For example, are there non-physical objects that are quite acceptable to contemporary physicists? Jeffrey Poland thinks that there are. He writes:
“It should be understood that the primacy of physics in ontological matters does not mean that everything is an element of a strictly physical ontology… physicalism… allows for non-physical objects, properties, and relations… physicalism should not be equated with the identity theory in any of its forms… I prefer the idea of a hierarchically structured system of objects grounded in a physical basis by a relation of realization…” 
If you threw out “higher-level” mental states or properties solely on the grounds that they depend in a mysterious way on lower-level material phenomena, you would have to toss out all the special sciences as well.