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)

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.

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.

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 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 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)

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….

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)

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)

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.

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)

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)

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)

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)

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)

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)

The word “encyclopedia” comes to us from the Greek or, more precisely, is the deformed transcription, through Latin, of a erase in which we recognize a word composed of two elements, enkyklios and paideia, found in Quintilian in the ancient editions of De institutione oratoria (I, 10, 1). The expression itself, enkyklios paideia, appears only later, in the Hellenistic Age, under Roman domination, beginning with Dionysius of Halicarnassus (around the first century B.C.), but the concept goes back to the Eleatics, (...) especially to Hippias of Elis who, if we can believe the account in Plato's Dialogues, taught this total knowledge, later known with the term enkyklopaideia. (shrink)

We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability (...) of formulas with coefficients also works via verification of admissibility. (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.

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)

Ivan Karamazov’s famous dictum ‘If there is no God, anything is permitted’ in fact appears as a central meta-theme in many of Dostoevsky’s works. Western philosophers and writers repeatedly reinterpreted this idea. The most recent versions belong to the contemporary psychoanalytic and Freudian–Marxist philosophy. E.g. Jacques Lacan famously said that “if there is a God, then anything is permitted”, and Slavoy Zizek attributed this to Dostoevsky himself. The paper demonstrates which versions of this saying are present in Dostoevsky’s novel The (...) Brothers Karamazov, what meaning this meta-theme has within the integral structure of these literary works, and which of them express the author’s own position. The paper also provides insight into those bright reinterpretations of Dostoevsky’s central meta-theme that were given by certain representatives of contemporary European psychoanalytic philosophy. These readings are regarded as the significant attempts to explain the present from the standpoint of European psychoanalytic philosophy, made on the basis of elements of Dostoevsky’s artistic thinking. (shrink)

One of the main themes that Maxim Gorky developed throughout his life was that of the honest Russian man and the Russian intelligentsia’s endless role of enlightening him and protecting him...

'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.

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

In this paper the modal operator "x is provable in Peano Arithmetic" is incorporated into first-order theories. A provability extension of a theory is defined. Presburger Arithmetic of addition, Skolem Arithmetic of multiplication, and some first order theories of partial consistency statements are shown to remain decidable after natural provability extensions. It is also shown that natural provability extensions of a decidable theory may be undecidable.

Historical entitlement theories of property rights, which claim that individuals can acquire moral property rights over natural resources by appropriating them, traditionally face a strong objection: it is widely implausible that a single individual can unilaterally impose duties on everyone around him and yet, apparently, this is exactly what such theories allow. In this essay, I argue that the same problem appears in all other theories of distributive justice and if this problem was a reason to reject historical entitlement theories, (...) it would also be a reason to reject all rival theories. Which means that as long, as one is committed to any theory of distributive justice at all, she, at the risk of inconsistency, cannot rely on the aforementioned objection to criticize historical entitlement theories. (shrink)

The paper aims to present a critical analysis of the phenomenon and notion of exceptionalism in bioethics. The authors demonstrate that exceptionalism pertains to phenomena that are not (yet) entirely familiar to us and could potentially bear risks regarding their regulation. After an overview of the state of the art, we briefly describe the origins and evolution of the concept, compared to exception and exclusion. In the second step, they look at the overall development debates on genetic exceptionalism, compared to (...) other bioethical debates on exceptionalism, before presenting a detailed analysis of a specific case of early regulation of genetic screening. In the last part, the authors explain the historical background behind the connection between exceptionalism and exclusion in these debates. Their main conclusion is that while the initial stage of the discussion is shaped by the concept of exceptionalism and awareness of risks of exclusion, the later development centers around exceptions that are needed in detailed regulatory procedures. (shrink)

Neuroscience has established several brain pathways that process visual information. Distinct neural circuits analyze body appearance and movement providing information about the person’s cognitive and emotional states. The activity of the pathways depends on the salience of visual stimuli for the organism in the given circumstances. Since ballet performances are not among the crucial events for the viewer’s organism, not all viewers perceive and interpret bodily signs that express the mental state of the dancer. Treatment of the dancer as close (...) other activates the neural circuits that elaborate emotions, this enables the viewer to feel the internal state of the dancer and enrich the interpretation of the scenic action. (shrink)

This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive (...) bilattices with conflation. (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)

Tracing how the logic of inoperativity works in the domains of language, law, history and humanity, 'Agamben and Politics' systematically introduces the fundamental concepts of Agamben's political thought and a critically interprets his insights in the wider context of contemporary philosophy.

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)