 (It might seem odd to say that Russellian propositions are abstract objects. Consider, e.g., the Russellian proposition that Mars is red. This is an odd sort of hybrid object. It has two components, namely, Mars (the planet itself) and the property of redness. One of these components (namely, Mars) is a concrete object (where a concrete object is just a spatiotemporal object). Thus, even if redness is an abstract object, it does not seem that the Russellian proposition is completely non-spatiotemporal. Nonetheless, philosophers typically lump these objects together with abstract objects. And it's not just Russellian propositions; similar remarks can be made about various other kinds of objects. Think, for instance, of impure sets--e.g., the set containing Mars and Jupiter. This seems to be a hybrid object of some kind as well, because while it has concrete objects as members, it's still a set, and on the standard view, sets are abstract objects. If we wanted to be really precise, it would probably be best to have another term for such objects--e.g., ‘hybrid object’, or ‘impure abstract object’--but, again, this isn't how philosophers typically talk; they usually just treat these things as abstract objects. None of this will matter very much in what follows, however, because this essay is almost entirely concerned with what might be called pure abstract objects--i.e., abstract objects that are completely non-spatiotemporal.) 