Φῠ́σῐς - Basis for Modern Science? Hi. Excuse me if this is somewhat obvious but it may be worth remembering "science" isn’t a single entity to be analyzed using identical systems following identical rules. There may only be one "true" reality of everything, but our current scientific understanding necessitates the deployment of different paradigms for different areas of research. It’s possible this may have something to do with the potentially irreconcilable disagreement I’m seeing here. Apologies in advance if I'm saying nothing new or interesting.
Postpositivism, which prioritizes predictive power, is a typically physicalist approach marrying the formal and physical sciences. Constructivism-interpretivism is a more lenient approach suiting the cognitive and social sciences. To a postpositivist, most hypothetical links from φυσις to modern science would be implausible because we can’t conduct a survey collecting testimonials of dead people, and that’s just too bad. (Lol.) To a constructivist-interprivist, however, it’s possible to sufficiently ground a hypothesis by extracting common themes and standpoints in the literature. For φυσις, this may invoke the "natural elements" of Indo-European mythology as an effort to properly bookend an account and thereby make it robust enough to be considered scientific. But even if it’s given that mythology is early evidence of proto-science as I contend, the notion is still, clearly, highly tentative. I mention this because, judging from post histories, paradigms haven't been given much mention, though I personally think they bring a lot of clarifying power to any discussion. Hopefully that can be appreciated here to at least some degree.
As for the question of φυσις being some kind of weird non-divine driving force of science, it may actually be a question of what one thinks science is supposed to do. If science tells us how, then φυσις is probably an antiquated and superstitious container of convenience which is probably no longer relevant. If science tells us why, though, then I’m afraid the spectre of φυσις is transformed into what are mysteriously now known as the "Laws of Nature" (not "Natural Laws"), which appear to serve as a kind of “known-unknown” foundation for coherent scientific explanation despite being.. somewhat ad hoc.