Hobbes was a nominalist, in that he believed that “there is nothing universal but names” (EL 5.6), so there are neither universal things nor universal ideas. But why did he believe this?
In chapter 5 of the Elements of Law, having introduced names, Hobbes distinguishes between universal and singular names: singular names name one thing, while universal names name more than one thing. As an example of a universal name he gives ‘man’, which is a name given “to every particular of mankind” (EL 5.5), that is, to every individual man.
Having distinguished the two sorts of name, Hobbes goes on to note that the universality of certain names has lead some to think that there are also universal things (EL 5.6). On this view
besides Peter and John, and all the rest of the men that are, have been, or shall be in the world, there is yet somewhat else that we call man, (viz.) man in general, deceiving themselves by taking the universal, or general appellation, for the thing it signifieth (EL 5.6).
So on this view there is some sort of universal thing man, as well as the universal name ‘man’. But this view is, Hobbes thinks, wrong. The name is universal, but the thing signified is not universal, for there are no universal things to signify. (In this text Hobbes appears to talk interchangeably of naming and signifying.)
In support of his view, Hobbes imagines someone asking a painter for a painting of “a man, which is as much as to say, man in general” (EL 5.6). All that is being asked for, Hobbes says, is a painting of some man or other. There is no other thing, man in general, of which one wishes a picture.
It seems, however, that Hobbes’s opponents might handle the example without much difficulty. To ask for a picture of a man, they might say, is indeed just to ask for a picture of some man or other. There is another thing, the universal man, but it’s not what ‘paint me a picture of a man’ is asking for a picture of. You might do that with another request: ‘paint me a picture of the universal man’. But we don’t do that, perhaps just because the universal man is not the sort of thing that can be pictured.
Lurking in the background of Hobbes’s discussion of the example is, perhaps, his basically imagistic view about thought. If we think using images, then there will be no way to think about something of which we can produce no image. So there will be no way to think about, or believe in the existence of, any alleged universal object that cannot be pictured.
An argument for nominalism that draws on Hobbes’s imagism is not explicit in this text. But Hobbes’s thinking along these lines would explain why he thinks that the example of what can be painted should persuade us that there are no universal things, only universal names. A painting that resembles the painted object is not, for Hobbes, just one example of representation. Rather, it is an example that is very much like the most basic sort of mental representation, mental images resembling the things they represent. And perhaps this imagism could also be used to explain Hobbes’s attachment to the view that names and not ideas are universal, something he appears to believe at this point, but not to argue for.