I think some confusion is generated by his use of the term “reductionism” to describe the naturalistic position of which he is critical. Materialism is typically divided into three types, eliminative, reductive, and non-reductive materialism. On the face of things, by concentrating on reductive materialism, it might seem that he is letting the non-reductive materialists off the hook with his arguments, and this perhaps comprises the largest group of philosophers that call themselves materialist.
William Hasker, in The Emergent Self, (Ithaca, 1999), developed a tripartite definition of minimal materialism which, I believe works also for naturalism. That is, I don’t think any view can be thought to be genuinely naturalistic unless it satisfies these three requirements. And I think a position with these three characteristics is what Nagel is thinking of when he talks about reductive materialism. It is the view that
1) At the basic level, reality is mechanistic. That is, it lacks intentionality, subjectivity, purposiveness, and normativity. None of these items can enter into a description of reality at the basic level of analysis.
2) The basic level of analysis (which we typically call physics), is causally closed.
3) Whatever else exists must supervene on the basic level. It must be the sort of think that must be the way it is because the physical is the way it is.
Andrew Melnyk maintains that “Naturalism claims that nothing has a fundamentally purposeful explanation…Naturalism says that whenever an occurrence has a purposeful explanation, it has that explanation in virtue of certain nonpurposeful (e.g. merely causal) facts.” And the failure to the mental on the ground floor of reality, so say that our minds can understand the world, ultimately, because mind is fundamental to reality and not simply a byproduct of it, is what Nagel sees as ultimately wrong with the all the positions he is calling “reductivist.”