modern techniques of graph-theory (though not very heavy ones) to make sense of matters.

The doctrine of emptiness has always been controversial—even within Buddhism. Many have felt that it gives rise to a vicious regress. In Chapter 12 we see that it does not. In particular, we see why the regress in question, unlike the Bradley regress, is not vicious. Again, modern mathematical techniques are brought in at this point. This time, non-well-founded sets.

Ideas from Buddhist philosophy are also to be found in the other chapters in this part. Chapter 13 deals with the relationship between language (or our concepts) and the world. We will see how the notion of emptiness drives between the horns of idealism and realism. Buddhist philosophy often deals with the ineffable—and indeed, runs into paradox, since it talks about the ineffable. We will see how gluon theory makes sense of this. The final two chapters of this part concern ethics. Central to these is the view that persons, like all things, are empty, and the consequent ramifications of this concerning the virtue of compassion.

Evidently, this part of the book makes use, and I hope fruitful use, of ideas from Buddhist philosophy. That one may do this may be surprising news to many contemporary Western philosophers, whose conception of philosophy is myopically Eurocentric. If the book were to do nothing more than show this to be possible, it would serve a useful function.

P.5 Paraconsistency

So much for the preview. The material depends on ideas for which I have argued in other books. It seems otiose to argue for them again here; but I should at least spell out what I am presupposing. Chief amongst these ideas is dialetheism and the consequent paraconsistency

Dialetheism is a metaphysical view: that some contradictions are true. That is, where ¬ is negation, there are sentences, propositions (or whatever one takes truth-bearers to be), A, such that A and ¬A are both true. Given that A is false iff (if and only if) its negation is true, this is to say that there are some As which are both true and false.

Paraconsistency is a property of a relation of logical consequence. Explosion is the property of such a relation according to which any contradiction implies anything.That is, a relation of logical consequence, ⊢, is explosive iff for all A and B, {AA} ⊢ B. A consequence relation is paraconsistent iff it is not explosive. There is, of course, a connection between dialetheism and paraconsistency. In particular, if one is a dialetheist, one had better hold that the appropriate logical consequence relation is paraconsistent, on pain of accepting everything: triviality.

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