Dialetheism

This paper discusses the logical possibility of testing inconsistent empirical theories. The main challenge for answering this affirmatively is to avoid that the inconsistent consequences of a theory both corroborate it and falsify it. I answer affirmatively by showing that we can define a class of empirical sentences whose truth would force us to abandon such inconsistent theory: the class of its potential rejecters. Despite this, I show that the observational contradictions implied by a theory could only be verified (provided (...) we make some assumptions), but not rejected. From this, it follows that, although inconsistent theories are rejectable, they cannot be rejected qua inconsistent. (shrink)

The possibility of testing contradictory statements about the factual world has been suggested but barely discussed in the relevant literature. Here I argue that if we assume that there are contradictory observation sentences, it would be logically impossible to falsify them. Accordingly, the extension of the dialetheist programme into empirical science would be non-advisable, for it would introduce logically unfalsifiable claims.

Jc Beall is known for defending modest dialetheism; this is the view that there are dialetheia, but only in the form of “spandrels” arising otherwise reasonable semantic terminology (e.g., the Liar paradox). Beall also regards his view as modest in partaking of a deflationary view of truth, a view where ‘true’ is a device of disquotational inference which expresses no “substantive property.” Beall supports deflationism by an appeal to Ockham’s razor; however, the premise that ‘true’ is always disquotational is found (...) dubious. Nonetheless, we can craft an ultra-modest dialetheism which says merely that at least one utterance of ‘This sentence is not true’ uses ‘true’ as a disquotational device, and maintains neturality on whether it expresses a substantive property. This is shown sufficient for the existence of at least one dialetheia in first-degree entailment (a non-explosive logic that also assigns the Liar a truth-value gap). The limited scope of the ultra-modest view will be disappointing to formal semanticists hoping to capture the behavior of ‘true’ throughout the language. But its modest basis gives dialetheism the best hope for wider acceptance in the discipline. (shrink)

Metaphysical dialetheism is the belief that there are contradictions in the world. I will argue that metaphysical dialetheism is, rightfully understood, the most controversial form of dialetheism, and further that it remains an open possibility. Dialetheism can come in many different forms, but all share the same belief in “dialethas”. Depending on how we understand what it means to be a contradiction, we will develop correspondingly different understandings of dialetheism. I will explore what different versions of the position might look (...) like, and how some of these versions of dialetheism could be more plausible than others, and argue that metaphysical dialetheism is the most interesting form of dialetheism. While few authors have considered the possibility of metaphysical dialetheism, there are some important arguments against the position to consider. Frederick Kroon argued in his 2004 article, _Realism and Dialetheism_, that in so far as we find arguments for dialetheism persuasive, we also have good reason to reject realism. Tumoas Tahko argued against the possibility of metaphysical dialetheism by explicitly arguing for a metaphysical definition of contradiction, and a metaphysical version of LNC. Graham Priest also challenged the idea of a “consistent” metaphysics in principle. This paper will take up all of these challenges, and defend the possibility of a metaphysical dialetheist position. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.

A Correction to this paper has been published: 10.1007/s11225-021-09980-z.

The first half of this article is critical: it develops an interpretation of Kant as trying, and failing, to limit our judgments to phenomena and abstain from making claims about noumena, and an interpretation of Wittgenstein as trying, and failing, to develop a theory of meaning that abstains from attempting to say the unsayable. On the reading offered, both Kant and Wittgenstein find themselves saying things that by their own lights cannot be said: in Kant’s case, claims about noumena, and (...) in Wittgenstein’s case, structural claims. While Kant attempts a solution of the problem which also fails, Wittgenstein bites the bullet and leaves his Tractatus, for the most part, void and meaningless. The suggested response is a dialetheic approach—either as an alternative or, potentially, as an amendment to a Kantian or Wittgensteinian theory. According to this approach, certain problems in philosophy arise from true contradictions and thus require a theory that makes sense of contradiction. A subgroup of these problems (among them the noumenal and structural issues in Kant and Wittgenstein) are about things that both are and are not ineffable. The second half of the paper develops a dialetheic account of ineffability and a concise formal theory to ensure that contradiction at the limits of language does not spread to other areas. (shrink)

