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)
Dialetheism is the view that there are true contradictions. Classical dialetheism holds further the view that the law of excluded middle is indeed a logical law. Most famous dialetheists, such as G. Priest and J. Beall, are classical dialetheists; they take classical dialetheism to be the only plausible solution to the semantic paradoxes. The main contention of the paper is, however, that their views should be rejected. Based on inspecting Priest’s and Beall’s dialetheist theories from a special (...) perspective, this paper contends that classical dialetheism has no natural and plausible way to assign truth values to various truth-ineliminable sentences, i.e., sentences whose truth-conditions essentially involve the property of being true . Several examples of such truth-ineliminable sentences are given in the paper, and two classical dialetheist strategies for assigning them truth values are inspected. This paper argues that none of these strategies is successful. (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)
A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.
In the first part the paper rehearses the main arguments why to be a dialetheist (i.e. why to assume that some contradictions are true). Dialetheism, however, has been criticised as irrational or self-refutating. Therefore the second part of the paper outlines one way to make dialetheism rational assertable. True contradictions turn out to be both believable and assertable. The argument proceeds by setting out basic principles of assertion and denial, and employing bivalent truth value operators.
Over the past 25 years, Graham Priest has ably presented and defended dialetheism, the view that certain sentences are properly characterized as true with true negations. Our goal here is neither to quibble with the tenability of true, assertable contradictions nor, really, with the arguments for dialetheism. Rather, we wish to address the dialetheist's treatment of cases of semantic pathology and to pose a worry for dialetheism that has not been adequately considered. The problem that we present (...) seems to have broader bite, afflicting both consistent and inconsistent proposals for resolving semantic pathology. Thus, while our primary goal is to uncover some important connections between dialetheism, semantic pathology, and other, more general issues, the problem that we pose might be a worry for anyone who aims to resolve semantic pathology - consistently or not. (shrink)
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.
A dialetheia is a sentence, A, such that both it and its negation, A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and (...) false. (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)
Graham Priest's book In Contradiction (Dordrecht: Martinus Nijhoff, 1987) is a bold and well argued for defense of the existence of true contradictions. Priest's case for true contradictions -- or «dialetheias», as he calls them -- is by no means the only one in contemporary analytical philosophy, let alone in philosophy tout court . In some sense, other defenses of the existence of true contradictions are less philosophically «heterodox» than his is, since, unlike Priest's orientation, other approaches are closer to (...) prevailing ideas in mainstream («Quinean») analytical philosophy, whereas Priest's leanings are strongly anti realist, and not distant from the logical empiricism of the thirties. (shrink)
A Liar sentence is a sentence that, paradoxically, we cannot evaluate for truth in accordance with classical logic and semantics without arriving at a contradiction. For example, consider L If we assume that L is true, then given that what L says is ‘L is false,’ it follows that L is false. On the other hand, if we assume that L is false, then given that what L says is ‘L is false,’ it follows that L is true. Thus, L (...) is an example of a Liar sentence. Several philosophers have proposed that the Liar paradox, and related paradoxes, can be solved by accepting the contradictions that these paradoxes seem to imply (including Priest 2006, Rescher and Brandom 1980). The theory that there are true .. (shrink)
Neil Tennant and Joseph Salerno have recently attempted to rigorously formalize Michael Dummett's argument for logical revision. Surprisingly, both conclude that Dummett commits elementary logical errors, and hence fails to offer an argument that is even prima facie valid. After explicating the arguments Salerno and Tennant attribute to Dummett, I show how broader attention to Dummett's writings on the theory of meaning allows one to discern, and formalize, a valid argument for logical revision. Then, after correctly providing a rigorous statement (...) of the argument, I am able to delineate four possible anti-Dummettian responses. Following recent work by Stewart Shapiro and Crispin Wright, I conclude that progress in the anti-realist's dialectic requires greater clarity about the key modal notions used in Dummett's proof. (shrink)
In this paper, I reassess Floridi’s solution to the Bar-Hillel–Carnap paradox (the information yield of inconsistent propositions is maximal) by questioning the orthodox view that contradictions cannot be true. The main part of the paper is devoted to showing that the veridicality thesis (semantic information has to be true) is compatible with dialetheism (there are true contradictions) and that, unless we accept the additional non-falsity thesis (information cannot be false), there is no reason to presuppose that there is no (...) such thing like contradictory information. (shrink)
