Abstract

The sparseness thesis has notably gained momentum among contemporary realists about universals: indeed, most of them hold that some but not all predicates true of particulars are ontologically rooted in correlative universal properties, viz. some but not all predicates are property-predicates. Armstrong is one the main advocates of this position as he put forward a cluster of arguments to the conclusion that in mapping predicates onto universals we find gaps and discontinuity. One of the main Armstrongian arguments of this kind pivots on the crucial application of the apparently highly intuitive genuine identity test for universals. In this paper I will examine Armstrong’s argument from genuine identity against disjunctive properties and evaluate its strength.