties of the molecules themselves.
So the chemist may know all about these emergent properties of H2O while still not being able to predict the behavior of any given body of water very far into the future at all.
Similarly with living things. In the 19th century it was fashionable to believe that life was made up of tiny molecular machines, but that the machines themselves were not alive. They needed “élan vital” to really work properly, and this special property was not contained among the properties of the constituent molecules. That view is clearly pseudoscientific. There is a short discussion of all this in the wiki page on Vitalism.