The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the world. For example, (...) there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (shrink)
Beginning with the paradoxes of zombie twins, we present an argument that dualism is both true and false. We show that avoiding this contradiction is impossible. Our diagnosis is that consciousness itself engenders this contradiction by producing contradictory points of view. This result has a large effect on the realism/anti-realism debate, namely, it suggests that this debate is intractable, and furthermore, it explains why this debate is intractable. We close with some comments on what our results mean for metaphysics and (...) philosophy, in general. (shrink)
This article argues that Nietzsche's transvaluation project refers not to a mere inversion or negation of a set of values but, instead, to a different conception of what a value is and how it functions. Traditional values function within a standard logical framework and claim legitimacy and bindingness based on exogenous authority with absolute extension. Nietzsche regards this framework as unnecessarily reductive in its attempted exclusion of contradiction and real opposition among competing values and proposes a nonstandard, dialetheic model of (...) valuation. (shrink)
Philosophical work on truth covers two streams of inquiry, one concerning the nature (if any) of truth, the other concerning truth-related paradox, especially the Liar. For the most part these streams have proceeded fairly independently of each other. In his Deflationary Truth and the Liar (JPL 28:455–488, 1999) Keith Simmons argues that the two streams bear on one another in an important way; specifically, the Liar poses a greater problem for deflationary conceptions of truth than it does for inflationist conceptions. (...) We agree with Simmons on this point; however, we disagree with his main conclusion. In a nutshell, Simmons' main conclusion is that deflationists can solve the Liar only by compromising deflationism. If Simmons is right, then deflationists cannot solve the Liar paradox. In this paper we argue that, pace Simmons, there is an approach to the Liar that is available to deflationists, namely dialetheism. (shrink)
A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)
Semantic dialetheists astutely dodge Explosion, the logical contagion of everything being true if a single contradiction is true. A dialetheia is contained in their semantics, and sustained by a paraconsistent logic. Graham Priest has shown that this is a solution to the Liar paradox. I use the Pinocchio paradox, devised by Veronique Eldridge-Smith, as a counter-example. The Pinocchio paradox turns on the truth of Pinocchio, whose nose grows if and only if what he is saying is not true, saying ‘My (...) nose is growing’. It is not just a matter of interpretation whether Pinocchio’s nose is and is not growing. (shrink)
: Nagarjuna seems willing to embrace contradictions while at the same time making use of classic reductio arguments. He asserts that he rejects all philosophical views including his own-that he asserts nothing-and appears to mean it. It is argued here that he, like many philosophers in the West and, indeed, like many of his Buddhist colleagues, discovers and explores true contradictions arising at the limits of thought. For those who share a dialetheist's comfort with the possibility of true contradictions commanding (...) rational assent, for Nagarjuna to endorse such contradictions would not undermine but instead confirm the impression that he is indeed a highly rational thinker. It is argued that the contradictions he discovers are structurally analogous to many discovered by Western philosophers and mathematicians. (shrink)
It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical (...) reading of Quine does not exempt logic from the attack on analyticity and a priority. Logical truths and inferences are themselves part of the web of belief, and the same global methodology applies to logic as to any other part of the web, such as theoretical chemistry or ordinary beliefs about ordinary objects. Everything, including logic, is up for grabs in our struggle for holistic confirmation. The purpose of this paper is to examine the law of non-contradiction, and the concomitant principle of ex falso quodlibet, from the perspective of the principles advocated by the radical Quine. I show that he has no compelling reason to accept either of these. To put it bluntly, neither the law of non-contradiction nor the rule of ex falso quodlibet is empirically confirmed, and these principles fare poorly on the various criteria for theory acceptance on the methodology of the radical Quine. So the radical Quine is led rather quickly and rather directly into something in the neighborhood of Graham Priest’s dialetheism. (shrink)
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)
In Contradiction advocates and defends the view that there are true contradictions (dialetheism), a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author's reflections on developments over the last two decades. Further aspects of dialetheism are (...) discussed in the companion volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)
Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defense of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.
