The paper is a discussion of a result of Hilbert and Bernays in their Grundlagen der Mathemnatik. Their interpretation of the result is similar to the standard intepretation of Tarski's Theorem. This and other interpretations are discussed and shown to be inadequate. Instead, it is argued, the result refutes certain versions of Meinongianism. In addition, it poses new problems for classical logic that are solved by dialetheism.

Anyone who is accustomed to the view that contradictions cannot be true, and cannot be accepted, and who reads texts in the Buddhists traditions will be struck by the fact that they frequently contain contradictions. Just consider, for example.

The Hooded Man Paradox of Eubulides concerns the apparent failure of the substitutivity of identicals in epistemic (and other intentional) contexts. This paper formulates a number of different versions of the paradox and shows how these may be solved using semantics for quantified epistemic logic. In particular, two semantics are given which invalidate substitution, even when rigid designators are involved.

In both occidental and oriental traditions, philosophers have long treated the martial arts as pursuits worthy of philosophical reflection. This is the first substantial academic book to lay out the philosophical terrain within the study and understanding of the martial arts and to explore the significance of this fascinating subject for contemporary philosophy. The book is divided into three sections. The first section concerns what philosophical reflection can teach us about the martial arts, and especially the nature and value of (...) its practice. The second section deals with the other direction of the dialectical interplay between philosophy and the martial arts: how the martial arts can inform philosophical issues important in their own right. Finally, because many of the notable martial arts are of Asian origin, there are particularly close links between the arts and Asian philosophies - and Buddhism in particular - and therefore the last section is devoted to this topic. The essays in this collection deal with a wide range of philosophical issues: normative ethics, meta-ethics, aesthetics, phenomenology, the philosophy of mind, Ancient Greek and Buddhist thought. By demonstrating the very real nature of the engagement between the martial arts and philosophy, this book is essential reading for any serious student or scholar with an interest in the martial arts, Eastern philosophy, the philosophy of sport, or the study of physical culture. (shrink)

Dialetheists believe some sentences are both true and false. Objectors have argued that this makes it unclear how people can disagree with each other because, given the dialetheist’s commitments, if I make a claim and you tell me my claim is false, we might both be correct. Graham Priest (2006a) thinks that people disagree by rejecting or denying what is said rather than ascribing falsehood to it. We build on the work of Julien Murzi and Massimiliano Carrara (2015) and (...) show that Priest’s approach cannot succeed: given the same dialetheist’s commitments you may be correct to reject a claim that I correctly believe. We argue further that any attempt to solve the problem by identifying a new attitude of disagreement will also fail. The culprit, we claim, is the attempt to find a pair of attitudes that satisfy ‘exclusivity’—that is, attitudes such that both cannot be simultaneously correct. Instead of identifying disagreement by the kinds of attitudes involved, we propose dialetheists focus on the normative landscape and identify it in part by whether parties have reasons to change their attitudes. We offer our own normative theory of disagreement to help dialetheists with this challenge. (shrink)

Graham Priest, ampiamente considerato una figura di tutto rilievo nel panorama filosofico contemporaneo, è conosciuto prevalentemente per i suoi contributi nel campo delle logiche non-classiche, e per essere uno dei fondatori della controversa tesi filosofica denominata dialeteismo. Non sorprende che, come per molti degli autori che vengono comunemente inseriti nella tradizione analitica, due delle aree in cui il suo pensiero è stato più fecondo siano la logica e la metafisica. Ciò che sorprende, invece, è la sua capacità di usare (...) le teorie formali e le tesi metafisiche da lui stesso concepite come via di accesso per terreni filosofici normalmente considerati distanti da quello anglosassone. In particolare, sono numerose le occasioni in cui l’attenzione di Priest si è rivolta ad Oriente, e più nello specifico al Buddismo. The Fifth Corner of Four, il suo ultimo libro, può essere considerato a buon diritto la manifestazione più evidente di questo grande e perdurante interesse. (shrink)

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do (...) not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes. (shrink)

