IDENTITY AND GLUONS 17
from each of the other parts. If this is the case, then there is room, as it were, for something to be inserted between 中 and a, and so on. Or to use another metaphor, there is a metaphysical space between 中 and a, and one requires something in the space to make the join. Thus, the regress will be broken if 中 is identical to a. There will then be no space, or need, for anything to be inserted.
Of course, 中 must be identical with b, c, d, for exactly the same reason.Thus, 中 is able to combine the parts into a unity by being identical with each one (including itself). The situation may be depicted thus:
The explanation of how it is that the gluon manages to unite the disparate bunch is, then, that it is identical with each of them. Consider, if it helps, an analogy. Suppose that one wants to join two physical bricks together with physical glue. The glue is inserted between the bricks. It bonds to each one, and so joins them. It does not make the two bricks one, but the molecules of the glue and each brick become physically indissoluble. In the metaphysical case, the parts of an object do not become identical either, but the gluon bonds with each part in the most intimate way, by being identical with it.
It should be immediately obvious that the relation of identity invoked here will not behave in the way that identity is often supposed to behave. In particular, the transitivity of identity will fail. We have a = 中 and 中 = c, but we will not have a = c. Two bricks of a house are not identical. It might be doubted that there is any such coherent notion, or that, if there is, it is really one of identity. These concerns cannot be set aside lightly, and the only way to assuage them is to provide a precise theory of identity which delivers what is required. Let us turn to this.
2 Of course, the parts of an object can themselves have parts.Thus, it could be the case that, for example, c has parts m and n. These will be joined by a gluon, 中’. So we will have m = 中’ = n. If one takes the parthood relation to be transitive, m, 中’, and n, are also parts of the original object. So we will have 中 = m, 中 = 中’, and so on.