Whatever the parts are, though, and whatever form is, the form is something that binds the parts into a whole. But now we have a contradiction. It is, after all, something, an object. (I have just spoken about it.) On the other hand, it cannot be an object. If it were, the collection of parts plus the form constitute a plurality, just as much the original. So the problem of binding would not be solved. In Frege, note, the role of binding is played by concept-senses; it is therefore these which occupy the contradictory role.

Here, then, is our problem of unity. Let me lay it out in abstract terms. Take any thing, object, entity, with parts, p1, . . . , pn. (Suppose that there is a finite number of these; nothing hangs on this.) A thing is not merely a plurality of parts: it is a unity. There must, therefore, be something9 which constitutes them as a single thing, a unity. Let us call it, neutrally (and with a nod in the direction of particle physics), the gluon of the object, g.10 Now what of this gluon? Ask whether it itself is a thing, object, entity? It both is and is not. It is, since we have just talked about it, referred to it, thought about it. But it is not, since, if it is, p1, . . . , pn, g, would appear to form a congeries, a plurality, just as much as the original one. If its behaviour is to provide an explanation of unity, it cannot simply be an object.

As is clear, the problem is posed by the contrast between an object, which has a unity, and a congeries, which is a plurality. It might be thought that when we refer to a plurality, we are referring to some one thing, in which case the supposed distinction disappears. But ‘is a congeries’ is not a predicate that applies to a single object. It is a predicate of a plurality, the parts of the object. I will return to the topic of plural reference in Section 6.10.11

1.4 The Bradley Regress

It will pay to become clearer about why a gluon cannot be an object. A vicious regress stands behind this.12

9 Or some things; but it will turn out that there is only one.

10 The name was coined, with essentially this meaning, in the Conclusion to Priest (1995a).

11 Relatedly, one might be tempted to ask what it is in virtue of which a bunch of objects is a plurality. Are there anti-gluons? But such a question would make little sense. A gluon is whatever it is that answers the question about how parts cooperate to form a whole. If one asks how it is that objects cooperate to form a plurality, the answer is that they do not. No cooperation of any kind is necessary to be a disparate and disconnected bunch of things.

12 This kind of regress argument is very old. In the form of the “third man argument” it is used in Plato’s Parmenides as an argument against the theory of forms. Plato is there concerned with what makes all, for example, red things one (namely, red). Invoking a formof redness produces the regress. Being one by being red is not the same thing as being one by being parts of something, and Plato’s form is not (obviously) a gluon. However, structurally, the situations are similar.We will come to the third man argument itself in Chapter 8.

One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness by Graham Priest