In his book review of Graham Priest's The Fifth Corner of Four, Mark Siderits, while criticising Priest's philology, suggests that Priest's work is 'of considerable interest' for two reasons. First, 'when two independent traditions use similar methods to work on similar issues, it is always possible that one may have hit on approaches that the other missed'. Second, 'the decentering that can be induced by looking at another tradition may trigger fresh insights, even if those insights are not ones that (...) were actually developed by the tradition marked 'other''. The main task of this paper is to unpack Siderits' thought. By analysing some of Priest's work, I will suggest a decentering that must have taken place in China when Buddhism was 'exported to China in Buddhist shipping containers'. For anyone familiar with the forms of Buddhist philosophy developed in India, various forms of Chinese Buddhism can often look strange. Some ideas that were debated and defended by Indian Buddhists do not appear anywhere in Chinese Buddhism and some assumptions have been quietly added to Buddhism by Chinese Buddhists. By showing that Priest's work brings out the 'innovation' that Chinese Buddhists gave to Buddhism, I will suggest that it is this decentering that Siderits suggests Priest makes use of. (shrink)

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’. (shrink)

In philosophy, as in any other theoretical endeavor, it is not rare to find conflicting but equally well grounded positions. Besides defending one of the positions and criticizing the other, philosophers can opt for pursuing other, more sophisticated, approaches aimed at incorporating the insights, intuitions, and arguments from both sides of the debate into a unified theory: Dialetheism, Analetheism, Gradualism, Pluralism and Relativism. The purpose of this article is to present each strategy's basic argumentative structure, relative strengths, and challenges, trying (...) to determine in which situations one is more appropriate than the others. Despite substantial differences between them, all four options have deep structural similarities; and which option is better for which dilemma or paradox will depend ultimately on a combination of epistemological, linguistic, and metaphysical factors. (shrink)

I argue that one need not be an inferentialist in order to model inconsistent concepts, contrary to what some have thought. Representationalists can do so by adopting a form of bilateralism about contents. It remains unclear, however, why conceptual inconsistency would constitute a defect to be eliminated, rather than a vindication of dialetheism to be embraced. I suggest some answers to explore that involve accepting a descriptive form of dialetheism but denying its normative forms.

This paper is a response to Baumann's comments on "Can Knowledge Really be Non-fative?" In this paper Baumann's suggestions for how those who deny the factivty of knowledge might deal with the argument from inconsistency and explosion are addressed.

Book Review of Impossible Worlds, by Francesco Berto and Mark Jago. Oxford: Oxford University Press, 2019.

In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of (...) the systems have the variable sharing property). I emphasize the intuitive content of the semantics and discuss how natural informational considerations underly each of the examined systems. (shrink)

The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...) logic. The first is the theological contradiction in question. The second is the type of paraconsistent logic. Both components are integral to a contradictory theology in general. I argue that there can be no such thing as an Islamic contradictory theology. I make the case by establishing two points. These points correspond to both integral components of a contradictory theology in general. The first is that an Islamic theological contradiction does not entail an actual (logical) contradiction. The second is that FDE logic, including alternative sub-classical systems of logic, are not adequate in tolerating an Islamic theological contradiction. (shrink)

Suppose that some contradictions are true – for example, that as I walk through the door, I’m inside and I’m not inside. Then we argue 'if I'm walking through the door, I'm inside; I'm not inside; therefore, I'm not walking through the door' is an invalid instance of modus tollens.

