I've written lots of articles on naturalism. My approach to the matter is largely pragmatic. In my view, nature is whatever is subject to scientific explanation and to technological control. Nature is thus the cosmos in something like the ancient Greek sense: it's a unified whole, an intelligible causal order. While Plato did denigrate the realm of the many, as a distracting shadow of reality, and glorified an abstract realm, that dualism has been vindicated by theoretical physics which likewise drives a wedge between the world of commonsense and the underlying (e.g. quantum) reality.

In any case, yeah, I'd tie the extent of nature to the efficacy of science. How would you define "nature" without implicitly appealing to the scientific method?

Quine attended the Vienna Circle, and he was an extreme empiricist. That's what positivism is: scientistic empiricism, or a cult-like fetishization of science. As I learned in my philosophy of science courses, the positivists themselves undermined their worship of science. That's the difference between philosophy and theology: philosophers are more skeptical so they're more likely to correct their mistakes. Positivism may have been a scientistic cult, but it was also philosophical. So Quine did indeed cast doubt on the positivist creed. He took the positivist's spirit of scientism with him, though.

That spirit lives on in the unlikeliest of places, such as in economics, which is likewise prejudiced against any form of knowledge which isn't at least superficially scientific. That prejudice allows economists to escape censure for their role in undermining democracy: they can pretend their discipline isn't normative and that they're just stating the objective facts. The early economists had no such pretense since economics started as "political economy," which was a branch of moral philosophy. That's why Adam Smith wrote a treatise on morality, and Marx was overtly ideological.