Closed timelike curves (CTCs) appear in many solutions of the Einstein equation, even with reasonable matter sources. These solutions appear to violate causality and so are considered problematic. Since CTCs reflect the global properties of a spacetime, one can attempt to extend a local CTC-free patch of such a spacetime in a way that does not give rise to CTCs. One such procedure is informally known as unwrapping. However, changes in global identifications tend to lead to local effects, and unwrapping (...) is no exception, as it introduces a special kind of singularity, called quasi-regular. This “unwrapping” singularity is similar to the string singularities. We define an unwrapping of a (locally) axisymmetric spacetime as the universal cover of the spacetime after one or more of the local axes of symmetry is removed. We give two examples of unwrapping of essentially 2+1 dimensional spacetimes with CTCs, the Gott spacetime and the Gödel spacetime. We show that the unwrapped Gott spacetime, while singular, is at least devoid of CTCs. In contrast, the unwrapped Gödel spacetime still contains CTCs through every point. A “multiple unwrapping” procedure is devised to remove the remaining circular CTCs. We conclude that, based on the given examples, CTCs appearing in the solutions of the Einstein equation are not simply a mathematical artifact of coordinate identifications. Alternative extensions of spacetimes with CTCs tend to lead to other pathologies, such as naked quasi-regular singularities. (shrink)

In Il’enkov’s “Cosmology of mind,” written in his younger days in the tradition of Spinoza and Engels, the thinking mind appears as a necessary attribute of matter. Like all other main forms of matter in motion, the mind has its cosmic purpose and predestination. Il’enkov argued that it has to close the beginning and the end of the Big Cycle in order to return the dying Universe to its fiery youth. Il’enkov believed that this is the sole way to save (...) the Universe from “thermal death” following the inevitable increase in entropy. (shrink)

Im Zentrum der Monographie von Claudia Rapp steht die Figur des christlichen Bischofs im Kontext der spätantiken Gesellschaft. Das Buch besteht aus zwei Teilen und einem Epilog. Der erste Teil (S. 1–152) erfüllt eine zweifache Aufgabe: Er bietet (1.) eine Übersicht über die relevante Forschungsliteratur und Positionierung der vorliegenden Arbeit in der Forschungslandschaft und (2.) die Präsentation des von der Verf. entworfenen Erklärungsmodells, das die gesamte Untersuchung konzeptuell bestimmt. Im zweiten Teil (S. 155–289) betrachtet die Verf. die Entwicklung der Rolle (...) des christlichen Bischofs im Kontext spätantiker Städte und Römischen Reiches vom 3. bis zum 6. Jahrhundert anhand von archäologischem, hagiographischem und juristischem Quellenmaterial. Im Epilog (S. 290–302) wird die Figur des Bischofs im Spiegel der Grabinschriften prominenter Amtsträger skizziert. Ein Quellen- und Literaturverzeichnis sowie ein Index beschließen den Band (S. 303–346). (shrink)

Die Glosse Suda ε 1756 wird in der Forschung mit der von Damaskios von Damaskos verfaßten Vita des Philosophen Isidoros in Verbindung gebracht. Tatsächlich aber steht sie in engerem Zusammenhang mit der aus dem Werk des Johannes Antiocheus entnommenen Glosse Suda β 246 und ist daher aus dem Corpus des Damaskios zu streichen und Ioannes Antiocheus zuzuschreiben.

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)

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)

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)

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)

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)

Let ???? be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of ???? in which the image of R (¬R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on ???? and R, a necessary and sufficient condition for the existence of a computable copy ℬ of ???? in which the image of R (¬R, resp.) (...) is simple (immune, resp.). (shrink)

The article takes Giorgio Agamben’s declaration of his optimism with regard to the possibilities of global political transformation as a point of departure for the inquiry into the affirmative aspects of Agamben’s political thought, frequently overshadowed by his more famous critical claims. We reconstitute three principles grounding Agamben’s optimism that pertain respectively to the total crisis of the contemporary biopolitical apparatuses, the possibility of a radically different form-of-life on the basis of their residue and the minimalist character of this transformation (...) that consists entirely in the subtraction of existence from these apparatuses. While the first two principles are unproblematic in the wider context of Agamben’s work, the third principle introduces the problematic of will that remains highly ambiguous in his philosophy. In the remainder of the article we address this ambiguity in an analysis of Agamben’s reading of Melville’s ‘Bartleby the Scrivener’ and conclude that Agamben’s optimism ultimately consists in the affirmation of absolute contingency, beyond both will and necessity. (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)

This work treats the problem of axiomatizing the truth and falsity consequence relations, $ \vDash _t $ and $ \vDash _f $, determined via truth and falsity orderings on the trilattice SIXTEEN₃. The approach is based on a representation of SIXTEEN₃ as a twist-structure over the two-element Boolean algebra.

