During the 'sixties and 'seventies, Hilary Putnam, Jerry Fodor, and Richard Boyd, among others, developed a type of materialism that eschews reductionist claims.¹ In this view, explana- tions, natural kinds, and properties in psychology do not reduce to counterparts in more basic sciences, such as neurophysiology or physics. Nevertheless, all token psychological entities-- states, processes, and faculties--are wholly constituted of physical entities, ultimately out of entities over which microphysics quantifies. This view quickly became the standard position in philosophy of mind, (...) and reductionism fell out of favor. Recently, however, reductionism has been experiencing a rebirth, and many have suggested that the non-reductive approach was accepted too quickly and too uncritically. In this paper, we attempt to provide a more thorough account of the anti-reductionist position, and, in the process, to defend it against its recent critics. (shrink)