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.

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)

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)

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)

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.

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)

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)

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.

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)

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)

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.

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.

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)

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)

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 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)

Why does the theory of law have such a significant role in Russian liberalism, and how is this related to the state of the legal system in Russia and to the public’s legal consciousness? This intro...

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….

'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.

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)

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)

Early normative studies of human behavior revealed a gap between the norms of practical rationality (what humans ought to do) and the actual human behavior (what they do). It has been suggested that, to close the gap between the descriptive and the normative, one has to revise norms of practical rationality according to the Quinean, engineering view of normativity. On this view, the norms must be designed such that they effectively account for behavior. I review recent studies of human perception (...) which pursued normative modeling and which found good agreement between the normative prescriptions and the actual behavior. I make the case that the goals and methods of this work have been incompatible with those of the engineering approach. I argue that norms of perception and action are observer-independent properties of biological agents; the norms are discovered using methods of natural sciences rather than the norms are designed to fit the observed behavior. (shrink)

The book represents a comprehensive account of the principles of the philosophy of the pseudoabsolute and is intended for readers interested in the issues of theoretical philosophy. It is also meant for a wide range of readers interested in the relative and absolute nature of human mentality.

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)

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)

Стаття присвячена темі ролі любовної прихильності в соціальному житті тварин і людини. Звертається увага на значущість емпатії серед деяких видів моногамних ссавців, яка зіграла важливу роль у розвитку любовних стосунків. Розглядається гіпотеза антрополога Оуена Лавджоя, згідно з якою любов і турбота зіграли винятково важливу роль в еволюції ранніх гомінідів, що стало можливою причиною редукції ікл, прихованої овуляції, розвитку двоногості та збільшення обсягу мозку. Іншими словами, сімейні стосунки древніх ардипітеків виявляються ключем до розуміння еволюції Homo sapiens. Аналізується гіпотеза Чорної Королеви, яка (...) пропонує одне з пояснень популярності статевого розмноження серед еукаріотичних організмів. (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)

Name der Zeitschrift: Byzantinische Zeitschrift Jahrgang: 107 Heft: 1 Seiten: 113-138.

The present paper concentrates on the comments of Michael of Ephesus to the 10th book of the Nicomachean Ethics. In particular it investigates the way in which Michael of Ephesus conceived the relationship between political and theoretical happiness. Doing so allows to evidence the theoretical ties that connect Michael of Ephesus with the Peripatetic philosopher Aspasius and demonstrates the influence of Proclus on Michael of Ephesus.

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)