Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

Many pigmented heterokonts are able to synthesize elements of their cell walls (the frustules) of dense biogenic silica. These include diatom algae, which occupy a significant place in the biosphere. The siliceous frustules of diatoms have species‐specific patterns of surface structures between 10 and a few hundred nanometers. The present review considers possible mechanisms of uptake of silicic acid from the aquatic environment, its transport across the plasmalemma, and intracellular transport and deposition of silica inside the specialized Silica Deposition Vesicle (...) (SDV) where elements of the new frustule are formed. It is proposed that a complex of silicic acid with positively charged proteins silaffins and polypropylamines remains a homogeneous solution during the intracellular transport to SDV, where biogenic silica precipitates. The high density of the deposited biogenic silica may be due to removal of water from the SDV by aquaporins followed by syneresis—a process during which pore water is expelled from the network of the contracting gel. The pattern of aquaporins in the silicalemma, the membrane embracing the SDV, can determine the pattern of species‐specific siliceous nanostructures. BioEssays 30:328–337, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

Byzantine intellectuals not only had direct access to Neoplatonic sources in the original language but also, at times, showed a particular interest in them. During the Early Byzantine period Platonism significantly contributed to the development of Christian doctrines and, paradoxically, remained a rival world view that was perceived by many Christian thinkers as a serious threat to their own intellectual identity. This problematic relationship was to become even more complex during the following centuries. Byzantine authors made numerous attempts to harmonize (...) Neoplatonic doctrines with Christianity as well as to criticize, refute and even condemn them. The papers assembled in this volume discuss a number of specific questions and concerns that drew the interest of Byzantine scholars in different periods towards Neoplatonic sources in an attempt to identify and explore the central issues in the reception of Neoplatonic texts during the Byzantine era. This is the first volume of the sub-series "Byzantinisches Archiv - Series Philosophica", which will be dedicated to the rapidly growing field of research in Byzantine philosophical texts. (shrink)

The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. Moreover, (...) a tableau calculus is defined for the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. It is shown that MBL can be faithfully embedded into the bimodal logic \ over the non-modal vocabulary of MBL. On the way from \ to MBL, the Fischer Servi-style modal logic \ is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE, and \ is shown to be characterized by the class of all models for \. Moreover, \ is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for \. Moreover, the notion of definitional equivalence is suitably weakened, so as to show that \ and \ are weakly definitionally equivalent. (shrink)

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...) resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus. (shrink)

N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. (...) Finally, subdirectly irreducible N4-lattices are described. (shrink)

Coronavirus disease 2019 (COVID-19) first appeared in China in late 2019 and since then it has become a pandemic. Various countries, in accordance with their cultures, have adopted different approaches to deal with the spread of this disease. The dimensions of this disease and its global spread are such that it will certainly have enormous effects on various aspects of human life for many years. One of these issues is examining the approach of religious countries in dealing with this crisis. (...) The issue of science and religion is one of the main issues in the philosophy of religion. A historical event that human society is struggling with today is the COVID-19 crisis. The issues of religion and science were intertwined during the COVID-19 outbreak, contrary to what some thought. This shows that the opposition between religion and science is not real but aims to attack religion without a valid reason. Given the importance of the subject, this article addresses two aspects of people’s exposure to religion during the COVID-19 period. On the one hand, the researchers’ field observations indicate that group of citizens has turned towards religious teachings since the beginning of the COVID-19 crisis. On the other hand, another group of citizens have distanced themselves from religiosity, raising the duality of science and religion.Contribution: This article describes the dual attitude of citizens towards religiosity due to the occurrence of COVID-19, which has not been previously considered in research. (shrink)

We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides with the logic characterized by the (...) class of all involutive Routley star information frames. This result provides a much simplified semantics for HYPE and also a simplified axiomatization, which shows that HYPE is identical with the modal symmetric propositional calculus introduced by G. Moisil in 1942. Moreover, it is shown that HYPE can be faithfully embedded into a normal bi-modal logic based on classical logic. Against this background, we discuss the notion of hyperintensionality. (shrink)