Suppose Alice asserts p, and the Caterpillar wants to disagree. If the Caterpillar accepts classical logic, he has an easy way to indicate this disagreement: he can simply assert ¬p. Sometimes, though, things are not so easy. For example, suppose the Cheshire Cat is a paracompletist who thinks that p ∨ ¬p fails (in familiar (if possibly misleading) language, the Cheshire Cat thinks p is a gap). Then he surely disagrees with Alice's assertion of p, but should himself be unwilling (...) to assert ¬p. So he cannot simply use the classical solution. Dually, suppose the Mad Hatter is a dialetheist who thinks that p ∧ ¬p holds (that is, he thinks p is a glut). Then he may assert ¬p, but it should not be taken to indicate that he disagrees with Alice; he doesn't. So he too can't use the classical solution. The Cheshire Cat and the Mad Hatter, then, have a common problem, and philosophers with opinions like theirs have adopted a common solution to this problem: appeal to denial. Denial, these philosophers suppose, is a speech act like assertion, but it is not to be understood as in any way reducing to assertion. Importantly, denial is something different from the assertion of a negation; this is what allows it to work even in cases where assertion of negation does not. Just as importantly, denial must express disagreement, since this is the job it's being enlisted to do. (shrink)
Hartry Field’s book, Saving Truth from Paradox, is without question among the best works on truth and the liar paradox in the analytic tradition—it should become the standard reference on the liar paradox for years to come. Field offers lucid, technically accurate, but accessible discussions of most of the approaches to the liar paradox that are currently being debated in the literature. He also defends his favored approach, which requires a change from classical to paracomplete logic. After a brief flirtation (...) with dialetheism around the turn of the century, he now offers a novel, powerful, and technically dazzling way of dealing with the liar paradox to accompany his influential version of disquotationalism.2 Together they provide a unified view of the nature and logic of truth.3 Field’s solution to the liar together with his fair and charitable discussion of the alternatives make this book required reading by anyone remotely interested in issues associated with truth, philosophical logic, and philosophy of language. The book covers much the same ground as several of Field’s recent papers on the liar paradox4, but this is not a collection; instead, Field has written the book from scratch in a way that informs the.. (shrink)
All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give arguments against Priest’s use (...) of IS in favour of dialetheism. IS fails to identify sufficient conditions for having a paradox of self-reference. That means that, even if we identified a problem common to any reasoning satisfying IS, that problem would not explain why some of those reasonings are paradoxical and some others are not. Therefore IS cannot justify by itself the claim that some particular theory offers the best solution to the paradoxes of self-reference. We still need to consider aspects concerning the content and context of occurrence of every paradox. (shrink)
Consideration of a paradox originally discovered by John Buridan provides a springboard for a general solution to paradoxes within the Liar family. The solution rests on a philosophical defence of truth-value-gaps and is consistent (non-dialetheist), avoids ‘revenge’ problems, imports no ad hoc assumptions, is not applicable to only a proper subset of the semantic paradoxes and implies no restriction of the expressive capacities of language.
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, 0) 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)
In my ‘Deep Inconsistency’ (2002a) (henceforth DI), I criticized Graham Priest’s dialetheism by unfavorably comparing it to my preferred view on the liar paradox, a view I will here call the meaning–inconsistency view. Perhaps the main claim in Jc Beall and Priest’s reply (henceforth B&P)1 is that I am guilty of an ignoratio: in DI, I argue that Priest (1987) fails to establish the analyticity of certain principles, but, B&P say, Priest (1987) isn’t concerned to argue for the (...) analyticity of these principles. Among other criticisms B&P level against DI can be mentioned especially the following: (i) Since I do not in fact defend a particular theory of truth I am ‘out of the game’, not really participating in the debate which others participate in; (ii) I lack—for principled reasons—an account of in virtue of what principles are meaning–constitutive. Here is what I will do in this reply. First I will briefly rehearse the main elements of both my own view and the criticisms of dialetheism raised in DI. Then I will respond to the charges listed from B&P. Lastly I will make some remarks on the strengthened liar. (shrink)
In a recent article M. Colyvan has argued that Quinean forms of scientific realism are faced with an unexpected upshot. Realism concerning a given class of entities, along with this route to realism, can be vindicated by running an indispensability argument to the effect that the entities postulated by our best scientific theories exist. Colyvan observes that among our best scientific theories some are inconsistent, and so concludes that, by resorting to the very same argument, we may incur a commitment (...) to inconsistent entities. Colyvan’s argument could be interpreted, and in part is presented, as a reductio of Quinean scientific realism; yet, Colyvan in the end manifests some willingness to bite the bullet, and provides some reasons why we shouldn’t feel too uncomfortable with those entities. In this paper we wish to indicate a way out to the scientific realist, by arguing that no indispensability argument of the kind suggested by Colyvan is actually available. To begin with, in order to run such an indispensability argument we should be justified in believing that an inconsistent theory is true; yet, in so far as the logic we accept is a consistent one it is arguable that our epistemic predicament could not be possibly one in which we are justified in so believing. Moreover, also if our logic admitted true contradictions, as Dialetheism does, it is arguable that Colyvan’s indispensability argument could not rest on a true premise. As we will try to show, dialetheists do not admit true contradictions for cheap: they do so just as a way out of paradox, namely whenever we are second-level ignorant as to the metaphysical possibility of evidence breaking the parity among two or more inconsistent claims; Colyvan’s examples, however, are not of this nature. So, even under the generous assumption that Dialetheism is true, we will conclude that Colyvan’s argument doesn’t achieve its surprising conclusion. (shrink)
