Multiple realizability
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Multiple realizability, in the philosophy of mind, is the thesis that the same mental property, state, or event can be implemented by different physical properties, states or events. The idea is widely believed to have its roots in the late 1960s and early 1970s when a number of philosophers, most prominently Hilary Putnam and Jerry Fodor, put it forth as an argument against reductionist accounts of the relation between mental and physical kinds.
Kim's argument
Jaegwon Kim has recently argued against non-reductive physicalism on the grounds that it violates the causal closure of the physical. Roughly, the idea is that physics provides a full explanation of physical events. If mental properties are causally efficacious, they must either be identical to physical properties, or there must be widespread overdetermination. The latter is often held to be either unlikely or even impossible on conceptual grounds. If this is right, then the options seem to be either reduction or elimination.