Abstract
Abstract It is often said that although some mental properties are irreducibly non-material, not open to any behavioural or functionalist analysis, still every mental property is or even has to be owned by a material substance, by a brain or body. And from this the conclusion is drawn that a certain vestigial materialism can be preserved, property irreducibility notwithstanding. If a material (or mental) substance is just a particular which instantiates a material (or mental) property, then the thesis that every mental property is or must be owned by a material substance can be joined without inconsistency to the parallel thesis that every material property is or must be owned by a mental substance.
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