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.

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)

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.

Paradigms of historiography of philosophy in India have being changed since late 19th c. till present, depending on the social and cultural context of the history of Indian philosophy as a part of contemporary Indian culture. This change manifests itself in the conceptions of Indian historians concerning the teaching of Buddhist Mahāyāna school of Yogācāra (4th c. and later). Historians of colonial times, basing themselves on the philosophy of Neovedаntism (S. Radhakrishnan, S. Dasgupta), regarded Buddhism as a derivate of late (...) Vedic culture and Yogācāra as a teaching that reflected - though in an essentially transmuted form - the ideology of Upaniṣads. The latter, according to Neovedantists, was based on the postulate of the existence of the single cosmic soul - Brahman, the true human Self (Ātman) being identical to it. Historians of the late colonial and early postcolonial times (P.T. Raju, D.P. Chattopadhyaya, A.K. Chatterjee, partly also S. Dasgupta) brought Yogācāra closer to the teachings of European idealism, mainly to conceptions of G. Berkeley, G.W.F. Hegel, F. Bradley, J.E. McTaggart, trying to demonstrate a principal identity of fundamental problems in Indian and Western philosophy. At the same time, they brought Yogācāra together with the teaching of Brāhmaṇic school, Advaita Vedānta, regarded as another form of Indian idealism. In later times, following the evolution of contemporary Indian culture and changings in its social and political context, historians like D.J. Kalupahana became to analyze Yogācāra as a kind of philosophy of mind. All these facts show the dependence of strategies of historico-philosophical studies in India on its social, political and cultural context: in the Yogācāra teaching mainly those aspects call attention that a historian sees as the closest to the problematic field of contemporary philosophy. (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 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)

The research is devoted to the study of the phenomenon of spiritual culture of Modern times - creationism. Authors analyze the causes of creationist teachings, as well as develop a classification of forms of creationism. As such, the following are distinguished and analyzed: biblical creationism, scientific creationism, theological evolutionism, teleological creationism, alterism, missionary creationism. Biblical creationism is a literal understanding of the texts of the Bible relating to the creation of the Earth and man. Scientific creationism is an attempt by (...) individual scientists to combine scientific knowledge with religious beliefs. It gathers scientific evidence in favor of the biblical narrative, and, at the same time, rational arguments against the scientific theory of evolution. On the contrary, theological evolutionism, especially in the form of concordism, tries to reconcile the scientific and religious view of evolution. This is achieved through the interpretation of Biblical symbols through modern scientific concepts, or by the creation of a new pseudo-religion (for example, Teilhardism). Teleological creationism, in the modern form of Intelligent Design theory, popular in Western Protestantism, using the data of natural sciences, criticizes the foundations of the theory of biological evolution, thus demonstrating the gap of natural causality in order to justify the supernatural purposefulness of the Universe. Alterism asserts that the very nature of the world before original sin was different, therefore, the current knowledge of nature cannot correspond to the original plan of God reflected in the Bible. For the first time, highlighted and explored in this work, missionary creationism seeks to interpret the Bible from the point of view of concepts of modern science in order to bring a person with an already formed scientific picture of the world to faith. It is shown that most of the above forms demonstrate a pseudoscientific or pseudo-religious essence. The authors make an assumption about the origins of creationist teachings rooted in the introduction of elements of Neoplatonic philosophy into Christian teaching. The seeming contradiction between science and religion in understanding the evolution of nature finds its explanation through the disclosure of creationism's claim to understand the world as a "thing in itself". (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)

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)

