  There have been other proposals as to how to characterise abstract objects. One approach defines abstract objects as those the understanding of whose names involves a recognition that the named object is in the range of a certain functional expression (Dummett 1973, 485). It has also been thought that an abstract object is one that either couldn't possibly exist or couldn't possibly be concrete, depending on whether you interpret the predicate ‘E!’ (used to formally represent the definition of ‘abstract’) as an existence predicate or a concreteness predicate (Zalta 1983, 60, 50-52). On another conception of abstract objects these are objects that cannot exist separately from other entities (Lowe 1995,   514).[3]   (For a discussion of the various ways of characterising the abstract/concrete distinction see Burgess and Rosen 1997, 13–25.)