Standard modal logic for alethic modalities analyses modalities as ranging over all possible worlds. This leaves very little room in the space of worlds to entertain impossible things. My proposal is to liberate the Leibnizian universe and reinforce the relative aspect of possibility; worlds are possible with respect to some worlds, and impossible for others. The central idea is to isolate relative possibility from conditionality. To accommodate counterpossibles, I provide a dialetheic conditional modal logic, a theory that is dialetheic at (...) every level, in the logic as well as in the set theory behind it. (shrink)

There is an eminent tradition of thought that sees in the phenomenon of time something contradictory. This tradition has been recently revived by some contemporary proponents of dialethism – the view that there are true contradictions. In this paper, I will contribute to this line of thinking by tracing the first steps of a dialethic account of time-consciousness. In particular, I will argue that the experiential flow of time can be accounted for in the framework of an intentionalist approach (...) to temporal perception if we conceive of time-consciousness as a quasi-multiplicity, i.e., a multiplicity of non-self-identical parts, hence the embrace of dialethism. Section 1 introduces dialethism, discusses Priest's dialethic theory of motion and time, and motivates the project of a dialethic account of time-consciousness. Section 2 introduces the intentionalist approach to time-consciousness and distinguishes pure intentionalism from sense-data intentionalism; both subscribes to a certain Principle of Simultaneous Awareness but interprets it differently. In Sect. 3, I offer an in-depth analysis of this principle and identify its core as the requirement of self-unification, i.e., the requirement that time-consciousness unifies itself in flowing without any higher-order act of unification. Section 4 then argues that pure intentionalism can satisfy this requirement by embracing dialethism. I conclude by noting how the dialethic account of time-consciousness incorporates a central extensionalist insight within an intentionalist outlook. (shrink)

The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not “fall foul” of Curry’s Paradox by invalidating an inference rule called “Absorption” (or “Contraction”) and the classical logical theorem called “Assertion”. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priest’s counterexamples to Absorption and Assertion use (...) in the metalanguage a dialetheically unacceptable principle. Furthermore, we show that the rejection of Assertion undermines Priest’s claim that the entailment connective expresses the notion of logical consequence. (shrink)

This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) we propose our \ logic. Finally, we show how \ supports the dialetheic solution of the liar paradox. (shrink)

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. (shrink)

Aim of the paper is to analyze Priest’s dialetheic solution to Curry’s paradox. It has been shown that a solution refuting ABS, accepting MPP and consequently refuting CP meets some difficulties. Here I just concentrate on one difficulty: one obtains the validity of MPP just using FA in the metalanguage, an invalid rule for a dialetheist.

According to one prominent strand of mainstream logic and metaphysics, identity is indistinguishability. Priest has recently argued that this permits counterexamples to the transitivity and substitutivity of identity within dialetheic metaphysics, even in paradigmatically extensional contexts. This paper investigates two alternative regimentations of indistinguishability. Although classically equivalent to the standard regimentation on which Priest focuses, these alternatives are strictly stronger than it in dialetheic settings. Both regimentations are transitive, and one satisfies substitutivity. It is argued that both regimentations provide better (...) candidates to occupy the core theoretical role of numerical identity than does the standard regimentation. (shrink)

Minimalists, following Horwich, claim that all that can be said about truth is comprised by all and only the nonparadoxical instances of (E) p is true iff p. It is, accordingly, standard in the literature on truth and paradox to ask how the minimalist will restrict (E) so as to rule out paradox-inducing sentences (alternatively: propositions). In this paper, we consider a prior question: On what grounds does the minimalist restrict (E) so as to rule out paradox-inducing sentences and, thereby, (...) avoid contradictions? We argue that there is no good reason for thinking that the minimalist can furnish such grounds. Accordingly, while we are tempted to conclude from this that the minimalist should acknowledge the contradictoriness of truth, instead, we end with a challenge: Provide grounds, compatible with minimalism, for banning the paradoxical instances of (E), or embrace dialetheism. (shrink)

