Graham Priest

The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial.

Martial arts and philosophy have always gone hand in hand, as well as fist in throat. Philosophical argument is closely paralleled with hand-to-hand combat. And all of today’s Asian martial arts were developed to embody and apply philosophical ideas. In his interview with Bodidharma, Graham Priest brings out aspects of Buddhist philosophy behind Shaolin Kung-Fu — how fighting monks are seeking Buddhahood, not brawls. But as Scott Farrell’s chapter reveals, Eastern martial arts have no monopoly on philosophical traditions: Western chivalry is an education in and living revival of Aristotelian ethical theories. Several chapters look at ethical problems raised by the fighting arts. How can the sweaty and brutal be exquisitely beautiful? Every chapter is easily understandable by readers new to martial arts or new to philosophy.

A motivation behind one kind of logical pluralism is the thought that there are different kinds of objects, and that reasoning about situations involving these different kinds requires different kinds of logics. Given this picture, a natural question arises: what kind of logical apparatus is appropriate for situations which concern more than one kind of objects, such as may arise, for example, when considering the interactions between the different kinds? The paper articulates an answer to this question, deploying the methodology of Chunk and Permeate, developed in a different context by Brown and Priest (J Philos Log 33:379–388, 2004).

ConclusionIf, to return to the image with which I started this paper we consider the path of papers written on the logical paradoxes, then there is much to be learnt from the more recent additions, those by Chihara, Dowden and Woodruff included. However, the case for the paraconsistent approach to the paradoxes has not been weakened. In fact, it seems to me to have been strengthened. If we consider the path of papers, not as a signle line, but branching according to the approach to the paradoxes advocated, then the “Logic of Paradox” would, I still submit, be on the right track.

Validity : what follows from what? -- Truth functions,or not -- Names and quantifiers : is nothing something? -- Descriptions and existence : did the greeks worship Zeus? -- Self-reference : what is this chapter about? -- Necessity and possibility : what will be must be? -- Conditionals: what's in an if? -- The future and the past : is time real?? -- Identity and change : is anything ever the same? -- Vaguenes : how do you stop sliding down a slippery slope? -- Probability : the strange case of the missing reference class? -- Inverse probability : you can't be indifferent about it! -- Decision theory : great expectations? -- A little history and some further reading?

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.

In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues—especially so called "higher order" vagueness

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal, of the rationals, or of any other order type that can be embedded in the rationals in a certain way.

In recent years, many people writing on set theory have invoked the notion of an indefinitely extensible concept. The notion, it is usually claimed, plays an important role in solving the paradoxes of absolute infinity. It is not clear, however, how the notion should be formulated in a coherent way, since it appears to run into a number of problems concerning, for example, unrestricted quantification. In fact, the notion makes perfectly good sense if one endorses a dialetheic solution to the paradoxes. It then morphs from a supposed solution to the paradoxes into a diagnosis of their structure. In this paper I show how