To be, in the relevant sense, is to be one. Any world where an object is one (that is, any world) it is, and vice versa.

One might object. It would seem that we have plural forms of reference.Thus, we can say, for example, that Russell and Whitehead wrote Principia Mathematica, and that they were in Cambridge together at the time. The conjunctive noun phrase and pronoun appear to refer to objects that are inherently plural. Similarly, one can say that something is a square; but one also can say that some things have the same shape as each other. The italicized quantifier is plural, and refers to a plurality.8 There are, then, objects that are, but are not one, being a plurality. Russell and Whitehead, for example, is (an object), but it is not one object.

The reply is simple, however.The machinery does not allow us to refer to objects which are plural, but to a plurality of objects.Thus, when we say that Russell and Whitehead wrote Principia, we are not referring to some strange object, Russell and Whitehead; we are referring to Russell and to Whitehead. (One cannot say: ‘Russell and Whitehead wrote Principia, and it was in Cambridge at the time.) Similarly if we use plural pronouns and quantification we are referring to multiple objects. If something is, it is one, a unity; and if some things are, they are ones, unities. The machinery of plural reference does indeed enable one to refer to a plurality of objects, but each is one. So to be is still to be one.9

Let us now put all these thoughts together. The being of something is that in virtue of which it is. To be is to be one. So the being of something is that in virtue of which it is one. And what is it in virtue of which something is one? By definition, its gluon, g. The being of something is therefore its gluon. We have answered Heidegger’s question as to the nature of being.

It is worth being clear about the exact form of this argument, lest one take it to be an application of SI. We have established that the conditions ‘x is one thing’ and ‘x is’ are coextensive (at every world). Hence, the inference: ‘g makes it the case that x is one thing; hence g makes it the case that x is’ is an application of the substitutivity of such equivalents.

4.4 Heidegger’s Aporia

Let us look more closely at Heidegger.10

Heidegger asked, famously, what constitutes a thing’s being: what is it for it to be? He says (p. 4f):

8 See, for example, Yi (2005).

9 I will return to the topic of plural reference in Chapter 6.

10 For a more detailed discussion of some of these matters, see Priest (2001).

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