Graham Priest

I take paraconsistent logic to be one of the most important and significant developments in logic and metaphysics in the last 100 years, challenging, as it does, one of the deepest dogmas entrenched in Western philosophy: that consistency is a sine qua non of rational thought. This paper looks back at the modern development of the subject. It is partial, in that it concerns only what one might call the formative years of the subject. It is personal, in that I describe my own involvement in some areas. The first part of the paper concerns paraconsistency as such. It starts with the name itself, its origin and its meaning. After a brief look at the history before the 20th century, it notes the work of the early pioneers: Orlov, Jaśkowski, Halldén, Smiley, Val and Richard Routley, and da Costa. For each of these, it describes both what motivated them, and the techniques they used in their constructions. It then describes the early reception of paraconsistency, and the way that it became a global movement. Next, the paper turns to dialetheism, again starting with the name itself and its meaning. After a brief look at the history of the notion before the 20th century, it describes the origin of the modern subject in the work of Richard Routley/Sylvan and myself. Finally, it turns to one of the major applications of paraconsistency: inconsistent mathematics—and specifically set-theory, arithmetic, and geometry. It notes the work of da Costa, Routley/Sylvan, Meyer, Mortensen, and others, describing some of the results concerning the mathematical theories they investigated.

Many issues in Western philosophy were discussed with great sophistication in the Eastern philosophical traditions. A prime example of this is metaphysical dependence. This is absolutely central to Buddhist metaphysics. Indeed, there is a wide variety of views about the structure of metaphysical dependence. This paper explains some of these views and discusses some of their connections with issues in Western philosophy. Three Buddhist views, in particular, are discussed. The first is the oldest tradition, Abhidharma, which was foundationalist. The second is the Madhyamaka view, which is infinitist. The third is the Chinese Huayan view, which is coherentist. Issues from Western philosophy discussed include mereology, causation, and universals. The paper presupposes no knowledge of the history and philosophy of Buddhism.

Graham Priest presents an original exploration of philosophical questions concerning the one and the many. He covers a wide range of issues in metaphysics--including unity, identity, grounding, mereology, universals, being, intentionality, and nothingness--and deploys the techniques of paraconsistent logic in order to offer a radically new treatment of unity. Priest brings together traditions of Western and Asian thought that are usually kept separate in academic philosophy: he draws on ideas from Plato, Heidegger, and Nagarjuna, among other philosophers.

The Routley-Meyer semantics for relevant logic employ a ternary relation in stating the truth conditions for conditionals. Many critics have objected to the semantics on the ground that this relation is a "merely technical device" and so "philosophically unilluminating". This chapter starts by discussing what it takes for a semantic notion to be more than a merely technical device. It then offers an account of the ternary relation which shows it to be so. Essentially, the idea is that a conditional expresses a function of a certain kind. The ternary relation expresses, in a certain way, the relation between the function, its input, and its output.

As far as disputes in the philosophy of pure mathematics goes, these are usually between classical mathematics, intuitionist mathematics, paraconsistent mathematics, and so on. My own view is that of a mathematical pluralist: all these different kinds of mathematics are equally legitimate. Applied mathematics is a different matter. In this, a piece of pure mathematics is applied in an empirical area, such as physics, biology, or economics. There can then certainly be a disputes about what the correct pure mathematics to apply is. Such disputes may be settled by the standard criteria of scientific theory selection (adequacy of empirical predications, simplicity, etc.) But what, exactly is it to apply a piece of pure mathematics? How is mathematics applied? By and large, philosophers of mathematics have cared more about pure mathematics than applied mathematics, and not a lot of thought has gone into this question. In this paper I will address the issue and some of its implications.

The doctrine of the two truths - a conventional truth and an ultimate truth - is central to Buddhist metaphysics and epistemology. The two truths (or two realities), the distinction between them, and the relation between them is understood variously in different Buddhist schools; it is of special importance to the Madhyamaka school. One theory is articulated with particular force by Nagarjuna (2nd ct CE) who famously claims that the two truths are identical to one another and yet distinct. One of the most influential interpretations of Nagarjuna's difficult doctrine derives from the commentary of Candrakirti (6th ct CE). In view of its special soteriological role, much attention has been devoted to explaining the nature of the ultimate truth; less, however, has been paid to understanding the nature of conventional truth, which is often described as "deceptive," "illusion," or "truth for fools." But because of the close relation between the two truths in Madhyamaka, conventional truth also demands analysis. Moonshadows, the product of years of collaboration by ten cowherds engaged in Philosophy and Buddhist Studies, provides this analysis. The book asks, "what is true about conventional truth?" and "what are the implications of an understanding of conventional truth for our lives?" Moonshadows begins with a philosophical exploration of classical Indian and Tibetan texts articulating Candrakati's view, and uses this textual exploration as a basis for a more systematic philosophical consideration of the issues raised by his account.