This article addresses the relationship between ontology and politics in Jean-Luc Nancy’s theory of democracy by probing the implications of his latest ontological innovation, the concept of struction. We argue that Nancy’s democracy is a mode of politics that makes the radical pluralism of struction legitimate, opening and guarding a political space for the coexistence of the incommensurable. From this perspective, and despite Nancy’s own skepticism about the concept of biopolitics, the notion of struction opens a pathway for theorizing democracy (...) in a biopolitical key as the regime of coexistence of radically incommensurable forms of life in the absence of any coordinating principle. We nonetheless take issue with Nancy’s prescription for democracy to remain devoid of any political affirmation of its own. Instead, we suggest that the prescriptive content of democracy consists in the affirmation of the contingency of all the forms of life that coexist in it, which implies their freedom, equality, and comm... (shrink)

We outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflectionA→KAis valid and the factivity of knowledge holds in the formKA→ ¬¬A‘known propositions cannot be false’.We show that the traditional form of factivityKA→Ais a distinctly classical principle which, liketertium non datur A∨ ¬A, does not hold intuitionistically, but, along with the whole of (...) classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA¬A).Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it. (shrink)

Sergei Prozorov challenges the assumption that the biopolitical governance means the end of democracy, arguing for a positive synthesis of biopolitics and democracy. He develops a vision of democratic biopolitics where diverse forms of life can coexist on the basis of their reciprocal recognition as free, equal and in common.

We challenge the popular classification of the trolley problem as a series of thought experiments in possible worlds. The trolley world is, in fact, impossible. It is, rather, a fantasy world of role-playing language game within a graphic narrative. The trolley world has all the characteristics of a game that game designers seek to reproduce. Thus, the following paper is a spoilsport, revealing the playful aspects of the trolley problem. Historically, the trolley problem substantially contributed to ethical discourse. Nowadays, attempts (...) to resolve it generate few applications and weigh down the theoretical discourse. We argue that it makes less sense to view the trolley problem as a flawed problem-solving, probative, or heuristic tool, than to view it as a strong intuition pump, well suited to teach fundamental ethical issues. While the process of engaging with the trolley problem may be prolific, the problem itself is not of our world. (shrink)

The article critically engages with Giorgio Agamben’s reading of Rousseau in order to explore the affinities between the two authors’ subtractive approach to political subjectivation. In The Kingdom and the Glory. Agamben argues that Rousseau’s Social Contract reproduces, in a secularized manner, the providential paradigm of government, whose origins Agamben finds in early Christianity. This paradigm establishes a fictitious articulation between transcendent sovereignty and immanent government, presenting particular acts of government as emanating from general divine laws. We shall demonstrate that (...) Rousseau was neither unaware of the problematic character of this paradigm nor did he venture to conceal its problems, but, on the contrary, he highlighted them throughout the Social Contract, whose key motif was the danger of the contamination of general will by particular acts, identities or interests. The same wariness of particularism characterizes Rousseau’s Reveries of the Solitary Walker, often read as entirely heterogeneous to the political project of the Social Contract. By reading these two works together as the affirmation of generic existence against all forms of particularism, we bring Rousseau’s analysis closer to Agamben’s own attempts to rethink politics as subtracted from all identity predicates and contained in the affirmation of ‘whatever being’. The elucidation of affinities between Rousseau and Agamben will permit us to identify the limits of this subtractive approach to politics and outline an alternative to it. (shrink)

'Ontological Semantics' introduces a comprehensive approach to the treatment of text meaning by computer, arguing that being able to use meaning is crucial to the success of natural language processing applications.

This work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ t and ⊨ f, determined via truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN 3 as a twist-structure over the two-element Boolean algebra.

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions (...) and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK. (shrink)

In this paper individual proofs are integrated into provability logic. Systems of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure. Completeness theorems with respect to the arithmetical interpretation are proved.

The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.