This paper intends to offer a new assessment of the “Ontological Difference”, one of Martin Heidegger’s mainstays, in the light of the metaphysical view called “dialetheism”. In the first paragraph I briefly summarize the main argument of Heidegger’s contradiction of Being, where OD is present as a premise. In the second paragraph I introduce dialetheism, indicate two kinds of dialetheic solutions to the paradox and explain why they face comeback troubles from OD. The third paragraph is devoted to a review (...) of Heidegger’s uses of OD and underlines the crucial role of negation in it. In the fourth paragraph I investigate the philosopher’s account of negation and show similarities with the account provided by the paraconsistent logic called “Logic of Paradox”. The fifth paragraph puts forward two possible readings of OD, the first based on the classical notion of negation and the second on the notion of negation pointed out in the previous paragraph. The second reading is proved suitable for dialetheists and in accordance with the exegesis of some textual passages from Heidegger’s late works. (shrink)

ABSTRACTIt is well known that, from the beginning to the end of his philosophical trajectory, Martin Heidegger tries to develop a fundamental ontology which aims at answering the so-called question...

David Lewis famously dismisses genuine impossible worlds on the basis that a contradiction bound within the scope of his modifier ‘at w’ amounts to a contradiction tout court—an unacceptable consequence. Motivated by the rising demand for impossible worlds in philosophical theorising, this paper examines whether anything coherent can be said about an extension of Lewis’ theory of genuine, concrete possible worlds into genuine, concrete impossible worlds. Lewis’ reasoning reveals two ways to carve out conceptual space for the genuinely impossible. The (...) first is to abandon Lewis’ classical translation schema for negation, on the basis that it begs the question against incomplete and inconsistent worlds. I argue that, whilst this option incurs some loss in the semantics, it preserves the core spirit of Lewis’ metaphysics. The alternative is to bite the bullet, abandon classical logic and embrace true contradictions. The key challenge with this strategy is that the resulting theory seems committed to a particularly strong kind of dialethism—one that even dialethists would be reluctant to accept. I motivate such a dialethic account of genuine impossibilia using Lewis’ own methodology and defend it against triviality objections. I close with a few comments on why impossible worlds should not be reduced to set theoretic constructs out of possible worlds. (shrink)

Graham Priest has brilliantly analyzed Hegel's dialectics, as far as its logical and abstract ontological (metaphysical) structure goes, and has successfully related it to his own logically sophisticated dialethism. After briefly reminding the reader of his account, the paper turns to the other, not purely logical side of Hegel's dialectics, and points to his strategy of bringing together ontological, anthropological and historical matters together with the logical structure, in a manner quite foreign to analytic tradition. It concludes with the (...) proposal that Hegel's way of directly connecting logical ontological, anthropological and historical matters has played the crucial role in the birth of what later became known as specifically ``continental'' philosophy. The paper concludes by raising the question of the relation between the two, the abstract logico-ontological approach, favored by Priest, and the rich, anthropologically and historically informed one found in all major works of Hegel. (shrink)

Various early modern philosophers affirm the traditional distinction between ‘things above reason’ and ‘things contrary to reason.’ However, it is Robert Boyle who goes furthest to rework and defend the division, and to explore its ramifications in detail. My aim here is to examine the logical structure of Boyle’s version of the distinction, and his concomitant account of the sphere of truths beyond human understanding. I also weigh the philosophical merits of the account and clarify the relationship between Boyle’s characterization (...) of things above reason and his alleged dialethism. (shrink)

In this paper we first develop a Dialetheic Logic with Exclusive Assumptions and Conclusions, DLEAC. We adopt the semantics of the logic of paradox (LP) extended with a notion of model suitable for DLEAC, and we modify its proof theory by refining the notions of assumption and conclusion, which are understood as speech acts. We introduce a new paradox – the rejectability paradox – first informally, then formally. We then provide its derivation in an extension of DLEAC contanining the rejectability (...) predicate. (shrink)

Dialethism is the view that there are sentences that are both true and false. Paraconsistent logics are those denying the principle of explosion (that is, they do not licence arbitrary conclusions...

Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly (...) addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary. (shrink)

Graham Priest has influentially claimed that the Sorites paradox is an Inclosure paradox, concluding that his favored dialetheic solution to the Inclosure paradoxes should be extended to the Sorites paradox. We argue that, given Priest’s dialetheic solution to the Sorites paradox, the argument purporting to show that that paradox is an Inclosure is unsound, and discuss some issues surrounding this fact.

This paper argues that modal realism has a problem with mathematical impossibilities. Due to the peculiar way it treats both propositions and mathematical objects, modal realism cannot distinguish the content of different mathematically impossible beliefs. While one might be happy to identify all logically impossible beliefs, there are many different mathematically impossible beliefs, none of which is a belief in a logical contradiction. The fact that it cannot distinguish these beliefs speaks against adopting modal realism.

According to dialetheism, there are some true contradictions. According to the A-theory, the passage of time is a mind-independent feature of reality. On some A-theories, the passage of time involves the movement of the present. I show that by appealing to dialetheism one can explain why the present moves. I then argue that A-theorists should adopt this explanation. To do this, I defend two claims. First, that the dialetheic explanation is an improvement on the only other explanation available for why (...) the present moves and, second, that adopting the explanation is better than leaving the motion of the present unexplained. Assuming that A- theorists should adopt the best available version of their view, it follows that they should adopt a dialetheic explanation of why time passes. (shrink)

In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.

There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...) hold unrestrictedly – that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor’s and Russell’s), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics – non-classical logics in which the admission of contradictions does not lead to logical chaos –, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel’s celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle’s ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. (shrink)

This monograph examines truth in fiction by applying the techniques of a naturalized logic of human cognitive practices. The author structures his project around two focal questions. What would it take to write a book about truth in literary discourse with reasonable promise of getting it right? What would it take to write a book about truth in fiction as true to the facts of lived literary experience as objectivity allows? It is argued that the most semantically distinctive feature of (...) the sentences of fiction is that they are unambiguously true and false together. It is true that Sherlock Holmes lived at 221B Baker Street and also concurrently false that he did. A second distinctive feature of fiction is that the reader at large knows of this inconsistency and isn't in the least cognitively molested by it. Why, it is asked, would this be so? What would explain it? Two answers are developed. According to the no-contradiction thesis, the semantically tangled sentences of fiction are indeed logically inconsistent but not logically contradictory. According to the no-bother thesis, if the inconsistencies of fiction were contradictory, a properly contrived logic for the rational management of inconsistency would explain why readers at large are not thrown off cognitive stride by their embrace of those contradictions. As developed here, the account of fiction suggests the presence of an underlying three - or four-valued dialethic logic. The author shows this to be a mistaken impression. There are only two truth-values in his logic of fiction. The naturalized logic of Truth in Fiction jettisons some of the standard assumptions and analytical tools of contemporary philosophy, chiefly because the neurotypical linguistic and cognitive behaviour of humanity at large is at variance with them. Using the resources of a causal response epistemology in tandem with the naturalized logic, the theory produced here is data-driven, empirically sensitive, and open to a circumspect collaboration with the empirical sciences of language and cognition. (shrink)

The inclosure schema has been proposed by Priest as the structure of many paradoxes. The inclosure analysis has many virtues, especially as a step toward a uniform solution to the paradoxes. Inclosure suggests that paradoxes arise at the limits of thought because the limits can be surpassed, and also not; and so dialetheism is true. I explore the consequences of accepting Priest’s proposal. From a thoroughly dialetheic perspective, then, I find that the import of inclosure changes: some limit phenomena cannot (...) be contradictory, on pain of absurdity, and true contradictions are better thought of as local, not “limit” phenomena. Dialetheism leads back from the edge of thought, to the inconsistent in the every day. (shrink)