This essay marks the first steps towards a viable glut-theoretic (contradictory) solution to the longstanding foreknowledge and free will dilemma. Specifically, I offer a solution to the dilemma that accommodates omniscience (foreknowledge) and human freedom (as the ability to do otherwise) in a simple, flat-footed way. This goal is accomplished via viewing the theological fatalist argument not as a problem, but as a sound argument: omniscience and human free will are contradictory and by dropping to a weaker underlying account of (...) logical consequence, we can embrace them in their full-throated, robust (though contradictory) interpretations. That said, the primary aim of this paper is one of exploration: how does a subclassical solution to the foreknowledge and free will dilemma stack up in comparison to the traditional solutions on offer in the literature. This essay represents the beginning of such an exploration. (shrink)

The aim of this paper is to lay bare the roots of dialetheism in discussions about dialectics and dialectical logic at the time of the first development of paraconsistent logics. In other words, th...

The aim of this paper is to show how the invention of imaginary logic by Nikolaj A. Vasil’ev, forerunner of various logical and metaphysical theories appeared in the 20th century, is grounded on a revaluation of Aristotelian ontology. I shall introduce the reason why Aristotle believes that the study of the principle of contradiction is part of ontology (§ 2); I shall explain why Vasil’ev considers the law of contradiction an empirical law, and not a logical one (§ 3.1). I (...) will show his conception of contradiction (§ 3.2) and I will discuss how he believes that it’s possible to renounce this law; (§ 3.3). I shall then explain the fundamental features of imaginary logic (§ 4.1 and § 4.2); and, finally I shall claim how, in spite of a convergence from the logical point of view (§ 5.1), the incompatibility of the two authors takes place on an ontological level (§ 5.2). In order to do so, I shall implement the analysis of the Aristotelian syllogistic conducted by the Polish logician and philosopher Jan Łukasiewicz, together with a crucial distinction between two concepts: the one of ‘law’ and the one of ‘principle’. -/- . (shrink)

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.

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)

Popper restricted his definition of falsifiability to consistent theories through what we may call his requirement of consistency. His main argument was that an inconsistent theory does not distinguish the sentences that corroborate it from those that contradict it, for all sentences follow from it. I propose to replace this requirement by the more basic requirement that the classes of potential corroborators and falsifiers of a theory do not overlap. This results not only in an unrestricted definition of falsifiability but (...) also in some inconsistent theories being falsifiable whenever that inconsistency is not located among its observational statements. Although this assumes a restriction of the principle of explosion or ex contradictione sequitur quodlibet (ECQ), it does not depend on any particular system or approach of paraconsistent logic. Finally, I propose to define the class of potential refuters of a theory, which is obtained by subtracting the class of potential corroborators from the class of potential falsifiers. Given that, by definition, the classes of potential refuters and corroborators of a theory do not overlap, it immediately follows that some observationally inconsistent theories are refutable in this sense. This establishes the bases for a new and more general formal theory of falsifiability of scientific factual/empirical theories. (shrink)

It is often said that a correct logical system should have no counterexample to its logical rules and the system must be revised if its rules have a counterexample. If a logical system (or theory) has a counterexample to its logical rules, do we have to revise the system? In this paper, focussing on the role of counterexamples to logical rules, we deal with the question. -/- We investigate two mutually exclusive theories of arithmetic - intuitionistic and paraconsistent theories. The (...) paraconsistent theory provides a (strong) counterexample to Ex Contradiction Quodlibet (ECQ). On the other hand, the intuitionistic theory gives a (weak) counterexample to the Double Negation Elimination (DNE) of the paraconsistent theory. If any counterexample undermines the legitimate use of logical rules, both theories must be revised. -/- After we investigate a paraconsistent counterexample to ECQ and the intuitionist’s answer against it, we arrive at the unwelcome conclusion that ECQ has both a justification and a counterexample. Moreover, we argue that if a logical rule were abolished whenever it has a counterexample, a promising conclusion would be logical nihilism which is the view that there is no valid logical inference, and so a correct logical system does not exist. Provided that the logical revisionist is not a logical nihilist, we claim that not every counterexample is the ground for logical revision. While logical rules of a given system have a justification, the existence of a counterexample loses its role for logical revision unless the rules and the counterexample share the same structure. (shrink)

