172 BUDDHIST THEMES

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*.