The work is the presentation of a logical theory - Logic in Reality (LIR) - and of applications of that theory in natural science and philosophy, including ...

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)

Georg Wilhelm Friedrich Hegel (1770-1831) est probablement l’un des plus importants penseurs et philosophes de notre époque. On peut dire que les sciences humaines en général et la philosophie en particulier doivent prendre une position positive ou négative concernant la philosophie hégélienne avant de procéder à d’autres développements qui leur seraient propres. Plus précisément, ce collectif trouve sa racine dans une double urgence : les menaces des crises environnementale, politique et économique, les nouveaux enjeux qu’elles entraînent, d’une part, et l’absence (...) jusqu’à présent de réponses prometteuses, de l’autre. Il est temps de faire le point et de contribuer à fournir de nouvelles pistes de réflexion. Le présent ouvrage, bilingue, est le fruit de la collaboration d’éminents spécialistes internationaux qui ont répondu avec enthousiasme à notre invitation. Les 14 textes qui y sont réunis sont distribués selon trois thématiques et, tout en respectant la nature de la pensée hégélienne, leurs thèmes se chevauchent inévitablement. La première partie, « Aspects de la pensée de Hegel / Aspects of Hegel’s Thought », regroupe les textes qui discutent en profondeur d’un aspect de la pensée de Hegel, tout en analysant un enjeu qui se trouve dans ses propres œuvres. Les contributions de la deuxième partie, « Marx et Hegel / Marx and Hegel », examinent la relation entre ces deux philosophes. Comment faut-il comprendre les passages dans lesquels Marx accuse Hegel d’idéalisme, dont celui, largement cité, dans la préface du premier tome du Capital, n’est qu’un exemple? Dans la troisième partie, « Hegel à l’époque contemporaine / Hegel in Modern Times », les auteurs se penchent sur l’influence de la pensée de Hegel sur plusieurs penseurs. (shrink)

In 2023, Beall and Ficara present what they call Hegelian conjunctions. A Hegelian conjunction is a true conjunction of contradictory opposites in which the conjuncts, separately taken, are untrue and for which simplification fails. The analysis in Beall & Ficara History and Philosophy of Logic 44 (2) 119-131, 2023 is important for various reasons. First, for overcoming the deleterious state of estrangement between two ways of conceiving and practicing logic, the “dialectical” or “continental” and the “analytical” one. Second, for strengthening (...) a new, promising way of conceiving conjunction in paraconsistency (d’Agostini Synthese 199, 6845 6874, 2021). Yet it needs an enlargement, mainly in two dimensions, a hermeneutical and a logical one. The former concerns the textual basis used by Beall and Ficara for motivating their account (the focus of their analysis is a small part of the early Hegelian fragment on Vereinigung – unification/conjunction). The latter is the semantics proposed by Beall and Ficara. In this paper, I focus on the first dimension, in the conviction that the condition for making the chief formal characteristics of dialectics (the logical dimension) clearer is a grasp of the Hegelian fragment in its entirety and complexity. The fragment is crucial for thinking about the logic, metaphysics and epistemology of true contradictions. Yet it counts as obscure. My aim is to make its content more accessible, and to present its relevance for conjunctive paraconsistency. (shrink)

Deleuze never explicitly formulates his philosophy of logical truth‐values. It thus remains an open question as to the number and types he held there to be. Despite his explicit comments on these matters, additional textual evidence suggests that in his thinking on the event, he favored a third truth‐value, holding either the analetheic view that some truth‐bearers can be truth‐valueless or the dialetheic view that some truth‐bearers can be both true and false. I first argue that taking a logical approach (...) to Deleuze's thinking is feasible, despite his and others' claims that might suggest otherwise. Next, I examine his explicit statements to show that they cannot be taken at face value and that, rather, we need to transpose his claims into contemporary terminology in order to accurately assess them. I lastly turn to his Leibniz‐inspired philosophy of time to argue that the affirmations involved in this conception strongly suggest a dialetheic tendency in his thinking. (shrink)

1. In both Benedetto Croce's and Hegel's own terminology, dialectics can be understood as dottrina degli opposti (the doctrine of the opposites – Lehre der Gegensätze).1 In the dialectical process,...

The idea at the basis of this special issue is that reopening the old debate about the logical status of Hegel’s dialectics is extremely interesting, for various reasons.1 The first reason is that...

1. Dialectic, in the sense of Hegel and Marx, is a dynamic process in which contradictions arise and are aufgehoben—an impossible word to translate into English, since it means both removed and pre...

