"Don't y'all find it a little suspicious that so many people think "emergence" is a useful concept, yet have different definitions of what it is?"

I think "bias" is a useful concept, despite the tendency for people to disagree over what regions of failurespace count as "bias." (Uh, ahem).

Here is David Chalmer's short philosophical stab at what emergence is and ain't.

I don't buy the analogy between emergence and phlogiston or vitalism. Offering up "emergence!" as an explanation of a phenomenon is a category mistake, to be sure, and is a semantic stopsign when misunderstood this way.

As other commenters have noted, however, there is a proper understanding of emergence that is useful. (In philosophy, for instance, it's an admittedly sloppy but still useful term to classify different kinds of explanations of consciousness). This doesn't seem true of explanations that appeal to phlogiston or vitalism. Vitalist explanations aren't category mistakes. They're simply vacuous explanations, full stop.