What does "undirected emergent order" mean?
It means order emerging from the interactions of multiple subsystems as a result of their intrinsic properties, without external guidance or direction. Popular examples are starling murmurations or schools of fish. The patterns generated by cellular automata like Game of Life, or fractals like the Mandelbrot Set are also examples.
"Emergent" properties are those that have no observable cause. "Emergent" implies the whole is somehow greater than its parts. Philosophically, claiming an "emergent" property violates First Principles, ie., Principle of Sufficient Reason. How does adding the modifier "undirected" clarify the "emergent" assumption? "Emergent", like "random", admits of ignorance.
Not really. Emergent properties may not be predictable from those of the subsystems, but they have observable causes (the interactions of the subsystems). The idea that the whole is greater than the sum of its parts is rather ambiguous - it's more the case that the behaviour of the whole is quite different from that of its parts. See
Emergence.
There's no conflict with the Principle of Sufficient Reason, emergence is inherently deterministic.
The modifier 'undirected' is to distinguish the self-organisation I'm describing from the directed form you suggested in
#753. As I said, the idea of
self-organisation carries the implication of being the result of intrinsic rather than extrinsic influence.