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

In 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...

This article is an inquiry into how the relationship between the principle of non-contradiction and the limits of thought has been understood by thinkers as diverse as Hegel, Heidegger, Levinas, and Graham Priest. While Heidegger and Levinas focus on the question of temporality and Priest takes a formal approach, all these philosophers effectively maintain that the principle of non-contradiction imposes a restriction on thought that disables it from adequately accounting for its own limits and thus what lies beyond those limits, (...) the implication being that the violation of the principle is necessary for such an accounting to take place. However, the ultimate argument here is that, contrary to Priest’s interpretation, Hegel’s philosophy can be convincingly read as supporting the idea that the mind’s ability to go beyond any particular limit of thought can actually be said to involve an adherence to a normative demand to locate and dispel the contradictions that emerge through the very setting of determinative limits. This is a non-formal consistency that evinces a “logic” that is unknowingly followed by the Heideggerian and Levinasian phenomenological philosophies of transcendence. (shrink)

Three disciplines address the codified forms and rules of human thought and reasoning: logic, available since antiquity; dialectics as a process of logical reasoning; and semiotics which focuses on the epistemological properties of the extant domain. However, both the paradigmatic-historical model of knowledge and the logical-semiotic model of thought tend to incorrectly emphasize the separation and differences between the respective domains vs. their overlap and interactions. We propose a sublation of linguistic logics of objects and static forms by a dynamic (...) logic of real physical-mental processes designated as the Logic in Reality (LIR). In our generalized logical theory, dialectics and semiotics are recovered from reductionist interpretations and reunited in a new synthetic paradigm centered on meaning and its communication. Our theory constitutes a meta-thesis composed of elements from science, logic and philosophy. We apply the theory to gain new insights into the structure and role of semiosis, information and communication and propose the concept of ‘ontolon’ to define the element of reasoning as a real dynamic process. It is part of a project within natural philosophy, which will address broader aspects of the dynamics of the growth of civilizations and their potential implications for the information society. (shrink)

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

This thesis argues that new readings of Hegel’s philosophical system generate a post-secular, philosophical political theology. This political theology is able to engage with the apocalyptic elements of the Christian tradition in order to understand the dual function of religion: the cultivation of social solidarity and the annihilation of the present world. After an initial discussion of Hegel’s role in the development of political theology and the current divisions in Hegel scholarship, this study turns to the significance of Hegel’s understanding (...) of religion as representation. In particular it focuses on the implications of the ‘non-metaphysical’ reading of Hegel. In this reading, religion is not concerned with an external, transcendent deity, but represents the emergence of a self-conscious, self-determining community. While drawing on this shift in the nature of religion, this thesis argues that the ‘non-metaphysical’ reading subordinates religion to the state, diminishing religion’s role in social critique. This subordination to the state can be corrected by introducing apocalypticism as a representation of the negative moment of Hegel’s philosophical system, resulting in a greater emphasis on contingency and contradiction. This expanded understanding of religion is the basis of an apocalyptic, Hegelian political theology. Precedent for this form political theology is found in the work of Jacob Taubes. In addition to analysing Taubes’s explicit discussions of Hegel, this study argues that Hegel’s philosophy of religion draws out the methodology behind Taubes’s intervention. Having drawn out these underlying Hegelian aspects, affinities between Taubes and contemporary work on Hegel becomes apparent. In particular, Catherine Malabou’s understanding of plasticity is shown to closely parallel Taubes’s understanding of apocalypse. Reading Malabou and Taubes together results in a political theology of plastic apocalypticism. This political theology is a model of a post-secular theology operating, beyond the contradiction between philosophy and theology. (shrink)

In this paper I argue that Hegel’s treatment of dialectical inferences, in particular of Plato’s dialectics in the Lectures on the History of Philosophy, belongs to the history of the logical rule that, from Gerolamo Cardano to Bertrand Russell, is known as consequentia mirabilis. In 1906 Russell formalises it as follows: and its correspondent positive form as My paper has two parts. First, I show that dialectical inferences, for Hegel, involve sentences of the form and. Hegel, following Plato, stresses that (...) these inferences are das Wunderbare, the marvellous element of dialectical reasoning. In this sense Hegel’s view belongs to the history of CM from a perspective that is both terminological and logical. Second, I stress the peculiarity of Hegel’s CM. In a classical setting, the conditional is admissible and from we can, by CM, derive, and from, by CM, infer. However, in Hegel’s analysis it is evident that we can neither infer from, nor from. Rather, in dialectical inferences what we can vali... (shrink)

