Graham Priest and the Philosophy of the Paraconsistent

Abstract

(ProQuest-CSA LLC: ... denotes non-USASCII text omitted.) The paraconsistent movement is typically concerned with systems of which not everything follows from a contradiction. Systems which everything does follow from a contradiction (referred to the literature as ECQ-ex contradictione quodlibet) are said to be or explosive. As Bueno (2002, 547) points out, a sufficient condition for a system of paraconsistent arithmetic's being trivial is the ability to establish it that 1 = O. While much of the work the area of paraconsistency has dealt with the practical applications of paraconsistent logics-the logics are, for example, very useful for processing information collected in the field, where not all of the data agree with one another-a large amount has dealt with the philosophical implications of paraconsistency. In this regard, it is fair to say that the work of Graham Priest is among the most important. In the present essay, I shall look at some of Priest's ideas, paying particular attention to those essays where he considers the limits of the world of experience. These essays are especially interesting, because they appear to undercut the theoretical viewpoint argued for some of his other writings. To provide a convenient point of reference, I offer the following (necessarily reductive) classification of Priest's work on the paraconsistent: (1) The mainly technical essays, where he is concerned with the minutiae of various paraconsistent systems;1 (2) The philosophical essays, where he is concerned to defend the idea that the world of human experience can embrace the paraconsistent; and (3) The philosophical essays, where he seems, on the contrary, to place the locus of paraconsistency beyond the world of experience. Given that the present essay is primarily concerned with metaphysics, I shall have little to say about work that falls under the first classification, but I shall have a great deal to say about work that falls under the second and the third. After presenting some background information, my procedure will be to summarize a selection of material classification (2), paying particular attention to the criticisms that can be made of it. I shall argue that these criticisms fact imply the necessity for the stance that Priest takes the essays of classification (3). Along the way and conclusion I shall present my own ideas as to the philosophical implications of the paraconsistent. Priest and Paraconsistency the World of Experience In Motivations for Paraconsistency: The Slippery Slope from Classical Logic to Dialetheism, Priest takes an historical perspective with regard to the paraconsistent movement. His main reason for doing this is to try to pinpoint the origins of the idea that all inconsistent systems must be explosive.2 Significantly, his finding is largely negative: he observes that the idea of explosion is to be found neither Aristotelian syllogistic nor Stoic logic. In fact, the earliest appearance of the principle that Priest can find is the work of the twelfth century French logician William of Soissons.3 Priest's emphasis on the comparative modernity of the principle, however, ought not to be interpreted as implying some invocation of the appeal-to-tradition fallacy; for his finding that explosion becomes entrenched only with the adoption of the classical logic promulgated by Boole, Frege, et al. points to a genuine theoretical paucity of evidence favor of the principle. Priest goes on to observe that while the paraconsistent movement had precursors roughly contemporary with Frege's work, it was only after the second world war that the movement achieved momentum. He also distinguishes three strands or levels the movement. The first is a simple dissatisfaction with explosion as a valid principle of inference (Priest 2000, 227); and researchers on this level can be seen largely to be attempting to redress the historical imbalance already mentioned. …