Some of Aristotle’s statements about the indemonstrability of the Principle of Non-Contradiction (PNC) in Metaphysics Γ 4 merit more attention. The consensus seems to be that Aristotle provides two arguments against the demonstrability of the PNC, with one located in Γ 3 and the other found in the first paragraph of Γ 4. In this article, I argue that Aristotle also relies upon a third argument for the same conclusion: the argument from truth. Although Aristotle does not explicitly state this (...) argument, it is the best argument that he could use to defend some of his statements in the second paragraph of Γ 4. Since the argument relies on only a few of Aristotle’s core views about truth, I propose that it is faithful to his considered position throughout his corpus, and it may be the strongest argument he could offer for the indemonstrability of the PNC. (shrink)

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. (shrink)

Принято считать, что невозможность, неполнота, Парапоследовательность, Несоответствие, Случайность, вычислительность, парадокс, неопределенность и пределы разума являются разрозненными научными физическими или математическими вопросами, имеющими мало или ничего общего. Я полагаю, что они в значительной степени стандартные философские проблемы (т.е. языковые игры), которые были в основном решены Витгенштейном более 80 лет назад. -/- Я предоставляю краткое резюме некоторых из основных выводов двух из самых выдающихся студентов поведения о Fсовременности, Людвиг Витгенштейн и Джон Сирл, на логическую структуру преднамеренности (ум, язык, поведение), принимая в качестве (...) отправной точки фундаментальное открытие Витгенштейна, что все действительно "философские" проблемы одинаковы-путаницы AB,как использовать язык в частности контекст, и поэтому все решения одинаковы, глядя на то, как язык может быть использован в рассматриваемом контексте, так что его условия истины (Условия удовлетворенности или COS) ясны. Основная проблема заключается в том, что можно сказать что угодно, но нельзя означать (государство ясно COS для) любое произвольное высказывание и смысл возможен только в очень специфическом контексте. -/- Я вскрыть некоторые писания некоторых из основных комментаторов по этим вопросам с точки зрения Витгенштейна в framework современной точки зрения двух систем мысли (популяризировал как "мышление быстро, думая медленно"), используя новую таблицу преднамеренности и новых двойных систем номенклатуры. Я показываю, что это мощная эвристическая для описания истинной природы этих предположенных научных, физических или математических вопросов, которые действительно лучше всего подходить как стандартные философские проблемы использования языка (языковые игры в терминологии Витгенштейна). (shrink)

