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There is a fascinating debate that was initiated by Graham Priest, who is a chief proponent of dialetheism, about the possibility of legal gluts. In this essay, after critically evaluating the original cases for and against the possibility of legal gluts, I adjudicate a recent debate in this Journal regarding their possibility and provide new reasons for countenancing them. If my considerations are correct, then I will have provided new grounds for the possibility of legal gluts. [ABSTRACT FROM AUTHOR]

This article focuses on the applications of philosophical logic in the discipline of philosophy of religion of both 'Eastern' and 'Western' traditions, in which the problem of apparent ontological contradictions can be found. A number of philosophers have proposed using the work of those non-classical logicians who countenance the violation of the law of non-contradiction (LNC) to address this problem. I discuss (1) whether classical or non-classical account of logic is universal in applying to all true theories, and (2) whether there might be extra-logical considerations which affect what is the correct account of logic for the doctrines in question. With regard to Jc Beall's application of non-classical (FDE) logic to the doctrine of the Incarnation, I argue using the evidence from the writings of church fathers that the meaning of negation found in the core claims of the doctrine of the Incarnation should not be interpreted in accordance with Beall's FDE account, and that this extra-logical consideration refutes Beall's project. Moreover, the FDE's acceptance of the possibility of statements that are both true and false is contrary to what is allowed by the definition of negation in classical logic; therefore (contrary to Beall), Beall is in fact using a different definition of negation compared with the definition used by the classical account. I develop this point in interaction with contemporary philosophy of religion literature and explain its implications and significance for this discipline. [ABSTRACT FROM AUTHOR]

According to some dialetheists, we ought to reject the distinction between object and meta‐languages. Given that dialetheists advocate truth‐value gluts within their object‐language, whether in order to solve the liar paradox or for some other reason, this rejection of the object‐/meta‐language distinction comes with the commitment to use a glutty metatheory. While it has been pointed out that a glutty metatheory brings with it expressive deficiencies, we highlight here another complication arising from the use of a glutty metatheory, this time evidential in nature. According to this countermodel problem, while the thoroughgoing dialetheist who embraces a glutty metatheory can justify their acceptance of a rule of inference's invalidity using countermodels, to justify their renunciation of an unwanted rule they actually require the means to warrant their rejection of the rule's validity—which cannot be supplied by countermodels based on a standard dialetheic semantics. We end by sketching out a possible solution for the thoroughgoing dialetheist using a bilaterialist semantics. [ABSTRACT FROM AUTHOR]

Do inconsistent laws, which are in the form of inconsistent legal obligations, provide us with good reasons for accepting the possibility of legal gluts, which are true legal statements whose negations are also true? Given the contingencies of the law, it is unlikely that many will deny the possibility of inconsistent legal obligations, but it remains an ongoing debate whether these lead to any legal gluts. In a recent debate, Graham Priest [Priest, G. 2006. In 'Contradiction'. In First printed by Martinus Nijhoff in 1987. 2nd ed. Oxford: Oxford University Press; Priest, G. 2017. 'Where Laws Conflict: An Application of the Method of Chunk and Permeate'. In Law and the New Logics, edited by H. Glenn, and L. Smith, 168–180. Cambridge: Cambridge University Press] has argued from inconsistent obligations to legal gluts and JC Beall [Beall, JC 2017. 'On inconsistent laws and gluts'. In Law and the New Logics, edited by H. Glenn, and L. Smith, 199–207. Cambridge: Cambridge University Press.], while he has acknowledged that there are inconsistent obligations, has argued against Priest's arguments for legal gluts. In this paper, after reviewing the debate, I adjudicate it and provide reasons for resisting Beall's arguments again Priest thereby providing a possibility for legal gluts. [ABSTRACT FROM AUTHOR]

This article contributes to philosophy of literature discussions about possible worlds by presenting "possible world fiction" as a unique sub-branch of fiction, distinct from science fiction. I argue that there are four main categories of possible world fiction--alternative histories, time travel fiction, multiverse fiction, and contradictory possible world fiction--and I uncover core philosophical themes from each category, including insights from the Ancient Greek atomists, Leibniz, and contemporary dialetheism. One of the virtues of possible world fiction is that it predisposes us to think productively about paradoxes and contradiction. I argue that although all four categories predispose us in this way, only the fourth category--contradictory possible world fiction--does this outright. [ABSTRACT FROM AUTHOR]

We show that there is a simple derivation of triviality with very few assumptions involving the formula that the negated conditional entails the antecedent of the conditional. [ABSTRACT FROM AUTHOR]