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

Some authors have claimed that Hegel's ‘determinate negation’ should be distinguished from ‘logical’ or ‘formal’ negation, that is, from a view of negation as a contradictory forming operator. In contrast, I argue that dialectical determinate negation involves a view of negation as a contradictory forming operator, and can therefore count as formal negation in every respect. However, as it is clear in contemporary glutty semantics of negation, one may distinguish between different accounts of the relationship between negation, contradiction and content. (...) I suggest that, differently from classical negation, and as glutty negation, dialectical negation has partial content. (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)

The history of philosophy risks a self-opacity whereby we overestimate or underestimate our proximity to prior modes of thinking. This risk is relevant to assessing Hegel’s appropriation by McDowell and Priest. McDowell enlists Hegel for a quietist answer to the problem with assuming that concepts and reality belong to different orders, viz., how concepts are answerable to the world. If we accept Hegel’s absolute idealist view that the conceptual is boundless, this problem allegedly dissolves. Priest enlists Hegel for a dialetheist (...) answer to the problem with assuming that truth and falsity are mutually exclusive, viz., how certain sentences are both true and false. If we accept Hegel’s dialectical view that certain contradictions are necessary, this problem allegedly dissolves. For both McDowell and Priest, we find a true friend in Hegel. I argue that McDowell’s and Priest’s appropriations of Hegel overestimate Hegel’s affinity with quietism and dialetheism. McDowell reads Hegel as a quietist who silences metaphysical claims and the skeptical questions they raise against commonsense, but neglects Hegel’s adaptation of ancient skepticism against commonsense. Priest reads Hegel as a dialetheist who subordinates formal logic to dialectical logic by affirming the truth of certain contradictions, but neglects Hegel’s commitment to resolving contradictions for the sake of truth qua whole. I diagnose their misreadings in terms of what Hegel regards as the three moments of logic and argue that while McDowell jumps to its third moment, Priest stalls at its second moment. According to Hegel’s Encyclopedia Logic, logic has three “moments”: the abstractive moment of the understanding, which “stops short” at fixed categories; the negative moment of dialectic, which discovers the “genuine nature” of the categories, viz., that each “passes over, of itself, into its opposite”; and the positive moment of speculation, which grasps the “unity” of categories through the “dissolution” of their inner opposition. Hegel warns that if these moments are “kept separate from each other […] they are not considered in their truth”. I suggest that quietist and dialetheist readings of Hegel fail to consider truthfully the unified moments of his logic. In his quietist critique of metaphysics, McDowell enlists Hegel to dissolve the problem with assuming the duality of concept and reality. But McDowell helps himself directly to the third moment of logic, where the unity of the categories, and hence the boundlessness of the conceptual, would be fully articulated. Since he arrives at the third moment prematurely, ignoring its prior moments, he obscures its truth (§1). In his dialetheist critique of formal logic, Priest enlists Hegel to dissolve the problem with assuming the duality of truth and falsity. But Priest restricts himself gratuitously to the second moment of logic, where contradictions within the categories are not yet resolved. Since he stalls at the second moment, severed from its final moment, he obscures its truth (§2). I argue we can extricate Hegel from quietist and dialetheist misreadings only if we grasp the truth of the three moments of logic. (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.

One of the most interesting debates in Hegel scholarship today comes from the question of how to interpret Hegel’s treatment of contradiction in the Science of Logic.1 Some interpreters claim that Hegel defiantly disregards the basic law of noncontradiction, which states that something cannot both be and not be in the same time, manner, or place, proposing instead that for Hegel true contradictions really do exist, and not only in rational conception but equally in the very fabric of reality. However, (...) other interpreters propose less direct readings of Hegel’s thesis from productive contradiction, either by limiting Hegel’s conception of contradiction to only certain forms, such as only in... (shrink)

The advent of quantum mechanics in the early 20 th Century had profound consequences for science and mathematics, for philosophy (Schrödinger), and for logic (von Neumann). In 1968, Putnam wrote that quantum mechanics required a revolution in our understanding of logic per se. However, applications of quantum logics have been little explored outside the quantum domain. Dummett saw some implications of quantum logic for truth, but few philosophers applied similar intuitions to epistemology or ontology. Logic remained a truth-functional ’science’ of (...) correct propositional reasoning. Starting in 1935, the Franco-Romanian thinker Stéphane Lupasco described a logical system based on the inherent dialectics of energy and accordingly expressed in and applicable to complex real processes at higher levels of reality. Unfortunately, Lupasco’s fifteen major publications in French went unrecognized by mainstream logic and philosophy, and unnoticed outside a Francophone intellectual community, albeit with some translations into other Romance languages. In English, summaries of Lupasco’s logic appeared ca. 2000, but the first major treatment and extension of his system was published in 2008 (see Brenner 2008). This paper is a further attempt to establish Lupasco’s concepts as significant contributions to the history and philosophy of logic, in line with the work of Gödel, general relativity, and the ontological turn in philosophy. (shrink)