The aim of this paper is to show that Graham Priest's dialetheic account of semantic paradoxes and the paraconsistent logics employed cannot achieve semantic universality. Dialetheism therefore fails as a solution to semantic paradoxes for the same reason that consistent approaches did. It will be demonstrated that if dialetheism can express its own semantic principles, a strengthened liar paradox will result, which renders dialetheism trivial. In particular, the argument is not invalidated by relational valuations, which were brought (...) into paraconsistent logic in order to avoid strengthened liar paradoxes. (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)
In his recent Philosophers’ Imprint paper “The (mostly harmless) inconsistency of knowledge attributions” [Weiner, 2009], Matt Weiner argues that the semantics of the expression “knows that”, as it is used in attributions of knowledge like “Hannah knows that the bank will be open,” are inconsistent, but that this inconsistency is “mostly harmless.” He presents his view as an alternative to the invariantist, contextualist and relativist approaches currently prevalent in the literature, (e.g. [Stanley, 2005], [DeRose, 1995], [Hawthorne, 2006], [MacFarlane, 2005]) and (...) argues that it avoids important disadvantages of each. Yet in calling the supposed inconsistency of knowledge attributions “mostly harmless”, Weiner implies that his view does not have new disadvantages of its own. My purpose in the present paper is to argue that the inconsistency and harmlessness theses cannot be jointly maintained: if we accept that the semantics of ‘know’—or indeed any word—are inconsistent, then we face a dilemma: one horn is dialetheism, the view that there there are true contradictions, the other is the view that that semantic competence in English requires belief in, or similar commitment to, falsehoods. I will argue that neither of these options is well described as “mostly harmless.” The paper is structured as follows: in the first part I present Weiner’s view and his arguments for it. Then in section 2 I compare the question of whether the semantics of ‘knows that’ are inconsistent to the much older controversy over whether the semantics of the expression ‘is true’ are inconsistent. In section 3 I will present Hans Herzberger’s arguments from the 1960s for thinking that no expression in a natural language can have inconsistent semantics. Finally, in section 4 I argue that although Herzberger’s argument seems anachronistic today, both contemporary ways of avoiding his conclusion have significant disadvantages. (shrink)
B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever negation symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics — the preservationist logics — are (...) not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations — even those that emerge from dialetheic approaches — does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism. (shrink)
In the service of paraconsistent (indeed, ‘dialetheic’) theories, Graham Priest has long advanced a non-monotonic logic (viz., MiLP) as our ‘universal logic’ (at least for standard connectives), one that enjoys the familiar logic LP (for ‘logic of paradox’) as its monotonic core (Priest, G. In Contradiction , 2nd edn. Oxford: Oxford University Press. First printed by Martinus Nijhoff in 1987: Chs. 16 and 19). In this article, I show that MiLP faces a dilemma: either it is (plainly) unsuitable as a (...) universal logic or its role as a ‘universal logic’ (indeed, its role full stop) is a mystery. While familiarity with the basic ideas of dialetheism is assumed, formal details of the target logics are relegated to an appendix; the basic problem is evident without them. (shrink)
According to metaphysical realism, there may be features of reality which we cannot conceive. If this thesis of cognitive closure is inconsistent, then, pace dialetheism, metaphysical realism proves incoherent. Recently, Graham Priest has revived Berkeley's idealist argument meant to show that cognitive closure is inconsistent. If cogent, this argument poses a threat to metaphysical realism. I argue that while Priest's reconstruction of Berkeley's argument may be seen to be paradoxical on one interpretation of ‘conceive’, that interpretation is not the (...) intended one. On the intended interpretation, the argument fails and hence leaves metaphysical realism unassailed. (shrink)
This paper builds on work done by Graham Priest (1994, 1995, 1998b, 2000) but does not presuppose knowledge of that work. Priest established that many paradoxes, which had been traditionally divided into different families, have a structure in common – which he calls the Inclosure Schema – and, correlatively, that these paradoxes demand a uniform solution. The uniform solution favoured by Priest is a Dialetheist one. I show that, with minor modification, the Inclosure Schema becomes sufficiently embracing to exhibit the (...) underlying structure not just of the logico-semantical paradoxes discussed by Priest, but of some metaphysical paradoxes too. The uniform solution advocated here is a non-Dialetheist one. Although this is not the concern of the present paper, I am persuaded by some recent work (Bromand 2002; Simmons 1993, pp.80-2) that Dialetheism, whatever its other virtues, does not deliver a solution to the semantical paradoxes. (shrink)
The paper is a discussion of a result of Hilbert and Bernays in their Grundlagen der Mathematik. Their interpretation of the result is similar to the standard intepretation of Tarskis 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.