ويعتقد عادة أن الاستحالة، وعدم اكتمال، وParaconsistency، وعدم تحديد، العشوائية، والحوسبة، والمفارقة، وعدم اليقين وحدود العقل هي قضايا علمية مادية أو رياضية متباينة وجود القليل أو لا شيء في المشتركه. أقترح أنها مشاكل فلسفية قياسية إلى حد كبير (أي ألعاب اللغة) التي تم حلها في الغالب من قبل فيتغنشتاين أكثر من 80years منذ. -/- "إن ما نميل إلى قوله في مثل هذه الحالة هو، بطبيعة الحال، ليس فلسفة، ولكنه مادة خام. وهكذا، على سبيل المثال، ما يميل عالم الرياضيات إلى قوله (...) عن موضوعية وواقع الحقائق الرياضية، ليس فلسفة الرياضيات، بل شيء للعلاج الفلسفي". فيتغنشتاين بي 234 -/- "يرى الفلاسفة باستمرار طريقة العلم أمام أعينهم ويميلون بشكل لا يقاوم إلى طرح الأسئلة والإجابة عليها بالطريقة التي يفعلبها العلم. هذا الاتجاه هو المصدر الحقيقي للميتافيزيقيا ويقود الفيلسوف إلى الظلام الكامل". فيتغنشتاين -/- أقدم ملخصاً موجزاً لبعض النتائج الرئيسية لاثنين من أبرز الطلاب في السلوك في العصر الحديث، لودفيغ فيتغنشتاين وجون سيرل، على البنية المنطقية للتعمد (العقل واللغة والسلوك)، مع الأخذ كنقطة انطلاق لي اكتشاف فيتغنشتاين الأساسي - أن جميع المشاكل "الفلسفية" حقاهي نفسها - الالتباسات حول كيفية استخدام اللغة في سياق معين، وبالتالي فإن جميع الحلول هي نفسها - النظر في كيفية استخدام اللغة في السياق في القضية بحيث حقيقتها الشروط (شروط الرضا أو COS) واضحة. المشكلة الأساسية هي أن المرء يمكن أن يقول أي شيء، ولكن لا يمكن للمرء أن يعني (الدولة واضحة كوس ل) أي كلام ومعنى تعسفي غير ممكن إلا في سياق محدد جدا. -/- أنا تشريح بعض كتابات عدد قليل من المعلقين الرئيسيين على هذه القضايا من وجهة نظر Wittgensteinian في إطار المنظور الحديث للنظاميين الفكر (شعبية باسم 'التفكير السريع، والتفكير بطيئة')، وتوظيف جدول جديد من التعمد وتسميات النظم المزدوجة الجديدة. أنا تبين أن هذا هو سياحي قوي لوصف الطبيعة الحقيقية لهذه القضايا العلمية أو المادية أو الرياضية المفترضة التي يتم التعامل معها على أفضل وجه حقا كمشاكل فلسفية قياسية لكيفية استخدام اللغة (ألعاب اللغة في فيتغنشتاين المصطلحات). -/- هو زعمي أن جدول التعمد (العقلانية، العقل، الفكر، اللغة، الشخصية وما إلى ذلك) التي تبرز بشكل بارز هنا يصف أكثر أو أقل دقة، أو على الأقل بمثابة سياحية ل، وكيف نفكر وتصرف، وبالتالي فإنه لا يشمل مجرد فلسفة وعلم نفس، ولكن كل شيء آخر (التاريخ والأدب والرياضيات والسياسة الخ). لاحظ بشكل خاص أن التعمد والعقلانية كما أنا (جنبا إلى جنب مع سيرل، فيتغنشتاين وغيرها) عرض ذلك، ويشمل كل من النظام اللغوي التداولي الواعي 2 واللاوعي الآلي النظام قبل اللغوية 1 الإجراءات أو ردود الفعل. (shrink)

En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...) y lógica), que necesitan decidirse por unt cómo realmente usar palabras en contextos concretos. Cuando tenemos claro sobre qué juego de idiomas estamos jugando, estos temas son vistos como preguntas científicas y matemáticas ordinarias como cualquier otra. Las percepciones de Wittgenstein rara vez se han igualado y nunca superado y son tan pertinentes hoy como lo fueron hace 80 años cuando dictó los libros azul y marrón. A pesar de sus fallas — realmente una serie de notas en lugar de un libro terminado —, esta es una fuente única de la obra de estos tres eruditos famosos que han estado trabajando en los bordes sangrantes de la física, las matemáticas y la filosofía durante más de medio siglo. Da Costa y Doria son citados por Wolpert (ver abajo o mis artículos sobre Wolpert y mi reseña de ' los límites de la razón ' de Yanofsky) desde que escribieron en el cómputo universal, y entre sus muchos logros, da Costa es pionera en paraconsistencia. Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna dos sistemas punto de vista puede consultar mi libros Talking Monkeys 3ª ed (2019), Estructura Logica de Filosofia, Psicología, Mente y Lenguaje en Ludwig Wittgenstein y John Searle 2a ed (2019), Suicidio pela Democracia 4ª ed (2019), La Estructura Logica del Comportamiento Humano (2019), The Logical Structure de la Conciencia (2019, Entender las Conexiones entre Ciencia, Filosofía, Psicología, Religión, Política y Economía y Delirios Utópicos Suicidas en el siglo 21 5ª ed (2019), Observaciones sobre Imposibilidad, Incompletitud, Paraconsistencia, Indecidibilidad, Aleatoriedad, Computabilidad, Paradoja e Incertidumbre en Chaitin, Wittgenstein,. (shrink)