To better understand what information is and to explain information-related issues has become an essential philosophical task. General concepts from science, ethics and sociology are insufficient. As noted by Floridi, a new philosophy, a Philosophy of Information (PI), is needed. In the 80’s, Wu Kun proposed a “The Basic Theory of the Philosophy of Information”, which became available in English only in 2010. Wu and Joseph Brenner then found that the latter’s non-standard “Logic in Reality” provided critical logical support for (...) Wu’s theory. In Part I of our paper, we outline the two basic theories as a metaphilosophy and metalogic for information. We offer our two theories as a further contribution to an informational paradigm. In Part II [WuB14], we develop the relation between information and social value as a basis for the ethical development of the emerging Information Society. (shrink)

1. The label conjunctive paraconsistency has been adopted to mean a consequence relation whereby ‘p and not p’ does not imply ‘p’ and ‘not p’ separately, so that Simplification in case of contradic...

1. There is a sense in which, quite generally, with his logic Hegel can be considered the forerunner of many projects taken up by successive (non-classical) logics—and this despite the fact that He...

In this paper, we discuss Hintikka’s theory of interrogative approach to inquiry with a focus on bracketing. First, we dispute the use of bracketing in the interrogative model of inquiry arguing that bracketing provides an indispensable component of an inquiry. Then, we suggest a formal system based on strategy logic and logic of paradox to describe the epistemic aspects of an inquiry, and obtain a naturally paraconsistent system. We then apply our framework to some cases to illustrate its use.

Philosophy and Literature is an internationally renowned refereed journal founded by Denis Dutton at the University of Canterbury, Christchurch. It is now published by the Johns Hopkins University Press. Since its inception in 1976, Philosophy and Literature has been concerned with the relation between literary and philosophical studies, publishing articles on the philosophical interpretation of literature as well as the literary treatment of philosophy. Philosophy and Literature has sometimes been regarded as iconoclastic, in the sense that it repudiates academic pretensions, (...) insidious jargon and institutional vogue. Dutton, who remains the editor, still writes a regular column. A distinctive feature of Philosophy and Literature was the annual Bad Writing Contest, held from 1995–98, which sought to identify (and publish) the ‘most stylistically lamentable passages’ of academic prose, often to great amusement. (shrink)

Slavoj Žižek and Graham Priest are two philosphers who have a unique place within respectively postmodernist and formal-logic philosophy. They both defend Hegelianism within the two domains that could historically be characterized a anti-Hegelian. We characterize their formal Hegelianism through respectively the style form of chiasm and the inclosure schema. In addition to this, we make concrete the two movements in which they are situated on the basis of two prominent philosophers: Jacques Derrida and Bertrand Russell. We outline the two (...) Hegelians#39; criticism of these figures and in this way we come to a refinement of the analogy and difference between the them. Finally, we explain how they could be considered in relation to their movements in general. (shrink)

Este é um conto sobre visão, pensamento e contradição, bem como sobre o papel que desempenham na primeira metade da Ciência da Lógica de Hegel. A Lógica começa com uma descida, nesse caso, uma queda do Ser ao Nada. Posteriormente, aproximadamente na metade de cada texto, há um certo paradoxo em que tudo está em jogo, a categoria da contradição. Nesse exato momento, o pensamento ao mesmo tempo falha e é renovado em um viés especulativo. Nessa seção, nos debruçamos sobre (...) algumas das interpretações influentes do uso hegeliano da contradição. Para isso, voltamo-nos a uma curiosa obra de arte, Pleiades, de James Turrell, como um exemplo estético dessa primeira queda. Progrediremos, então, através do texto com pensamento e visão como nosso duplo norteador em um passo relativamente rápido, sem desacelerar até encontrarmos a história de Hegel da contradição, onde mostro a natureza explosiva da contradição. Isso nos permitirá ver como Hegel invoca o poder da contradição para gerar a segunda metade da história da Ciência da Lógica. Eu começo com a descida do Ser ao Nada, o momento em que a escuridão emerge. (shrink)