Identity and Gluons

2.1 How Gluons Glue

In the previous chapter we saw that there must be something which accounts for a unity composed of parts where one exists—a gluon; and we saw that a gluon may be expected to have contradictory properties. But we have not yet faced the question of how the gluon does its job: how does it bind the parts (including itself) into a whole? Its having contradictory properties does not immediately address this question (though, one might suspect, it is going to play an important role). In this chapter, we look at the answer.The key is breaking the Bradley regress.We will start by seeing how.

This will immediately launch us into a discussion of identity. Identity cannot work in the way that orthodoxy takes it to if gluons are to do their job. In particular, it must be non-transitive. How so? The rest of the chapter explains, and articulates the nature of gluons more precisely in this theoretical context. The ideas are spelled out informally. Full technical details can be found in the technical appendix to the chapter, Section 2.10, which can be skipped without loss of continuity by those with no taste for such things.

2.2 Breaking the Regress

The problem of unity is to explain how it is that gluons glue. What stands in the way of an explanation is the Bradley regress. As we saw in Section 1.4, this is vicious, and so it must be broken. But how?

Suppose that an object has parts a, b, c, and d, and that these are held together by a gluon 中.1 The Bradley regress is generated by the thought that 中 is distinct

1 The character 中 (Chinese: zhong; Japanese: chu) means centre, which seems like a pretty good symbol for a gluon. (By coincidence, it is also sometimes used as part of one of the Chinese names for Madhyamaka Buddhism: zhong dao zong.)As the amount of logic increases, it also seems a good time for Western logicians to move to some less familiar languages in search of symbols. Unfortunately, I will use the character in this section only, due to the current difficulty of typesetting Chinese characters in heavily symbolic contexts.

One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness by Graham Priest page 16