This paper first offers a standard modal extension of dialetheic logics that respect the normal semantics for negation and conjunction, in an attempt to adequately model absolutism, the thesis that there are true contradictions at metaphysically possible worlds. It is shown, however, that the modal extension has unsavoury consequences for both absolutism and dialetheism. While the logic commits the absolutist to dialetheism, it commits the dialetheist to the impossibility of the actual world. A new modal logic AV is then proposed (...) which avoids these unsavoury consequences by invalidating the interdefinability rules for the modal operators with the use of two valuation relations. However, while using AV carries no significant cost for the absolutist, the same isn't true for the dialetheist. Although using AV allows her to avoid the consequence that the actual world is an impossible world, it does so only on the condition that the dialetheist admits that she cannot give a dialetheic solution to all self-refe.. (shrink)

Supervaluational theories of vagueness have achieved considerable popularity in the past decades, as seen in eg [5], [12]. This popularity is only natural; supervaluations let us retain much of the power and simplicity of classical logic, while avoiding the commitment to strict bivalence that strikes many as implausible. Like many nonclassical logics, the supervaluationist system SP has a natural dual, the subvaluationist system SB, explored in eg [6], [28].1 As is usual for such dual systems, the classical features of SP (...) (typically viewed as benefits) appear in SB in ‘mirror-image’ form, and the nonclassical features of SP (typically viewed as costs) also appear in SB in ‘mirror-image’ form. Given this circumstance, it can be difficult to decide which of two dual systems is better suited for an approach to vagueness.2 The present paper starts from a consideration of these two approaches— the supervaluational and the subvaluational—and argues that neither of them is well-positioned to give a sensible logic for vague language. §2 presents the systems SP and SB and argues against their usefulness. Even if we suppose that the general picture of vague language they are often taken to embody is accurate, we ought not arrive at systems like SP and SB. Instead, such a picture should lead us to truth-functional systems like strong Kleene logic (K3) or its dual LP. §3 presents these systems, and argues that supervaluationist and subvaluationist understandings of language are better captured there; in particular, that a dialetheic approach to vagueness based on the logic LP is a more sensible approach. §4 goes on to consider the phenomenon of higher-order vagueness within an LP-based approach, and §5 closes with a consideration of the sorites argument itself. (shrink)

Life and the living (on Aristotelian biohorror) -- Supernatural horror as the paradigm for life -- Aristotle's De anima and the problem of life -- The ontology of life -- The entelechy of the weird -- Superlative life -- Life with or without limits -- Life as time in Plotinus -- On the superlative -- Superlative life I: Pseudo-Dionysius -- Negative vs. affirmative theology -- Superlative negation -- Negation and preexistent life -- Excess, evil, and non-being -- Superlative life II: (...) Eriugena -- Negation in the periphyseon -- The quaestio de nihilo: on nothing -- The quaestio de nihilo: superlative nothing -- Dark intelligible abyss -- Apophasis -- The apophatic logic -- Negation in Frege and Ayer -- Negation vs. subtraction in Badiou -- Negation and contradiction in Priest -- The dialetheic vitalism of negative theology -- Ellipses: Suhraward and the luminous void -- Univocal creatures -- On spiritual creatures -- Life as form in Aristotle -- The concept of the creature -- Univocity I: Duns Scotus vs. Aquinas -- Univocity in Aquinas' Summa theologica -- Univocity in Duns Scotus' Opus oxoniense -- The common nature of the creature -- Univocity II: Duns Scotus vs. Henry of Ghent -- Univocity in Henry of Ghent -- Negative vs. privative indetermination -- Absolute indetermination -- Univocity III: Deleuze's scholasticism three variations -- Spinoza et le problème de l'expression -- Différence et répétition -- Cours de Vincennes -- Univocal creatures -- Ellipses: Dgen and uncreated univocity -- Dark pantheism -- Everything and nothing -- Life as spirit in Aquinas -- The concept of the divine nature -- Immanence I: Eriugena's periphyseon -- Natura and the unthought -- Universal life -- Four statements on pantheism -- Immanence II: Duns Scotus' reportatio Ia -- Univocal immanence -- Actual infinity -- The pathology of the triple primacy -- Immanence III: Nicholas of Cusa's De docta ignorantia -- The coincidence of opposites -- The folds of life -- Absolute vs. contracted pantheism -- Speculative pantheism (Deleuze's interlocutors) -- Pantheism and pure immanence -- The insubordination of immanence in Deleuze -- Scholia I: the isomorphism of univocity and immanence -- Scholia II: the vitalist logic of common notions -- Scholia III: the life of substance -- Dark pantheism -- Ellipses: Wang Yangming and idealist naturalism -- Logic and life (on Kantian teratology) -- The wandering line from Aristotle to Kant -- Critique of life -- Spectral life and speculative realism -- Ontotheology in Kant, atheology in Bataille -- The night land. (shrink)