The first group of articles attempt to give some insight into how we behave that is reasonably free of theoretical delusions. In the next three groups I comment on three of the principal delusions preventing a sustainable world— technology, religion and politics (cooperative groups). People believe that society can be saved by them, so I provide some suggestions in the rest of the book as to why this is unlikely via short articles and reviews of recent books by well-known writers. (...) -/- America and the world are in the process of collapse from excessive population growth, most of it for the last century and now all of it due to 3rd world people. Consumption of resources and the addition of 4 billion more ca. 2100 will collapse industrial civilization and bring about starvation, disease, violence and war on a staggering scale. Billions will die and nuclear war is all but certain. In America this is being hugely accelerated by massive immigration and immigrant reproduction, combined with abuses made possible by democracy. Depraved human nature inexorably turns the dream of democracy and diversity into a nightmare of crime and poverty. The root cause of collapse is the inability of our innate psychology to adapt to the modern world, which leads people to treat unrelated persons as though they had common interests. This, plus ignorance of basic biology and psychology, leads to the social engineering delusions of the partially educated who control democratic societies. Few understand that if you help one person you harm someone else—there is no free lunch and every single item anyone consumes destroys the earth beyond repair. Consequently, social policies everywhere are unsustainable and one by one all societies without stringent controls on selfishness will collapse into anarchy or dictatorship. Without dramatic and immediate changes, there is no hope for preventing the collapse of America, or any country that follows a democratic system. Hence my essay “Suicide by Democracy”. It is also now clear that the seven sociopaths who rule China are winning world war 3, and so my concluding essay on them. The only greater threat is Artificial Intelligence which I comment on briefly in the last paragraph. (shrink)

Priest holds anti-exceptionalism about logic. That is, he holds that logic, as a theory, does not have any exceptional status in relation to the theories of empirical sciences. Crucial to Priest’s anti-exceptionalism is the existence of ‘data’ that can force the revision of logical theory. He claims that classical logic is inadequate to the available data and, thus, needs to be revised. But what kind of data can overturn classical logic? Priest claims that the data is our intuitions about the (...) validity of inferences. In order to make sense of this claim, I will appeal to the Madhyamaka Buddhist philosopher Candrakīrti. I will then pose a problem for Priest’s anti-exceptionalism. Finally, I will suggest a way out of the problem for Priest. Whether or not he accepts my solution, I will let him decide. (shrink)

Aristotle gave seven arguments for the law of non-contradiction. The first one is against a special case of dialetheism, the view that only some contradictions are true, and other six arguments are...

In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic---such as the relations |=_t, |=_f, and |=_i that each correspond to a lattice order in SIXTEEN_3; and |=, the intersection of |=_t and |=_f,. -/- It turns out that our method of characterising these semantic relations---as (...) intersections of auxiliary relations that can be captured with the help of a single calculus---lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that |=, when restricted to L_{tf}, the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano. (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)

Dialetheism is the view that some true sentences have a true negation as well. Defending dialetheism, Graham Priest argues that the correct account of negation should allow for true contradictions and \) without entailing triviality. A negation doing precisely that is said to have ‘surplus content’. Now, to defend that the correct account of negation does have surplus content, Priest advances arguments to hold that classical Boolean negation does not even make sense without begging the question against the dialetheist. We (...) shall argue that Priest’s arguments may be turned upon themselves, and that he may also be accused of begging the question against the classical logician. We then advance an argument to the effect that Priest’s account of negation falls short of satisfying his own desiderata on a correct account of a negation: a theory of negation that attempts to represent contradictions cannot coherently allow surplus content, and vice-versa, a negation allowing for surplus content bans contradiction. (shrink)

What sorts of things qualify as first principles of reasoning and what kind of justification for them can be offered? We think of principles like that of non-contradiction as first principles of reasoning. Laurence Bloom argues that Plato’s Republic, the first text that affords us a complete statement of the Principle of Non-contradiction, offers us a powerful, complex and detailed argument for taking form—specifically that of the good—as the first principle of both knowing and being.

