The Futility of Emergence
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"Even better: A colony is made of ants. We can successfully predict some aspects of colony behavior using models that include only individual ants, without any global colony variables, showing that we understand how those colony behaviors [emerge] from ant behaviors."
Emerge and arise are synonyms. I'll agree with your desire to quell the potential overuse of "emergent," however as is well outlined above there is a specific testable model being proposed when emergent is used closer to correctly. That is that there is no system-wide variable that leads to the observed outcome. Prove that variable or mechanism and the outcome doesn't emerge or arise - thus disproving that the system has emergent properties.