Artworks frequently are the objects of multiple and apparently conflicting aesthetic judgements. This commonplace of the artworld poses a challenge for realist metaphysics, because to assert conflicting judgements of an artwork seems to amount to asserting p & p. Critical pluralism is an ever-more frequently invoked solution to this impasse. What its varieties share in common is the claim that the disagreement between judgements is only an apparent one. I argue, however, that critical pluralism masquerades either as relativism or anti-realism. (...) I examine a number of pluralist proposals, including one that attempts to reconcile pluralism with critical monism, and argue that they are inadequate to their advertised task. Finally, I sketch a solution employing dialetheic logic that captures both intuitions about these cases: that sometimes, judgements about artworks can truly conflict and jointly be true. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

In this article, I consider the possibility of interpreting Hegel’s dialectic as dialetheism. After a first basic recapitulation about the meaning of the words ‘dialetheism’ and ‘dialectic’ and a consideration of Priest’s own account of the relation between dialectical and dialetheic logic in 1989, I discuss some controversial issues, not directly considered by Priest. As a matter of fact, the reflection on paraconsistent logics and dialetheism has enormously grown in recent years. In addition, the reception of Hegel’s logic and metaphysics (...) has also impressively improved. So I suggest that the discussion about the binomial dialectic/dialetheism should be reopened, on these new bases. (shrink)

Graham Priest's In Contradiction (Dordrecht: Martinus Nijhoff Publishers, 1987, chapter 3) contains an argument concerning the intuitive, or ‘naïve’ notion of (arithmetic) proof, or provability. He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, or (...) Church's thesis. We add Priest's dialetheic semantics to ordinary Peano arithmetic PA, to produce a recursively axiomatized formal system PA★ that contains its own truth predicate. Whether one is a dialetheist or not, PA★ is a legitimate, rigorously defined formal system, and one can explore its proof‐theoretic properties. The system is inconsistent (but presumably non‐trivial), and it proves its own Gödel sentence as well as its own soundness. Although this much is perhaps welcome to the dialetheist, it has some untoward consequences. There are purely arithmetic (indeed, Π0) sentences that are both provable and refutable in PA★. So if the dialetheist maintains that PA★ is sound, then he must hold that there are true contradictions in the most elementary language of arithmetic. Moreover, the thorough dialetheist must hold that there is a number g which both is and is not the code of a derivation of the indicated Gödel sentence of PA★. For the thorough dialetheist, it follows ordinary PA and even Robinson arithmetic are themselves inconsistent theories. I argue that this is a bitter pill for the dialetheist to swallow. (shrink)

The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relevant logics; a defense of dialetheic theory of negation; stable (...) negation in logic programming; antirealism and falsity; and negation, denial, and language change in philosophical logic. Suited to scholars and graduate students in the fields of philosophy, logic mathematics, computer science, and linguistics. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

The Liar paradox is an obstacle to a theory of truth, but a Liar sentence need not contain a semantic predicate. The Pinocchio paradox, devised by Veronique Eldridge-Smith, was the first published paradox to show this. Pinocchio’s nose grows if, and only if, what Pinocchio is saying is untrue. What happens if Pinocchio says that his nose is growing? Eldridge-Smith and Eldridge-Smith : 212-5, 2010) posed the Pinocchio paradox against the Tarskian-Kripkean solutions to the Liar paradox that use language hierarchies. (...) Eldridge-Smith : 306-8, 2011) also set the Pinocchio paradox against semantic dialetheic solutions to the Liar. Beall argued the Pinocchio story was just an impossible story. Eldridge-Smith : 749-752, 2012b) responded that unless the T-schema is a necessary truth of some sort, the Pinocchio principle is possible. Luna : 77–86, 2016) argues that the Pinocchio contradiction proves the principle is false. D’Agostini & Ficara discuss a more plausible physical truth-tracking trait, the Blushing Liar, and argue that the Pinocchio contradiction is not a metaphysical dialetheia. I respond to Luna, and D’Agostini & Ficara, and prove that the Pinocchio paradox is a counterexample to hierarchical solutions to the Liar. (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)