Ludwig Wittgenstein’s remarks on contradictions and paradoxes have been met with incomprehension and have fueled the widespread and long-standing prejudice that his later thoughts on the foundations of logic and mathematics are the “surprisingly insignificant product of a sparkling mind” (Kreisel, British Journal for the Philosophy of Science 9:135–158, 1959, p. 158). This paper disagrees; it argues that Wittgenstein’s remarks on semantic paradoxes suggest an account of the Liar and its kin that is not only of historical interest but also represents a hitherto unnoticed paraconsistent alternative to established approaches to the Liar. In what follows, a reading of Wittgenstein’s remarks will be offered according to which Wittgenstein subscribes to a form of dialetheism (that is, the view that there are sentences that are both true and false). In contrast to modern dialetheist approaches to the Liar, however, some of Wittgenstein’s remarks suggest combining a dialetheist position with what is called ‘logical nihilism’ (that is, the view that there are no universally valid inference rules). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Noniterative approaches to the sorites paradox accept single steps of soritical reasoning, but deny that these can be combined into valid chains of soritical reasoning. The distributed sorites is a puzzle designed to undermine noniterative approaches to the sorites paradox, by deriving an inconsistent conclusion using only single steps, but not chains, of soritical reasoning. This paper shows how a dialetheist version of the noniterative approach, the strict-tolerant approach, also solves the distributed sorites paradox, at no further cost, by accepting the inconsistent conclusion. [ABSTRACT FROM AUTHOR]

One of the most important debates in Sartre scholarship today comes from the question, how is it possible to be in bad faith? In other words, how is self-deception possible, given that, in lying to ourselves, we are both the liar and the lied to at the same time? On the face of it, this sounds paradoxical, if not downright contradictory. This article aims to address this question (1) by analyzing secondary literature on Sartre that tries to prove that bad faith is not a contradictory concept and (2) by defending the "dialetheism reading" of bad faith, that is, the reading that views bad faith to be evidence for the true existence of contradictions. [ABSTRACT FROM AUTHOR]

Hegel's approach to soritical arguments (as well as to paradoxes in general) can be read as a kind of conjunctive paraconsistency: the 'explosive' effect of contradictions is avoided by assuming 'the unity of the opposites', so that contradictory conjunctions are not simplifiable. The paper reconsiders what Hegel says about the Sorites and justifies the conjunctive interpretation. The first section introduces the analysis, presenting the role of the Einheit Entgegengesetzter for contemporary theories of paradoxes. In the second section, the focus is on Hegel's interpretation of the Sorites. The third section briefly considers some contemporary accounts of vagueness in the light of Hegel's view so reconstructed. The last section summarizes the main results and explores some ideas about how to formalize a Hegel-inspired conjunctive view. [ABSTRACT FROM AUTHOR]

I give a formal model of dialectical progression, as found in Hegel and Marx. The model is outlined in the first half of the paper, and deploys the tools of a formal paraconsistent logic. In the second half, I discuss a number of examples of dialectical progressions to be found in Hegel and Marx, showing how they fit the model. [ABSTRACT FROM AUTHOR]

The concept of “conceptual personae” is a contradiction in terms. On one sense of the term, personae are the characters in a work of art, such as a play or a novel. As characters, they are not common terms – King Lear is a particular; he is not a universal, for he cannot be shared in common. However, concepts are quite unlike King Lear. As universals, they are common terms that can be shared in common. “Conceptual personae” renders the particular universal and thereby declares the universal not to be universal. However, I argue that as long as philosophers maintain a traditional attitude toward conceptual truth, philosophers will not be able to successfully think the structure of being without appealing to the mythical imagination, of which conceptual personae form an essential constituent.

According to the dialetheist argument from the inconsistency of informal mathematics, the informal version of the Gödelian argument leads us to a true contradiction. On one hand, the dialetheist argues, we can prove that there is a mathematical claim that is neither provable nor refutable in informal mathematics. On the other, the proof of its unprovability is given in informal mathematics and proves that very sentence. We argue that the argument fails, because it relies on the unjustified and unlikely assumption that the informal Gödel sentence is informally provable. [ABSTRACT FROM AUTHOR]

In this study, I reconstruct and compare Alain Badiou’s Being and Event (2005) and Graham Priest’s One (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’s Parmenides as 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 upon the void and emptiness respectively, 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.