We prove here that the intuitionistic theory $T_{0}\upharpoonright + UMID_{N}$ , or even $EEJ\upharpoonright + UMID_{N}$ , of Explicit Mathematics has the strength of $\prod_{2}^{1} - CA_{0}$ . In Section I we give a double-negation translation for the classical second-order $\mu-calculus$ , which was shown in [ $M\ddot{o}02$ ] to have the strength of $\prod_{2}^{1}-CA_{0}$ . In Section 2 we interpret the intuitionistic $\mu-calculus$ in the theory $EETJ\upharpoonright + UMID_{N}$ . The question about the strength of monotone inductive definitions in (...) $T_{0}$ was asked by S. Feferman in 1982, and - assuming classical logic - was addressed by M. Rathjen. (shrink)

On peut distinguer trois cas de correspondances différentes entre les « scénarios schématiques » et le domaine narratif folklorico-littéraire : 1. La narration constitue la projection de la « dramaturgie de la vie » (une telle projection n’est évidemment ni directe ni complète) ;2. La structure de l’univers des personnages et la structure événementielle du narratif influencent la formation des « scénarios de la vie », en conditionnant l’apparence morphologico-compositionnelle de l’un et de l’autre ;3. La coincidence de la « (...) dramaturgie de la vie » et de la « dramaturgie de la narration»s’explique par le fait qu’elles ont des sources communes ; ces sources pourraient être les modèles mentaux de la tradition, qui dictent à un homme des « règles de comportement » d’une part, et qui s’incarnent dans la narration folklorico-littéraire d’autre part. Le « scénario schématique » possède une structure événementielle, situationnelle et actantielle. À cette structure correspond un certain niveau d’interprétation qui souvent la lie directement à la conscience religieuse et mythologique ; une telle conscience — compte tenu du fait qu’une conceptualisation globale de tous les aspects de la vie humaine caractérise le mythe — englobe, par sa nature même, les « blocs interprétatifs » pertinents pour pratiquement tous les précédents événementiels. Le « scénario schématique » est donc lié au domaine des croyances et concepts actuels, lié aussi aux systèmes de valeurs et normes éthiques, etc. ; il est possible de reconstituer nombre de ces croyances, concepts, valeurs et normes à l’aide de l’histoire vécue qui nous occupe. D’ordinaire, ces interprétations ne représentent pas le fond neutre des événements, mais un élément actif et dynamique qui agit directement sur le développement de ces événements. (shrink)

Two traditions have had a great impact on the theoretical and experimental research of perception. One tradition is statistical, stretching from Fechner's enunciation of psychophysics in 1860 to the modern view of perception as statistical decision making. The other tradition is phenomenological, from Brentano's “empirical standpoint” of 1874 to the Gestalt movement and the modern work on perceptual organization. Each tradition has at its core a distinctive assumption about the indivisible constituents of perception: the just-noticeable differences of sensation in the (...) tradition of Fechner vs. the phenomenological Gestalts in the tradition of Brentano. But some key results from the two traditions can be explained and connected using an approach that is neither statistical nor phenomenological. This approach rests on a basic property of any information exchange: a principle of measurement formulated in 1946 by Gabor as a part of his quantal theory of information. Here the indivisible components are units (quanta) of information that remain invariant under changes of precision of measurement. This approach helped to understand how sensory measurements are implemented by single neural cells. But recent analyses suggest that this approach has the power to explain larger-scale characteristics of sensory systems. (shrink)

Some scientists and philosophers, based on scientific discoveries and empirical evidence, argue that free will does not exist. Some authors defend the opposite opinion. The universality of their reasoning unites opponents. They seek to correlate scientific knowledge with the entire sum of human actions and, consequently justify the existence of freedom of will or its absence. In the paper, I propose to narrow the focus of the issue to the study of the degree of freedom of individual actions or certain (...) classes of actions. For this, I introduce the epistemic criterion, according to it, recognition of the action as not free requires knowledge of the causes of the action for which the agent is not responsible. I analyse two groups of cases: those where scientific knowledge reveals hidden causes of behavior and those where the causes remain unknown. Actions from the second group still constitute an essential part of our behavior. The amount of knowledge about the causes of actions will increase over time, but this knowledge will never be comprehensive. (shrink)

