The Golden Lion

This chapter turns to Huayan Buddhism, and the thought of Fazang. Huayan has a distinctive view of the nature of the interpenetration between conventional and ultimate reality. The notion of interpenetration draws on both Indian and Daoist thought. The chapter shows how to make precise sense of the notion of interpenetration with some simple graph-theoretic techniques.

And So On

The Sanlun thinker Jizang constructed a hierarchy of ultimate and conventional truths by alternately applying the third and fourth corners of the cateṣkoṭi. This chapter discusses the significance of the hierarchy and shows how to make precise formal sense of it.

Paradox and Ineffability

In Chapter 5 it transpired that certain states of affairs are ineffable; but, of course, much is said about them. This chapter shows how such a paradox can be handled with a plurivalent version of the five-valued cateṣkoṭi, in which states of affairs can have more than one value. That some Buddhist texts appear to endorse the thought that something can be effable and ineffable is then shown by a consideration of the Vimalakīrti Sūtra. An appendix to the chapter shows how Jain logic may also be seen as a plurivalent logic

Emptiness

This chapter looks at the rise of Mahāyāna Buddhism in the Prajñāpāramitā Sūtras, and the consequent attack on the Abhidharma picture launched by Nāgārjuna. In particular Nāgārjuna argues that all things are empty (śūnya) of svabhāva. The catuṣkoṭi is deployed in his arguments, but in the process a fifth possibility appears to emerge: ineffability

A Methodological Coda

The book has an unusual methodology, applying techniques of contemporary formal logic to ideas drawn from ancient and medieval Buddhist philosophical texts. This chapter comments on some reservations one might have about this methodology: that it ignores relevant religious, and especially experiential, aspects of Buddhism; that it is objectionably anachronistic; that it is Orientalist. The objections are found to be without substance.

The Fifth Corner

This chapter shows how this possibility (ineffability) can be incorporated into the logical machinery by adding a fifth value. In the process, the bearers of semantic values are reinterpreted as states of affairs, which are themselves empty. This is deployed to produce a correspondence theory of conventional truth.

Well-Founded Metaphysics

This chapter explains the metaphysical picture that emerges in the Abhidharma thought of the first five hundred years of Buddhism. This endorses an ultimate reality composed of dharmas, partless objects with svabhāva (self-nature), and a conventional reality composed of objects conceptually constructed out of these.

Quintum Non-Datur

This chapter looks at the appearance of the catuṣkoṭi in early sūtras. It then looks at the failure of attempts to accommodate it in `standard' logic. Next it shows how it can be accommodated in the logic of First Degree Entailment. Finally it looks at some early Buddhist hints that there might be more to matters than the simple catuṣkoṭi and how these matters cannot be accommodated by appealing to presupposition-failure.

General Background

This chapter explains the background of Buddhist philosophy needed to understand the rest of the book: its historical and geographical development in India and China, the foundational principles of the Four Noble Truths, and the notions of impermanence and no self.

Enlightenment

This chapter turns to Chan (Zen) Buddhism, and in particular its notion of enlightenment. The progress to enlightenment can be modelled by a sequence of plurivalent structures. In the light of this, the chapter then discusses a number of aspects of the thought of Dōgen. The chapter concludes by discussing the notion of non-duality, a theme that assumes increasing significance in the preceding chapters.