> In philosophy and esp. the philosophy of science, emergence is a relation between a whole and its parts such that a property of the whole does not obtain just in virtue of properties of its parts taken in isolation.
This is not a settled definition. I think everyone can agree that this applies epistemologically, where studying the parts in isolation cannot always yield sufficient information to predict macroscopic properties, but to claim that all properties of the whole do not reduce to the properties of its parts is controversial.
For instance, it seems unlikely that we would have predicted H2O's dipole moment and the phenomenon of surface tension just from studying hydrogen atoms and oxygen atoms in isolation, but it would be incorrect to say that surface tension is not the result of the properties of hydrogen and oxygen in isolation. We simply cannot discover all the relevant properties without studying them together.
Edit: to clarify, H2O's dipole moment seems obvious in hindsight when we have a good model for what's going on, and analogously, LLM's ability to do arithmetic seems obvious as a scale-dependent property in hindsight, but that doesn't mean it was obvious that this would happen before it was created.