This work presents the two surviving letters preserved from the extensive correspondence of V.E. Sesemann, a professor of philosophy at Vilnius University at the time (1961), and B.D. Dandaron, a Buddhist teacher who was a researcher at the Buryat Integrated Research Institute at that time. The letters discuss the authors’ current work and creative plans, as well as everyday life and resettling after release from prison in 1956. In his letter, B.D. Dandaron devotes significant attention to a list of literature (...) that he was using in writing a study on aesthetics and/or that was mentioned in the records of the lectures of V.E. Sesemann in the prison camp. The letters give some idea of the nature of the relations between the correspondents and the areas of their research interests. The publication is preceded by a preface, which offers reflections on the context of the appearance of lectures on aesthetics that formed the basis of B.D. Dandaron’s research interest in this issue. The preface also provides context on the prison camp “seminar” on philosophy, in which the correspondents were active participants. V.E. Sesemann lectured on a wide range of areas in Western philosophy, including aesthetics, the history of philosophy, and philosophical anthropology. B.D. Dandaron lectured on the philosophy and practice of Buddhism. B.D. Dandaron’s particular interest in aesthetic issues was due to the fact that in the system of Buddhist teachings he developed, he paid great attention to the development of emotional intuition (associated with aesthetic perception) as an intermediate link between the rational intuition inherent in every person and the emotional-mystical intuition developed during yogic practice. (shrink)

I argue that teaching evaluation tools may function as ethical codes, and answer certain demands that ECs cannot sufficiently fulfill. In order to be viable, an EC related to the teaching profession must assume a different form, and such a form is already present in several of the contemporary TETs. The TET matrix form allows for certain features that are incompatible with the EC form. The TET’s benchmark scale – ranging from below the acceptable to the ideal level across the (...) dimensions of teachers’ competence – allows it to answer the demands upon ECs, raised by the EC critics. TETs embrace both minimal requirements and lofty ideals, while ECs of different types have a hard time combining these two features. TETs relate to different dimensions of teacher competence, connecting ethical and professional components with didactical, managerial and cognitive components, without lumping them together. (shrink)

And so that there may be less difficulty in understanding what I shall say on this matter, I should like that those not versed in anatomy should take the trouble, before they read this, to have cut up before their eyes the heart of some large animal that has lungs—for it is in all respects sufficiently similar to the heart of man….

While Foucault’s work on biopolitics continues to inspire diverse studies in a variety of disciplines, it has largely been missing from the debates on the possibility of “affirmative biopolitics” which have been primarily influenced by the work of Agamben and Esposito. This article restores Foucault’s work to these debates, proposing that his final lecture course at the Collège de France in 1983–1984 developed a paradigm of affirmative biopolitics in the reading of the Cynic practice of truth-telling ( parrhesia). The Cynic (...) problematization of the relation between truth and life and their transvaluation of conventional truths by relocating them to the domain of bare life not only seeks to transform one’s life in accordance with the truth but also, through the confrontation with the existing conventions and norms, to transform the world as such. Cynic parrhesia is thus biopolitical, insofar as it reclaims the power of one’s life from the social order and its rationalities of government and applies it to oneself, investing one’s existence with truth. Since Foucault developed this reading of Cynicism in the context of his political engagement on behalf on East European dissidents, the article proceeds to analyse the resonances between parrhesia and Václav Havel’s idea of “living within the truth,” elaborating the biopolitical significance of both practices. We conclude by addressing the implications of our interpretation for Foucault scholarship and the wider debates on biopolitics. (shrink)

Pereboom and Caruso propose the quarantine model as an alternative to existing models of criminal justice. They appeal to the established public health practice of quarantining people, which is believed to be effective and morally justified, to explain why -in criminal justice- it is also morally acceptable to detain wrongdoers, without assuming the existence of a retrospective moral responsibility. Wrongdoers in their model are treated as carriers of dangerous diseases and as such should be preventively detained (or rehabilitated) until they (...) no longer pose a threat to society. Our main concern in this paper is that Pereboom and Caruso adopt an idiosyncratic meaning of quarantine regulations. We highlight a set of important disanalogies between their quarantine model and the quarantine regulations currently adopted in public health policies. More specifically, we argue that the similarities that Pereboom and Caruso propose to substantiate their analogy are not consistent—despite what they claim—with the regulations underlying quarantine as an epidemiological process. We also notice that certain quarantine procedures adopted in public health systems are inadequate to deal with criminal behaviors. On these grounds, we conclude that Pereboom and Caruso should not appeal to the quarantine analogy to substantiate their view, unless they address the issues and criticism we raise in this paper. (shrink)

Saul Aaron Kripke, the most influential philosopher and logician of his generation, died on September 15, 2022, at the age of 81.

