A redated post.
In Bassham and Walls ed. The Chronicles of Narnia and Philosophy (Open Court, 2005), Angus Menuge finds an implicit argument against materialism that is not pragmatic in nature. In "Why Eustace Almost Deserved His Name: Lewis's Critique of Modern Secularism" he writes:
The argument is left rather implicit, but Lewis is clearly attacking the intelligibility of the debunkers' claim that our ideas of "higher" things can derive from "lower" sources. How can the idea of something great derive from something lacking that greatness? Could the idea of eternity arise from the materialist's temporal world? Could the ideas of infinity and perfection derive from the finite, imperfect world of the secularist? Could the idea of a necessary being like God derive from the secularist's contingent universe? There is a good case to be made that material causes do not account for the content of those ideas. pp. 202-203.
This is reminiscent of an argument found in Descartes' Meditations.
See also this discussion.