Graham Priest's book In Contradiction is a bold defense of the existence of true contradictions. Although Priest's case is impressive, and many of his arguments are correct, his approach is not the only one allowing for true contradictions. As against Priest's, there is at least one contradictorialist approach which establishes a link between true contradictions and degrees of truth. All in all, such an alternative is more conservative, closer to mainstream analytical philosophy. The two approaches differ as regards the (...) floodgate problem. Priest espouses a confinement policy banning contradictions except in a few special domains, particularly those of pure semantics and set-theory , whereas the alternative approach admits two negations -- natural or weak negation and strong negation, the latter being classical; accordingly, the alternative approach prohibits any contradiction involving strong negation, thus providing a syntactic test of what contradictions have to be rejected. (shrink)

In his article ‘The Structure of Emptiness’, 467–80. doi: 10.1353/pew.0.0069[Crossref], [Web of Science ®] [Google Scholar]) Graham Priest examines the concept of emptiness in the Mādhyamaka school of Nāgārjuna and his commentators Candrakīırti and Tsongkhapa from a mathematical point of view. The approach attempted in this article does not involve any commitment to Priest's more controversial dialethic Mādhyamaka interpretation. The purpose of the present paper is to explain Priest's sketchy but very insightful interpretation of objects as non-well-founded sets in (...) greater detail. Some problems concerning his idea to model the Mādhyamaka claim of the emptiness of emptiness by means of this kind of framework will be noted. Moreover, we will also discuss the possibility to represent the Mādhyamika's denial of the existence of irreducible constituents of empirical reality within a well-founded system of set theory. Finally, some slight mistakes in Priest's mathematical construction need to be pointed out. (shrink)

Graham Priest's new book is about things being about things—about what it is for things which are about things, such as beliefs, hopes and fears, and the like, and sentences which express them, to be about the things they are about, and about the range of things about which things which are about are about—in a word, intentionality. It has two principal objectives—to develop a formal semantics for intentionality, and to promote and defend a philosophical thesis about what exists (...) and what does not. The semantics proposed is an extension of the familiar ‘world’1 semantics for modal logic. The philosophical thesis asserts that while some things exist, not everything does, or equivalently that while some things exist, some others do not. Priest, following Richard Routley , calls this Noneism to mark the divergence from Meinong's view, with which, nevertheless, it has a good deal in common. Meinong likewise denies that everything exists, and asserts that some things exist and some do not, but further holds that some things which, according to him, do not exist do have another ‘form of being’—they ‘subsist’ rather than exist—while other things which, according to him, do not exist do not exist simpliciter . Noneism avoids this complication, at least, and—or so Priest claims—avoids proliferating kinds of being altogether, requiring only a single kind of being and a distinction between two kinds of quantifier. In the noneist view, the basic universal and particular quantifiers are to be understood in an ontologically unloaded way, as ranging over a single all-inclusive domain of objects, some of which exist and some of which do not. The usual—existentially loaded—quantifiers are construed as a type of restricted quantifier, definable using an existence predicate: ‘GraphicxAx’ as ‘For some x, …. (shrink)

In Towards Non-Being Graham Priest proposes an informative criterion of identity across possible worlds. Roughly, the criterion says that whenever two objects satisfy the very same qualitative characteristics in every possible world they are identical. But Priest also maintains that there are qualitatively indiscernible possible worlds. It is argued in the paper that for this reason he should allow the existence of two numerically different but qualitatively identical objects, and that is in tension with the criterion of transworld identity (...) he has proposed. Thus Priest should reject either his criterion of transworld identity, or the thesis of possibleexistence of qualitatively indiscernible worlds. (shrink)

Graham Priest, One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness, Oxford University Press, 2014, 272 pp., ISBN 9780199688258.

The works by Graham Priest that I'm most familiar with are those of the 1980’s. I understand they belong to the logical part of his writing, as presented by the organizers of the “Towards Graham Priest” meeting at Szczecin University on 20 June, 2012. Myself, I read Priest’s works to be imprecise, to say the least. Thelack of precision is to be traced particularly in his interpretations of Alfred Tarski’s heritage. This applies to Tarski’s main points, namely: semantically (...) closedlanguages, the T-scheme, and the appreciation of natural language. The strange thing about it is that Priest does not mind other people expressing views opposite to his own, but admits he cannot determine which contradictions are true and gives only vague indications about how to judge the criticisms. (shrink)

Part of a book symposium on Graham Priest's Towards Non-Being.