This paper revisits Buridan’s Bridge paradox (Sophismata, chapter 8, Sophism 17), itself close kin to the Liar paradox, a version of which also appears in Bradwardine’s Insolubilia. Prompted by the occurrence of the paradox in Cervantes’s Don Quixote, I discuss and compare four distinct solutions to the problem, namely Bradwardine’s “just false” conception, Buridan’s “contingently true/false” theory, Cervantes’s “both true and false” view, and then the “neither true simpliciter nor false simpliciter” account proposed more recently by Jacquette. All have in common to accept that the Bridge expresses a truth-apt proposition, but only the latter three endorse the transparency of truth. Against some previous commentaries I first show that Buridan’s solution is fully compliant with an account of the paradox within classical logic. I then argue that Cervantes’s insights, as well as Jacquette’s treatment, are both supportive of a dialetheist account, and Jacquette’s in particular of the strict-tolerant account of truth. I defend dialetheist intuitions (whether in LP or ST guise) against two objections: one concerning the future, the other concerning the alleged simplicity of the Bridge compared to the Liar. [ABSTRACT FROM AUTHOR]

In this paper, we critically discuss the idea of a ‘philosophical interpretation’ of paraconsistent logics. We do so by considering the epistemic approach to paraconsistency, by Carnielli and Rodrigues (2019a), according to which paraconsistent logics should be interpreted exclusively in terms of non-conclusive evidence, and also, by considering counter-arguments by Barrio (2018) and Barrio and Da Re (2018), according to whom paraconsistent logics are not specially tied to any specific interpretation. We begin by presenting the positions involved, and by arguing that the debate may be profitably understood in terms of the distinction between pure and applied logics. We argue that dialetheism is not an interpretation of paraconsistent logics, but rather a view on truth and negation which requires use of paraconsistent logics. Something similar may be said about the epistemic approach itself. The result is that there is nothing distinctive to be called a philosophical interpretation of paraconsistent logics, but rather what we have are distinct applications of paraconsistent logics. Arguments by Barrio (2018) and Barrio and Da Re (2018) may be then re-framed more effectively. [ABSTRACT FROM AUTHOR]

Defending the truth of some contradictions in the actual world by means of Graham Priest’s views, To Welcome Contradiction written by Rahman Sharifzadeh is rarely problematic in the appearance - i.e in the edition. In addition to some suggestions, we have evaluated the content of the book and criticized the views of the author and/or the dialetheists in some cases. We have shown, for example, that the preface paradox and some borderline cases cannot be regarded as true contradictions. Again, there is no need to accept such counterintuitive affairs as negative facts to believe dialetheism. In evaluating the logic of paradox, we have corrected the truth table for the logical negation and implication: instead of saying ‌t = f, ‌p = p and ‌f = t, we must say: ‌t = f ˅ p, ‌p = t ˅ f and ‌f = t ˅ p; and instead of the truth value of p for t→p, p→p and p→f, we must say: t ˅ f. On the basis of such corrections, the objection to the validity of modus ponens rule in the logic of paradox is answered. All in all, the book is a necessary one in Persian.

Abstract In this paper, we discuss a family of arguments that show the inconsistency of the concept of omniscience, which is one of the central attributes of the theistic God. We introduce three member of this family: Grim’s Divine Liar Paradox, Milne’s Paradox and our own Divine Curry. They can be seen as theological counterparts of well-known semantic paradoxes. We argue that the very simple dialetheist response to these paradoxes doesn’t work well and then introduce our own response based on a framework that we call Logic of Impossible Truths (LIT). LIT is a non-dialetheist paraconsistent logic designed to represent divine ominiscience and to preserve the transparency of the truth predicate and which semantics rests on the concept of situation. Since some rules of classical logic are not valid in LIT, we are in a position to block the derivation of the paradoxes. Thus, LIT offers a way out of the dilemma of accepting that there are true contradictions (dialetheism) or giving up the idea that there is an all-powerful, omniscient and perfectly good being (atheism).

