Each special field or domain focuses on a particular aspect of reality. Snow's view appears to lean toward the scientistic, and scientism is not merely an available and defensible stance in the ring, but an incoherent position to begin with. The central claim of scientism—that empirical science is the only source of knowledge—is itself not a scientific claim and not one that empirical science can demonstrate. To establish the correctness of this proposition requires us to step outside or above empirical science in order to make empirical science itself an object of study. But as soon as we do that, we have by that very act disproven scientism. One can only wonder how such a basic philosophical error fails to figure into the reasoning of scientism's advocates, especially given the failure of logical positivism which crashed and burned for very similar reasons.
So, to reject scientism isn't to reject science for what it truly is. It is to reject sola scientia.
The solution to the problem must occur on a philosophical plane. Only on a philosophical plane can we ask (and answer!) "what does empirical science actually tell us?" or "what is the knowledge the humanities give us?". Only on a philosophical plane can be talk about metaphysics and the nature of being (where metaphysics is the general science, while all the others are special sciences). Only philosophy allows us to relate and to locate the fruits of every field in the larger patchwork of human knowledge.