Ontological emergence and systemic causation are an outright rejection of CoP, PHY and CIP because:
(1) The causal capacities of mental properties are not reducible to either the intrinsic or relational physical properties that underlie them, contra CIP.
(2) Mental properties are not synchronically realized by, composed of, determined by, etc. narrow or intrinsic physical realizer properties; therefore they are irreducibly relational or dispositional in nature, contra CoP.
(3) Mental properties are inherently diachronic and dynamical in that they result from both causal and non-causal (holistic) diachronic processes, and their determining influence is diachronic; for example, they form links in topologically complex causal chains.
(4) Systemic causation means admitting types of causation that go beyond eYcient causation to include causation as global constraints, teleological causation akin to Aristotles Wnal and formal causes, and the like.
-Michael Silberstein
So what reasons might we have to posit the existence of ontologically nondeterministic systems? Again, there are numerous arguments ranging from the logical issues of deterministic systems explaining recursive systems to arguments from quantam mechanics, but I find the most convincing arguments in dynamical systems theory and studies of cognition. For example, when it comes to certain types of dynamical systems, the system becomes (arguably) to complex to explain via the classical causal model:
"The stretching and folding operation of a chaotic attractor systematically removes the initial information and replaces it with new information: the stretch makes small-scale uncertainties larger, the fold brings widely separated trajectories together and erases large-scale information. Thus chaotic attractors act as a kind of pump bringing microscopic fluctuations up to a macroscopic expression. In this light it is clear that no exact solution, no short cut to tell the future, can exist. After a brief time interval the uncertainty specified by the initial measurement covers the entire attractor and all predictive power is lost: there is simply no causal connection between past and future."
James P. Crutchfield, J. Doyne Farmer, Norman H. Packard, and Robert S. Shaw
As for the brain or "mind," even a book could only scratch the surface, but to give an example of how a proponent of nondeterministic systems might summarize this field as evidence:
"A more dramatic example of mind brain causation comes from the world of neurophysiology. Recent work by Max Bennett (Bennett and Barden, 2001) in Australia has determined that neurons continually put out little tendrils that can link up with others and effectively rewire the brain on a time scale of twenty minutes! This seems to serve the function of adapting the neuro-circuitry to operate more effectively in the light of various mental experiences (e.g. learning to play a video game). To the physicist this looks deeply puzzling. How can a higher-level phenomenon like experience, which is also a global concept, have causal control over microscopic regions at the sub-neuronal level? The tendrils will be pushed and pulled by local forces (presumably good old electromagnetic ones). So how does a force at a point in space (the end of a tendril) know about, say, the thrill of a game?"
Paul Davies