Class identity as presupposing individual identity

Abstract

IN AN earlier paper, "Property Designation and Description," 1 I stated, almost as if it were obvious, that a definition of class identity presupposes a definition of individual identity. In his review 2 of a group of my papers, Professor Yehoshua Bar-Hillel states, as if it were obvious, that I am mistaken. I wish here to argue the case in detail. The thesis might be put as follows. You may lay down the usual identity conditions for classes: (1) Two classes are identical if and only if every individual which is a member of one class is a member of the other. a = /-df (X) (XEa -x3) But you have not really said anything unless you supplement (1) with a statement of individual identity conditions. The argument. Suppose, for the sake of an example, that the only cubical things are white sugar cubes and that the only white things are sugar cubes. Thus we should have the class of white things identical with the class of cubical things. Now suppose we wish to confirm this fact. We observe a sugar cube. We notice that something is white and we notice that something is cubical. But we have not yet got any confirming evidence for the identity of the two classes. For that, we need to assume that the something we perceive to be white is identical with the something we perceive to be cubical. And we need not make such an assumption. We might have it, on the contrary, that an individual may exemplify just one elementary property, that instances of two elementary properties are necessarily distinct. (Cubicity and whiteness are assumed to be "elementary.") Indeed, Wilfrid Sellars, in his paper "Particulars," 3 seriously advocated precisely this latter view. The possibility of distinguishing the two "somethings," shows, I think, that a separate judgment of identification (of the individuals) is required before we can assure ourselves that we have evidence for the identity of the class of white things and the class of cubical things. More generally, we should want such a judgment of identification based on a general doctrine of individual identity. In this simple case it would presumably be this principle: two individuals are identical if they are at the same place in space. Another example, more complex, but closer to ordinary concerns. Sup-