Dialetheism is the view that some contradictions are true. Resorting to either metaphysical dialetheism or semantic dialetheism may seem like an appropriate resolve to certain theological contradictions. At least for those who concede to theological contradictions, and take dialetheism seriously. However, I demonstrate that neither of these types of dialetheism would serve to be amenable in resolving an Islamic theological contradiction. This is a theological contradiction that I refer to as 'the paradox of an unknowable and ineffable God'. As a result of this, I propose an alternative type of dialetheism which aims to resolve the paradox of an unknowable and ineffable God. I call this type of dialetheism, 'mystical dialetheism'. [ABSTRACT FROM AUTHOR]

This paper is a contribution to the emerging field of comparative metaethics, which aims to analyse the metaethical views of philosophical traditions outside the Western mainstream. It argues that the metaethical views implicit in the mediaeval Chinese school of Tiantai Buddhism can be reconstructed in contemporary terms in order to develop two novel views. These views are moral dialetheism and moral trivialism. The taxonomy of contemporary metaethical views, in epistemic terms, is exhausted by either partial success, or complete error, theories. They claim, respectively, either that some moral judgments are true (and some false) or that all moral judgments are false. There are also noncognitivist and nonfactualist views, claiming that all moral judgments are technically neither true nor false. In opposition to this moral truth gap, moral dialetheism and moral trivialism offer a moral truth glut. These views say, respectively, that some moral judgments and their negations are true and that all moral judgments and their negations are true. The upshot of this metaethical reconstruction of Tiantai Buddhism is that it allows us to complete the contemporary metaethical taxonomy, and to contribute to the therapeutic goal of finding ways to utilize metaethical reflection for the sake of release from the pathologies of morality. [ABSTRACT FROM AUTHOR]

In his Lectures on the History of Philosophy, Hegel develops a subtle analysis of Megarian paradoxes: the Liar, the Veiled Man and the Sorites. In this paper, we focus on Hegel's interpretation of the Liar. We note that in Hegel's treatment there are positive suggestions for a new analysis of the paradox. Faced with the Liar's sentence 'µ' that says '"µ" is false', Hegel's idea is that the conjunction 'µ and not µ' is to be held true, but the two conjuncts 'µ' and 'not µ', separately taken, are untrue. Other parts of Hegel's work confirm the idea that a true contradiction for him is made of two untrue sentences, which is an interesting but unusual account of inconsistency. In this paper, we explore the plausibility of the hypothesis with the lens of the contemporary theories of paradoxes. We compare Hegel's view with standard dialetheism, and we present Hegel's idea of truth which underlies the theory. [ABSTRACT FROM AUTHOR]

In the paper two seemingly distinct areas of philosophical investigations are brought together: metaphor and dialetheism. They both turn out to be deeply related, which becomes visible against a background, i.e. the hybrid structure of metaphor delineated in the first part. This network elicits three variations of dissonance subsequently called: (1) phantom-contradiction, which is combined with unconventionality of metaphors; (2) indexed-bound contradiction, bearing some cognitive tension but no real truth value gluts and; (3) logical contradiction “spread” between the two layers of metaphorical structure. Finally, the analysis allows for approaching a theoretically pending question concerning the influence of dialetheic aspects of metaphor upon human cognition and thinking in general.

Putative examples of true contradictions in the social world have been given by dialetheists such as Graham Priest, Richard Routley, and Val Plumwood. However, we feel that it has not been decisively argued that these examples are in fact true contradictions rather than merely apparent. In this paper we adopt a new strategy to show that there are some true contradictions in the social world, and hence that dialetheism is correct. The strategy involves showing that a group of sincere dialetheists can, given an appropriately formed institution, bootstrap contradictions into existence. We discuss objections and consider the implications of this finding for debates over logic.

Putative examples of true contradictions in the social world have been given by dialetheists such as Graham Priest, Richard Routley, and Val Plumwood. However, we feel that it has not been decisively argued that these examples are in fact true contradictions rather than merely apparent. In this paper we adopt a new strategy to show that there are some true contradictions in the social world, and hence that dialetheism is correct. The strategy involves showing that a group of sincere dialetheists can, given an appropriately formed institution, bootstrap contradictions into existence. We discuss objections and consider the implications of this finding for debates over logic.

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true 'p and not p', the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. [ABSTRACT FROM AUTHOR]

