Be sure to read Nagel’s take on reductionism. We will pursue another angle here: There are many other approaches to the issues that Nagel raises. One of them is the universal materialism of the ancient Samkhya. There the existence of material complements to spiritual entities is assumed, by definition, however.
That leads me to a kind of ‘scifi’ response to Nagel’s perspective. Cf. the movie Avatar: as so often scifi writers stumble on thing, mixed with nonsense: there we see a technology of mind/soul able to transmit a personhood ‘electromagnetically’. Well, maybe. But the point is that a non-reductionist view of man’s mind and self is given a material, or at least, physicalist, substrate. We can take scifi no further.
So in that sense we can call ourselves materialists and still consider ‘spiritual’ entities.
We have also cited the writer J. G. Bennett here many times: he has a unique (probably a variant of Samkhya and ancient pre-buddhist psychologies, or else an unknown sufistic doctrine of the will) remix of the basics: instead of material and spiritual, a distinction that is marginalized, he speak of ‘Being, Function, Will’ in a triadic analysis of the nature of ‘reality’. The material disappears (although remaining as a useful shorthand), while the spiritual cease to be so named. The category of ‘being’ absorbs the ‘material’ at the low end and places consciousness symmetrically at the high end, as variants the one of the other. Independent category of will seems strange, but, most remarkably, this was first discovered in modern times by Schopenhauer. His usage of the term ‘will’ requires careful study, because it deviates from our sense of ‘will’ as ‘will power’. the framework of scientific laws also impinges on the category of will. That is very strange, but after careful study it is seen to be exactly right. In any case, creating ‘will’ as an independent category of reality solves many problems that the material/spiritual distinction confuses.
The material (which can remain as shorthand) is subsumed in the intersection of the categories of ‘being’ and ‘function’. While the ‘spiritual’ is a form of being at the higher end, where the material exteriorizes as ‘consciousness’. Again, the term ‘spiritual’ is thrown out, but can return as a shorthand.