We address an issue recently discussed by Graham Priest: whether the very nature of truth (understood as in correspondence theories) rules out true contradictions, and hence whether a correspondence-theoretic notion of truth rules against dialetheism. We argue that, notwithstanding appearances to the contrary, objections from within the correspondence theory do not stand in the way of dialetheism. We close by highlighting, but not attempting to resolve, two further challenges for dialetheism which arise out of familiar philosophical theorizing (...) about truth. (shrink)
In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 ). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ?clear sense? (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It (...) is not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ?Benedict XVI was born in Germany? lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 , pp. 27?28): ?(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies?. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well. (shrink)
The debate around “strong” paraconsistency or dialetheism (the view that there are true contradictions) has – apart from metaphysical concerns - centred on the questions whether dialetheism itself can be definitely asserted or has a unique truth value, and what it should mean, if it is possible at all, to believe a contradiction one knows to be contradictory (i.e. an explicit contradiction). And what should it mean, if it is possible at all, to assert a sentence one knows (...) to be contradictory? (shrink)
The concept of inconsistency has become recently the subject of many studies focused on the principle ex contradictione sequitur quodlibet which is a hallmark of the classical inconsistency. Stanisław Jaśkowski was the first who took a non-classical standpoint toward this principle building a system of propositional logic which rejects this classical principle. Rejecting it implies important consequences for the concept of classical negation, and poses the question in which properties the op-eration of negation should be endowed. The intention of this (...) article is to define the concept of inconsistency as well as the concept of negation in a way satisfying the main intuitions natural language users connect with the two notions occurring in propositions containing vague concepts. The vagueness of natural language dis-course leads to the phenomenon of the seeming contradiction characteristic of natural language. A non-standard consequence relation for such a language has been defined in terms of preferential semantics making use of the concept of most classical model. This non-standard consequence relation is applied to the ethical discourse. The concepts introduced in this article have been used to an interpretation of the contradictories of Plato's Parmenides, as well as to the rejection of dialetheism. (shrink)
It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or adopt artificial and ad (...) hoc means to avoid them. Others (“dialetheists”) argue that we can put the paradoxes to rest, but only by licensing the acceptance of some contradictions (presumably in a paraconsistent logic that prevents the contradictions from spreading everywhere). (shrink)
The Pinocchio paradox poses one dialetheia too many for semantic dialetheists (Eldridge-Smith 2011). However, Beall (2011) thinks that the Pinocchio scenario is merely an impossible story, like that of the village barber who shaves just those villagers who do not shave themselves. Meanwhile, Beall maintains that Liar paradoxes generate dialetheia. The Barber scenario is self-contradictory, yet the Pinocchio scenario requires a principle of truth for a contradiction. In this and other respects the Pinocchio paradox is a version of the Liar, (...) unlike the Barber. One wonders why some Liars would be impossible if others generate dialetheias. (shrink)
The arguments of the dialetheists for the rejection of the traditional law of noncontradiction are not yet conclusive. The reason is that the arguments that they have developed against this law uniformly fail to consider the logic of encoding as an analytic method that can resolve apparent contradictions. In this paper, we use Priest [1995] and [1987] as sample texts to illustrate this claim. In [1995], Priest examines certain crucial problems in the history of philosophy from the point of view (...) of someone without a prejudice in favor of classical logic. For each of these problems, the logic of encoding offers an alternative explanation of the phenomena---this alternative is not considered when Priest describes what options there are in classical logic for analyzing the problem at hand. (shrink)
This is an examination of the dialectical structure of deep disagreements about matters not open to empirical check. A dramatic case in point is the Law of Non- Contradiction (LNC). Dialetheists are notoriously of the view that, in some few cases.
