Properties multiply instantiated

These considerations are sufficient to show that multiply instantiated properties are as bad from the point of view of economical reduction as multiply realized properties. And this brings us to the issue of microbased properties. Kim borrows and endorses Armstrongs notion of a structural property to characterize the microbasis relation ... 

This is actually not quite right. Because M is multiply realizable, M could have occurred even if P had not occurred in the case where some physical property other than P instantiated M. So M could have had a different supervenience base other than P, say P2. The point is that M needs some sort of physical supervenience base to instantiate it and cannot occur independently of its supervenience base. Whatever supervenience base does instantiate M, it will be related to M by supervenience, and it and M will not be independent of one another. 

The lower-level-higher-level distinction is really just about multiple realizability. To say a property is a higher-level property just means that it is multiply realizable with respect to its lower-level instantiation. So, for instance, macroproperties like size can be higher-level properties, since size is multiply realizable. We could, for instance, have five balls that are the exact same size, but each ball could have an entirely different microstructure (e.g., one is made of plastic, one of metal, one of wood, etc.). 

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