One strategy for defending paraconsistent logics involves raising ‘normative arguments’ against the inference rule explosion. Florian Steinberger systematically criticises a wide variety of formulations of such arguments. I argue that, for one such formulation, Steinberger’s criticisms fail. I then sketch an argument, available to those who deny dialetheism, in defence of the formulation in question.

Instantaneous changes may well be thought to give rise to contradiction. If one endorses an explosive logic, where contradictions entail everything, this is entirely unacceptable. However, if one deploys a paraconsistent logic, which keeps contradictions under control, one may give perfectly coherent and precise models of such changes. In In Contradiction the author showed how and he explored the philosophical implications of the model. Here, the author revisits the issue in the light of a recent critique by Greg Littmann.

Hili Razinsky, free downlad at link. ABSTRACT: Emotional perceptions are objectivist (objectivity-directed or cognitive) and conscious, both attributes suggesting they cannot be ambivalent. Yet perceptions, including emotional perceptions of value, allow for strictly objectivist ambivalence in which a person unitarily perceives the object in mutually undermining ways. Emotional perceptions became an explicandum of emotion for philosophers who are sensitive to the unique conscious character of emotion, impressed by the objectivist character of perceptions, and believe that the perceptual account solves a (...) worry about the possibility of a conflict between an emotion and a judgement. Back into the 1980s Greenspan has argued that emotional ambivalence is possible, her reasons implying that objectivist accounts of emotion are inconsistent with ambivalence. Tappolet has more recently replied that perceptual accounts allow for emotional ambivalence since the opposed values seen in ambivalence are good or bad in different senses. The present paper identifies strict objectivist ambivalence between judgements and between emotional perceptions by contrasting them with such ambivalence of separate values such as evoked by Tappolet. (shrink)

In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking at (...) how we actually use words in particular contexts. When we get clear about which language game we are playing, these topics are seen to be ordinary scientific and mathematical questions like any others. Wittgenstein’s insights have seldom been equaled and never surpassed and are as pertinent today as they were 80 years ago when he dictated the Blue and Brown Books. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this article I first place Harman's challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms (...) for belief can be captured. (shrink)

In this paper we explain that the paraconsistent logic LP promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.

In this paper I shall consider two related avenues of argument that have been used to make the case for the inconsistency of mathematics: firstly, Gödel’s paradox which leads to a contradiction within mathematics and, secondly, the incompatibility of completeness and consistency established by Gödel’s incompleteness theorems. By bringing in considerations from the philosophy of mathematical practice on informal proofs, I suggest that we should add to the two axes of completeness and consistency a third axis of formality and informality. (...) I use this perspective to respond to the arguments for the inconsistency of mathematics made by Beall and Priest, presenting problems with the assumptions needed concerning formalisation, the unity of informal mathematics and the relation between the formal and informal. (shrink)

The concept of dialetheia and the claim of dialetheism has been examined and compared to such related concept as contradiction, antinomy, consistency and paraconsistency. Dialetheia is a true contradiction and dialetheism is the claim that there exists at least one dialetheia. It has been observed that dialetheism is equivalent to the negation of the traditional principle of contradiction. Hence, dialetheism itself is no new idea in whatsoever. The novelty of dialetheism consists in the arguments delivered for its case. Key justification (...) the partisans deliver for dialetheism has been examined and evaluated: antinomies, an alleged Gödel’s paradox, and existence of limits of thought. The structure of those arguments has been analyzed. It has been claimed that they share one and the same simple structure which may be called reverse paradox. The vital content dialetheists add to the traditional paradoxes is only the thesis of reliability of the vernacular prima facie knowledge. Three objections have been raised against the justification of dialetheism: firstly, it has been claimed that exactly the same argument supports principle of contradiction, secondly, it has been questioned whether the arguments preserve their value when logic is subject to revision, and thirdly, it has been claimed that the underlying logic of dialetheism is classical. (shrink)