Conceptualists hold that universals are in the first instance ideas or concepts in the mind. Unlike realists, they hold that universals have no reality or existence independent of the mind. We have an idea or concept of redness and any object which resembles our idea, or satisfies our concept of redness, has the universal redness. One problem here is that it is seemingly arbitrary which ideas or concepts minds form in the first place. We group together certain objects as red because they resemble our idea or satisfy our concept of redness, but the concept we form is not constrained by any universals existing independently of particulars or by any resemblances between particulars.
Nominalists claim that objects which possess the same universal do resemble each other.
Universals do not exist independently of their instances. But it is not simply arbitrary that we group certain things together as being red. Rather, we group certain things together as being red because they resemble each other in respect of their colour. Jack, Andrew, Dr. AJ Bloomsbury Guide to Human Thought 2. Metaphysics Bloomsbury Guide to Human Thought 3.