The creation of paraconsistent logics have expanded the boundaries of formal logic by introducing coherent systems that tolerate contradictions without triviality. Thanks to their novel approach and rigorous formalization they have already found many applications in computer science, linguistics and mathematics. As a natural next step, some philosophers have also tried to answer the question if human everyday reasoning could be accurately modelled with paraconsistent logics. The purpose of this article is to argue against the notion that human reasoning is paraconsistent. Numerous findings in the area of cognitive psychology and cognitive neuroscience go against the hypothesis that humans tolerate contradictions in their inferences. Humans experience severe stress and confusion when confronted with contradictions (i.e., the so-called cognitive dissonance). Experiments on the ways in which humans process contradictions point out that the first thing humans do is remove or modify one of the contradictory statements. From an evolutionary perspective, contradiction is useless and even more dangerous than lack of information because it takes up resources to process. Furthermore, it appears that when logicians, anthropologists or psychologists provide examples of contradictions in human culture and behaviour, their examples very rarely take the form of: (p ∧ ¬ p) . Instead, they are often conditional statements, probabilistic judgments, metaphors or seemingly incompatible beliefs. At different points in time humans are definitely able to hold contradictory beliefs, but within one reasoning leading to a particular behaviour, contradiction is never tolerated. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the epistemic approach to paraconsistency. This approach is advanced as an alternative to dialetheism on what concerns interpreting paraconsistency and contradictions; instead of having to accept that there are true contradictions (as dialetheists argue), it is suggested that we may understand such situations as involving only conflicting evidence, which restricts contradictions to a notion of evidence weaker than truth. In this paper, we first distinguish two conflicting programs entangled in the proposal: (1) interpreting paraconsistency in general through the notion of evidence, and (2) modeling reasoning with evidence by using paraconsistent logic. The first part of the program, we argue, does not succeed, on the grounds that it does not lead to a uniform proposal to the understanding of paraconsistency, and fails to engage with dialetheism in a legitimate dispute about interpretation of paraconsistency. Also, when seen through the lights of the second kind of approach, a 'logic as modeling' approach, weaknesses of dealing with evidence through paraconsistency come to light, basically because evidence does not seem to suggest the need of a paraconsistent treatment. As a result, one can neither approach paraconsistency in general through evidence, nor approach evidence with the use of paraconsistent logics. [ABSTRACT FROM AUTHOR]

According to Fogelin's account of deep disagreements, disputes caused by a clash in framework propositions are necessarily rationally irresolvable. Fogelin's thesis is a claim about real-life, and not purely hypothetical, arguments: there are such disagreements, and they are incapable of rational resolution. Surprisingly then, few attempts have been made to find such disputes in order to test Fogelin's thesis. This paper aims to rectify that failure. Firstly, it clarifies Fogelin's concept of deep disagreement and shows there are several different breeds of such disagreements. Thus, to fully assess Fogelin's thesis, it will be necessary to seek out cases of each breed to evaluate their rational irresolvability. Secondly, it begins this task by looking at a significant debate within the logical literature over the truth of contradictions. We demonstrate that, while the debate exemplifies a breed of deep disagreement, the parties involved can supply one another with rationally compelling reasons. [ABSTRACT FROM AUTHOR]

Radical glut and gap theorists deny—in opposite ways—that the liar sentence has exactly one of the two values true and not true. I describe a scenario where a signalman finds himself in a situation analogous to the liar paradox: if he lights a fire at a certain time, that is analogous to the liar being true, and if he does not, that is analogous to the liar not being true. It is obvious that he must make exactly one of those states of affairs come about. It is argued that there are no relevant differences between the liar and the signalman's dilemma, implying that the glut and gap theorists are wrong about the former. A further point is that whether or not the liar is true/the signalman lights the fire, language/the signalman is misleading relative to the conditions under which the liar/the fire "ought" to be true/lit. [ABSTRACT FROM AUTHOR]

That knowledge is factive, that is, that knowledge that p requires that p, has for a long time typically been treated as a truism. Recently, however, some authors have raised doubts about and arguments against this claim. In a recent paper in this journal, Michael Shaffer presents new arguments against the denial of the factivity of knowledge. This article discusses one of Shaffer's objections: the one from "inconsistency and explosion." I discuss two potential replies to Shaffer's problem: dialetheism plus paraconsistency and epistemic pluralism. This is not to be understood so much as a criticism of Shaffer's view but rather as a request to develop his very promising objection from inconsistency and explosion further. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a family of arguments that show the inconsistency of the concept of omniscience, which is one of the central attributes of the theistic God. We introduce three member of this family: Grim's Divine Liar Paradox, Milne's Paradox and our own Divine Curry. They can be seen as theological counterparts of well-known semantic paradoxes. We argue that the very simple dialetheist response to these paradoxes doesn't work well and then introduce our own response based on a framework that we call Logic of Impossible Truths (LIT). LIT is a non-dialetheist paraconsistent logic designed to represent divine ominiscience and to preserve the transparency of the truth predicate and which semantics rests on the concept of situation. Since some rules of classical logic are not valid in LIT, we are in a position to block the derivation of the paradoxes. Thus, LIT offers a way out of the dilemma of accepting that there are true contradictions (dialetheism) or giving up the idea that there is an all-powerful, omniscient and perfectly good being (atheism). [ABSTRACT FROM AUTHOR]