i2 is itself a universal, so a, F, i1, and i2 must be linked by yet another instantiation relation i3, and this regress continues without end

There are other, more specific arguments against universals. One is that postulating such things leads to a vicious infinite regress. For suppose there are universals, both monadic and relational, and that when an entity instantiates a universal, or a group of entities instantiate a relational universal, they are linked by an instantiation relation. Suppose now that a instantiates the universal F. Since there are many things that instantiate many universals, it is plausible to suppose that insta