One of the main fields of consciousness studies is the search for the function of consciousness. The article deals with the hypothesis of the function of imagination as an attribute of consciousness. In the regard of the issues of the attributes of consciousness, the author analyzes the phenomenon of aphantasia, that is, lack of imagination. Despite the lack of formalized ideas about the function of consciousness and despite the scientific trend of the narrowing research areas where subjective experience is necessary (...) for a normal behavior of brain, there is a tendency to expand the presence of consciousness in the world in the modern Western philosophy of consciousness. The result of this “emancipation of consciousness” is the idea of the theoretical essential closeness of a human being and other agents: animals, artificial intelligence, plants. A consequence of the “emancipation of consciousness” is the emergence of modern versions of panpsychism, which propose expanding the space of consciousness to the world as a whole. However, studies in the field of conscious cognitive processes show that the processes that need the participation of consciousness, according to the standard intuitions, in some cases successfully performed without it. For example, the phenomenon of aphantasia shows that the tasks of imagination are performed in the absence of the ability to imagine. Therefore, it is important to take also into account the theoretical possibility of the lack of the realization of the function of consciousness. This makes it possible to ask a question about the presence of consciousness in the space that is traditionally endowed with consciousness, according to the dominant views in philosophy. Therefore, by approaching the question of the attributes of consciousness, the author demonstrates the limitations of the program for the emancipation of consciousness and offers an alternative solution to the question of the scale of the presence of consciousness in the world. (shrink)

A paedophile is a person with a sexual attraction to children; some paedophiles commit child sex abuse offences. For such acts, they hold moral and legal responsibility, which presupposes that paedophiles are moral agents who can distinguish right from wrong and are capable of self-control. Like any other moral agents, paedophiles have moral duties. Some moral duties are universal, e.g., the duty not to steal. Whether there are any specific moral duties related to paedophilia is the topic of this paper. (...) I argue that the moral duty not to commit child sex abuse is universal, and the duty to reduce the individual risk of child sex abuse is specific to paedophiles. I further argue that any society has a moral duty to help paedophiles reduce the risk. Both duties provide grounds for moral judgement. Paedophiles should be judged not for their sexual interest but for their efforts to avoid child sex abuse. If a paedophile has an opportunity to reduce the risk of child sex abuse, he is obliged to do so. Unfortunately, societies rarely provide such opportunities and hence fail in their moral duty to paedophiles and children. (shrink)

The article addresses the critical strategy of profanation in the philosophy of Giorgio Agamben, focusing on the example of pornography. Agamben’s references to pornography as a site of radical political transformation have recently been criticized as abstruse, vacuous or absurd. Moreover, his own work on the concentration camps in the Homo Sacer series has been disparagingly referred to as ‘pornography of horror’. This article ventures to refute these accusations by interpreting Agamben’s paradigmatic use of pornography in the context of his (...) wider project of profanation, understood as the overcoming of all social separations and the return of objects of social praxis to free use. Read in this context, pornography is grasped as the paradigmatic site of the constitution of the unprofanable, the epitome of the late capitalist ‘society of the spectacle’ and thus the primary target of profanatory criticism. In the remainder of the article we elucidate the logic of Agamben’s profanatory strategy and conclude that, far from being politically irrelevant, profanation constitutes the condition of the actualization of Agamben’s messianic ideal of a generic and non-exclusive community. (shrink)

The article addresses the ‘messianic turn’ in contemporary continental philosophy, focusing on the concept of the katechon as the restraining force that delays the advent of the Antichrist in the Second Letter to the Thessalonians. While Carl Schmitt held the passage on the katechon to ground the Christian doctrine of state power, Giorgio Agamben’s reading of Pauline messianism rather posits the ‘removal’ of the katechon as the pathway for messianic redemption. In our argument, the significance of this text goes beyond (...) the persistence of a vestige of the theological in modern politics. On the contrary, the logic of the katechon only comes into its own under modern nihilism as the resolution of the problem of social order in the absence of the eschatological dimension. The article focuses on the lethal paradox of the logic of the katechon, whereby the function of protection and restraint is converted into violence and anomie, and global political order becomes indistinguishable from global civil war. We conclude by outlining the conditions for suspending the katechonic function in a critical engagement with Agamben’s messianic politics. (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.

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)

This article examines a still contentious question: how conservative and liberal elements are combined in Boris N. Chicherin’s worldview and political doctrine. It considers several points of view...

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...

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. 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)

In the following paper we relate to the terms such as ‘true’ and ‘real’ in conjecture with dual character concepts such as ‘scientist’ and ‘artist’. They are often integrated into phrases broadly viewed as persuasive definitions. We argue that persuasive definitions are usually intended to marginalize individuals, sub-groups, and even objects, within a group. They may also be employed to elevate or preserve the status of a group by disassociating it with its marginal members, their actions, and characteristics. For example, (...) ‘true’ art may be stipulatively defined as having certain features to persuade us to accept the marginalization of those objects of art that lack them, and to elevate the social status of the authors of the objects that have them. ‘No true Scotsman is cruel’ is uttered to distance the normative Scots from those who run afoul, so that they can maintain untarnished reputation and positive identity. (shrink)