I ll try a silly info-theoretic description of emergence:
Let K(.) be Kolmogorov complexity. Assume you have a system M consisting of and fully determined by n small identical parts C. Then M is ‘emergent’ if M can be well approximated by an object M’ such that K(M’) << n*K(C).
The particulars of the definition aren’t even important. What’s important is this is (or can be) a mathematical, rather than a scientific definition, something like the definition of derivative. Mathematical concepts seem more about description, representation, and modeling than about prediction, and falsifiability. Mathematical concepts may not increase our ability to predict directly, but they do indirectly as they form a part in larger scientific predictions. Derivatives don’t predict anything themselves, but many physical laws are stated in terms of derivatives.
I ll try a silly info-theoretic description of emergence:
Let K(.) be Kolmogorov complexity. Assume you have a system M consisting of and fully determined by n small identical parts C. Then M is ‘emergent’ if M can be well approximated by an object M’ such that K(M’) << n*K(C).
The particulars of the definition aren’t even important. What’s important is this is (or can be) a mathematical, rather than a scientific definition, something like the definition of derivative. Mathematical concepts seem more about description, representation, and modeling than about prediction, and falsifiability. Mathematical concepts may not increase our ability to predict directly, but they do indirectly as they form a part in larger scientific predictions. Derivatives don’t predict anything themselves, but many physical laws are stated in terms of derivatives.