The article addresses Giorgio Agamben’s critical commentary on the global governance of the Covid-19 pandemic as a paradigm of his political thought. While Agamben’s comments have been criticized as exaggerated and conspiratorial, they arise from the conceptual constellation that he has developed starting from the first volume of his Homo Sacer series. At the centre of this constellation is the relation between the concepts of sovereign power and bare life, whose articulation in the figure of homo sacer Agamben traces from (...) the Antiquity to the present. We shall demonstrate that any such articulation is impossible due to the belonging of these concepts to different planes, respectively empirical and transcendental, which Agamben brings together in a problematic fashion. His account of the sovereign state of exception collapses a plurality of empirical states of exception into a zone of indistinction between different exceptional states and the normal state and then elevates this very indistinction to the transcendental condition of intelligibility of politics as such. Conversely, the notion of bare life, originally posited as the transcendental condition of possibility of positive forms of life, is recast as an empirical figure, whose sole form is the absence of form. We conclude that this problematic articulation should be abandoned for a theory that rather highlights the non-relation between sovereign power and bare life, which conditions the possibility of resistance and transformation that remains obscure in Agamben’s thought. (shrink)

This paper argues that unusual coincidences, particularly those involving historical events, can be viewed as design patterns, suggesting an intelligent influence over the course of events. A compelling case examined in detail using probability theory concerns the presidencies of Abraham Lincoln (1809–1865) and John F. Kennedy (1917–1963). This and other coincidences involving historical figures disfavor the materialistic perspective and point to the presence of an intelligent agent acting on a global scale, beyond the arrow of time, influencing human lives and (...) the course of history. (shrink)

The problematic of biopolitics has become increasingly important in the social sciences. Inaugurated by Michel Foucault's genealogical research on the governance of sexuality, crime and mental illness in modern Europe, the research on biopolitics has developed into a broader interdisciplinary orientation, addressing the rationalities of power over living beings in diverse spatial and temporal contexts. The development of the research on biopolitics in recent years has been characterized by two tendencies: the increasingly sophisticated theoretical engagement with the idea of power (...) over and the government of life that both elaborated and challenged the Foucauldian canon and the detailed and empirically rich investigation of the concrete aspects of the government of life in contemporary societies. Unfortunately, the two tendencies have often developed in isolation from each other, resulting in the presence of at least two debates on biopolitics: the historico-philosophical and the empirical one. This Handbook brings these two debates together, combining theoretical sophistication and empirical rigour. The volume is divided into five sections. While the first two deal with the history of the concept and contemporary theoretical debates on it, the remaining three comprise the prime sites of contemporary interdisciplinary research on biopolitics: economy, security and technology. Featuring previously unpublished articles by the leading scholars in the field, this wide-ranging and accessible companion will both serve as an introduction to the diverse research on biopolitics for undergraduate students and appeal to more advanced audiences interested in the current state of the art in biopolitics studies. (shrink)

Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models . We show that Fitting models for Justification Logic naturally encode modular models and can be regarded as convenient pre-models of the (...) former. (shrink)

Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK -lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK -lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK . Finally, we describe invariants determining a twist-structure over a (...) modal algebra. (shrink)

We shall be concerned with the modal logic BK—which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding ‘strong negation’. Though all four values ‘truth’, ‘falsity’, ‘neither’ and ‘both’ are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for ‘neither’ or/and ‘both’ leads to quite unexpected results. To be more (...) precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics. (shrink)

The article presents a conception of the end of history, developed on the basis of Giorgio Agamben’s critical engagement with Alexandre Kojève’s reading of Hegel. Departing from Agamben’s concept of inoperosity as an originary feature of the human condition, we argue that the proper or ‘second’ end of history consists not in the fulfilment of its dialectical process but rather in the radical interruption of the dialectic that terminates the teleological dimension of social praxis. Introducing the figure of the ‘workless (...) slave’ into the scenario of the Master—Slave dialectic, the article demonstrates how the dialectic of history may be ended in a non-dialectical fashion through inoperative praxis that subtracts itself from the struggle for recognition. In the conclusion, the implication of this reading of the end of history for the understanding of Agamben’s ‘coming politics’ is addressed. (shrink)

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...) relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of /stability/: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting /stable knowability principle/ and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience. (shrink)