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

Many authors have considered that the notions of paraconsistency and dialetheism are intrinsically connected, in many cases, to the extent of confusing both phenomena. However, paraconsistency is a formal feature of some logics that consists in invalidating the rule of explosion, whereas dialetheism is a semantical/ontological position consisting in accepting true contradictions. In this paper, we argue against this connection and show that it is perfectly possible to adopt a paraconsistent logic and reject dialetheism, and, moreover, that there are examples (...) of non-paraconsistent logics that can be interpreted in a dialetheic way. (shrink)

The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into (...) a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading. This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them. (shrink)

Abstract:In the writings of the Chinese Madhyamaka master Jizang (549–623 c.e.), we often read arguments that deduce universal affirmation from universal negation. In previous scholarship, this seemingly paradoxical reasoning was often explained by ascribing to Jizang a type of transcendental realism—the view that reality transcends our ordinary language, logic, and reason—and reading it as his unique way of capturing such a transcendental nature of reality. More recently, an attempt at formalizing this transcendental realist interpretation of Jizang was made by Yasuo (...) Deguchi, who suggests that Jizang could have been tinkering with a type of dialethism. This article challenges the transcendental realist interpretation of Jizang by studying strong anti-realist tendencies found across his writings, and proposes a way to understand his deduction of universal affirmation from universal negation within the boundaries of ordinary reasoning and coherently with his anti-realist philosophy by introducing the modalities of "categorical truth" and "conditional truth.". (shrink)

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...) their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist. (shrink)

A new semantic paradox developed by Richard Heck and relying on very minimal logical and truth-theoretic resources is rehearsed. A theory of truth restricting the structural metarule of contraction is presented and some of the theory's relevant features are made explicit. It is then shown how the theory provides a principled solution to the paradox while preserving the extremely compelling truth-theoretic principles at stake, thus bringing out a significant advantage that the theory enjoys over virtually all other non-dialetheic theories. It (...) is finally argued that such advantage is amplified by theoretical considerations made available by the adoption of a correspondentist perspective in the philosophy of truth. (shrink)

The theory of Wahdat al-Wujūd, or as it is called in English the Oneness of Being, is the core idea of Sufism. The founder of this theory is Ibn ‘Arabī. There are contradictions in Ibn ‘Arabī’s theory of the Oneness of Being. The most important one, which is my main concern in this essay, occurs in his explanation of the relation between Being, which is, according to him, the only real being, and other beings. According to Ibn ‘Arabī, Being is (...) identical and also non-identical with beings. Different philosophers, through hundreds of years, tried to dissolve such contradictions, by proposing consistent readings of Ibn ‘Arabī’s theory of the Oneness of Being. I will not follow this path. Instead, I take the theory of the Oneness of Being to be a dialetheic one, that is, according to this theory there are true contradictions. Thus, I claim that one can have a paraconsistent semantics of the theory of the Oneness of Being. To do so, I appeal to Graham Priest’s Gluon theory. Gluon theory concerns the problem of unity, that is, what makes the plurality of an object’s parts into a whole? I give a translation of the theory of the Oneness of Being into Gluon theory, and show how Gluon theory explains the theory of the Oneness of Being. (shrink)

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

In this note I respond to Hartley Slater's argument 12 to the e ect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency which rejects the possible truth (...) of any contradictions. Against this position Slater's argument has no bite at all. Secondly, while the argument does show that for dialethic paraconsistency according to which contradictions can be true, certain other contradictions must be true, I show that this need not deter the dialethic paraconsistentist from their position. (shrink)