Emergence is a broad term for when things with definable, reproducable, novel, and predictable behaviors, which can be studied, quantified, and have math rules

Emergence is a broad term for when things with definable, reproducable, novel, and predictable behaviors, which can be studied, quantified, and have math rules written about them, arise spontaneously from the lower rule-sets they are built on. It's like when you can identify a separate and distinct set of behaviors in the causality chain, but yes the word 'causality' encompasses 'emergence' in a very vague way, and so vague that it's indistinguishable from 'time' itself.