relationships: to its parts at any time, the circumstances of its construction, its registration number, and so on. It is what it is in virtue of those relationships.

But what of things not in the causal flux? Obviously the matter is not exactly the same there. Not exactly the same; but effectively the same.The relations in the nature-constituting nexus need not just be causal. Take, for example, an abstract object, such as the number 3.This is what it is because of its place in (relation to) the natural number sequence, being the successor of 2, the predecessor of 4, and so on. Any object which related to those things in those ways would ipso facto be the number 3.13

We may, in fact, frame a quite general argument for relational quiddity.14 Any object is what it is in virtue of the properties it bears. Thus, for example space has various properties: being infinite in all directions, being inhabited by physical objects, and so on. (Every object has properties: if an object had no properties, it would have the property of having no properties!) Now, to be space just is to be the bearer of those properties. Any entity which bore those properties would be space. In other words, the quiddity of space is constituted by relations that include the instantiation relation. And so for any object.

Quite generally, then, the quiddity of an object is constituted by its locus in a network of relations.15 A natural question at this point is ‘which relations’? Set theoretically, a relation is just a set of ordered pairs. It can be gerrymandered at will. We are not talking about this sort of relation. Just as for properties (see Section 2.6), we may distinguish between sparse relations and abundant ones.The sparse relations are the ones that have metaphysical grunt. We are talking about these. We may take these to include, note, trans-temporal relations, such as my relation to my birth—and maybe death.16

But are all (sparse) relations relevant? Yes. Take me again, for example. All of my relations combine to make me what I am.Of course, some are more important than others. Arguably, the behaviour of my parents towards me in my infant years is more important in making me what I am than, say, the behaviour of my

13 This view is a familiar one from mathematical structuralism. See, for example, Resnik (1997), Shapiro (2000), Hellman (2001). I will return to the matter of mathematical structuralism in 12.6.

14 The argument is one Nāgārjuna himself uses in connection with space, in ch. 5 of the Mūlamadhyamakakārikā. See Garfield (1995), pp. 14–15 and 149–52.

15 What about the object everything? It might be thought that the analysis cannot apply to this, for there is nothing else for it to relate to. But there is. It can relate to each of its parts. Everything could not be what it is unless it had every other object as its part. Perhaps the most important one of these is nothing. Everything is, by definition, the complement of nothing. Each is what it is, in virtue of the other. More of nothing later.

16 These are B-series relations, not A series relations.Thus, my being in Melbourne now is not a sparse relation, though being in Melbourne on 14 January 2013 is. One might note that the fact that aRb is a sparse relation between a and b is no guarantee that the property λx.xRb is a sparse property of a.

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