The present article critically examines three aspects of Graham Priest's dialetheic analysis of very important kinds of limitations (the limit of what can be expressed, described, conceived, known, or the limit of some operation or other). First, it is shown that Priest's considerations focusing on Hegel's account of the infinite cannot be sustained, mainly because Priest seems to rely on a too restrictive notion of object. Second, we discuss Priest's treatment of the paradoxes in Cantorian set-theory. It is shown (...) that Priest does not address the issue in full generality; rather, he relies on a reading of Cantor which implicitly attributes a very strong principle concerning quantification over arbitrary domains to Cantor. Third, the main piece of Priest's work, the so-called “inclosure schema”, is investigated. This schema is supposed to formalize the core of many well-known paradoxes. We claim, however, that formally the schema is not sound. (shrink)

The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices whose underlying algebras are power algebras, where the power algebra of a given algebra has as elements textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis (...) of those of the given matrix. The present discussion stresses the continuity of Priest's work on the question of which matrices determine consequence relations which remain unaffected on passage to the consequence relation determined by the power matrix of the given matrix with the corresponding question in equational logic as to which identities holding in an algebra continue to hold in its power algebra. Both questions are sensitive to a decision as to whether or not to include the empty set as an element of the power algebra, and our main focus will be on the contrast, when it is included, between the power matrix semantics and the four-valued Dunn--Belnap semantics for first-degree entailment a la Anderson and Belnap) in terms of sets of classical values, in which the empty set figures in a somewhat different way, as Priest had remarked his 1984 study, `Hyper-contradictions', in which what we are calling the power matrix construction first appeared. (shrink)

Per il dialeteismo ci sono contraddizioni vere. Questa concezione filosofica ha assunto una forma chiara e definita a partire dal lavoro del filosofo e logico Graham Priest – uno dei suoi padri fondatori, nonché uno dei suoi più strenui difensori. Questo libro intende portare il dialeteismo all’attenzione di un ampio pubblico, che non sia solo quello degli addetti ai lavori. Il volume è suddiviso in due parti. La prima include le cinque lezioni su "Dialeteismo e storia della filosofia" tenute (...) da Priest e Filippo Casati a Padova nel 2016, in occasione del Corso di Eccellenza per il dottorato in filosofia dell’Università di Padova. La seconda contiene quattro contributi sul dialeteismo di autori italiani. (shrink)

In this study, I reconstruct and compare Alain Badiou’sBeing and Event(2005) and Graham Priest’sOne(2014), arguing that the ontologies pursued within the two texts are intriguingly analogous in a number of ways. Both Badiou and Priest are committed to thinking through classically ontological problems without denying the validity of the paradoxes they raise; both regard Plato’sParmenidesas an early and formative account of these paradoxes; both establish conclusions to the effect that unity – or “oneness” – is indeed a contradictory phenomenon; (...) and both, as a corollary of this conclusion, develop frameworks which confer ontological prominence uponthe voidandemptinessrespectively, thereby arriving at what appears to be a shared ontological nihilism. In this comparative study, I not only enquire whether the frameworks adopted by Badiou and Priest really do lead to nihilist conclusions, but also attempt to clearly outline their trajectories of thought for the benefit of those who might be tempted to dismiss their seemingly outlandish theses out of hand. (shrink)

Graham Priest has asked whether the consequence relation associated with the Anderson–Belnap system of Tautological Entailment,1 in the language with connectives ¬, ∧, ∨, and countably many propositional variables as tomic formulas, maximal amongst the substitution-invariant relevant consequence relations on this language. Here a consequence relation is said to be relevant just in case whenever for a set of formulas Γ and formula B, we have Γ B only if some propositional variable occurring in B occurs in at least (...) one formula in Γ. (It follows that relevant consequence relations are atheorematic in the sense that whenever Γ B for some such consequence relation , Γ = ∅.) Here I write up in more detail the upshot of the conversation – returning an affirmative answer to Priest’s question – about this in the common room that Greg Restall and I were participating in last Friday [ = October 6, 2006], dotting some “i”s and crossing some “t”s (and adding the odd further reflection). (shrink)

PriestGraham. Towards Non-Being: The Logic and Metaphysics of Intentionality. Oxford University Press, 2016. 2nd ed. ISBN 978-0-19-878359-6 ; 978-0-19-878360-2. Pp. xxxvi + 368.