"If anything is statistically unpredictable then it is beyond the capacity of science to explain it."
An ensemble of statistical unpredictable individuals may have a statistically determinist behavior.
Of course you are right. The particular rejoinder I was trying to cover myself against with the use of the word "statistical" was a poster responding that (for example) individual nuclear decay events are unpredictable. I was trying to include the concept that such events are still statistically predictable in their probability over time, and hence their study is still scientific.
"Chaotic systems and emergent phenomena are taken to be the sum result of a myriad of individually predictable actions."
Don't you mean "individually unpredictable actions"?
No but again I didn't explain the context that was in my mind when I wrote that sentence. If we take the neurons making up our brains, we could in principal describe in detail their individual responses to stimuli, according to reasonably well understood physical law and theory. They are "individually predictable". However their mass action gives rise to consciousness, memory, free will, etc, and this emergent phenomenon is not obviously predictable from physical law, despite that fact that it results from the sum of all the individual predictable behaviours.
Language seems a poor tool to handle such concepts, particularly in the hands of a buffoon.
Placemarker.