An Argument against Armstrong’s Analysis of the Resemblance of Universals

David Armstrong believes in universals. Once universals are accepted, it must also be accepted that they resemble one another to various degrees. Colors, for instance, fall into a complicated multidimensional resemblanceorder. Armstrong claims that all universals are complex universals, and that they resemble one another insofar as they have common universal constituents. Armstrong’s reductive account of resemblance in terms of overlap (or “partial identity”) is attractive because it explains the formal features of resemblance as special cases of the formal properties of overlap. However, David Lewis has pointed out that the composition of universals does not obey the mereological principle of uniqueness. I use Lewis’s point to construct a proof that Armstrong’s analysis is mistaken. It is now generally recognized that the Universals theory and the Trope theory are the leading solutions to the Problem of Natural Classes (or as it is traditionally called, the Problem of Universals). A great advantage of the Universals theory over the Trope Theory is that it promises to analyze all resemblance in terms of partial identity whereas the Trope theory must take resemblance as primitive and leave its formal properties unexplained. By showing that the Universals theory cannot deliver on this promise, my argument weakens the case for rejecting the Trope theory in favor of the Universals theory.