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.

At the present time, there are several interpretations and modes of Kant’s transcendental philosophy (TP). Which of these interpretations and modes of transcendentalism most adequately express the spirit of TP, i.e. can claim the title of the transcendental ones? For the explication of the ‘idea of transcendental philosophy’ [KrV, A1], here I distinguish two transcendental shifts: methodological and metaphysical ones, which in their totality predetermine the essence and set the specificity of Kant’s transcendental idealism. The methodological transcendental shift that Kant (...) postulates in his definitions of TP in the Critique of Pure Reason [KrV, A11; B25] represents a shift from studying of objects to the analysis and justification of our mode of cognition of objects. This shift sets a fairly wide range of a la Kantian a priori doctrines and predetermines the transcendental turn (Re–Transcendentalising) of modern philosophy. The metaphysical transcendental shift that can be correlated with “the altered method of our way of thinking [in metaphysics]” [KrV, BXVIII], is associated with the splitting of the “thing” into the actual object (or Kantian thing-in-itself) and object of experience (or Kantian appearance), and involves a transition from the study of thing-in-itself to the analysis of the appearance. More precisely, this shift finds its expression in the transcendental triad “object (thing-in-itself; Ding an sich) – appearance (Erscheinung) – representation (Vorstellung)”, which determines the ‘idea’ (essence) of transcendental idealism/metaphysics. (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)

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)

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)

The paper is devoted to the role (function) of reflection in cognition and its modes (types) as part of the cognitive ability. Along with logical and transcendental reflection, Kant's transcendental shift (turn) is discussed, as well as the role of reflection in Kant's schematism (the ability to judge) and the formation of schemas. Particular attention is paid to another mode of reflection – reflexive switching, which underlies not only the formation of pure rational concepts and schemes (Kant's concept of epigenesis; (...) metaphysical deduction of categories), but the epigenesis of a priori forms of sensibility of space and (especially) time, connected with the Kantian synthesis of apprehension in the intuition. The article proposes an original conception of time, the so-called onion model of time, which is based on a reflexive (iterative) apperceptive ladder. (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.

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)

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 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 my paper I argue, relying on Kantian definitions and conceptual distinctions, the thesis that Kantian transcen-dental philosophy, which he characterizes as a second-order system of transcendental idealism, is not [empirical] idealism, but a form of realism (resp. compatible with empirical realism [A370-1]). As arguments in favor of this “realistic” thesis, I consistently develop a realistic interpretation of the Kant’s concept of appearance (the theory of “two aspects”), as well as of Kantian Copernican revolution, of his theory of intuition as (...) cognitive ability which 'giving' ‘us objects, of the concept of double affection and noumenal causality. (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.

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.

Various connexive FDE-based modal logics are studied. Some of these logics contain a conditional that is both connexive and strict, thereby highlighting that strictness and connexivity of a conditional do not exclude each other. In particular, the connexive modal logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, cKN4, scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, cMBL, and scMBL are introduced semantically by means of classes of Kripke models. The logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and cKN4 are connexive variants of the FDE-based modal logics BK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and KN4 with a weak and a strong implication, respectively. The system cMBL is a connexive variant of the modal bilattice logic MBL. The latter is a modal extension of Arieli and Avron’s logic of logical bilattices and is characterized by a class of Kripke models with a four-valued accessibility relation. In the systems scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, and scMBL, the conditional is both connexive and strict. Sound and complete tableau calculi for all these logics are presented and used to show that the entailment relations of the systems under consideration are decidable for finite premise set. Moreover, the logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cBK}^-$$\end{document} and cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} are shown to be algebraizable. The algebraizability of cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} is derived from proving cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} to be definitionally equivalent to MBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {MBL}$$\end{document}. All connexive modal logics studied in this paper are decidable, paraconsistent, and inconsistent but non-trivial logics. (shrink)

In one of his works, the modern neurophilosopher G. Northoff, developing the problems of Kantian transcendental cognitive science (epistemology), introduces the metaphor of Kant’s mind. In this article, we attempt to explicate this metaphor in order to propose a cognitive model of Kant’s mind (the Kantian mind as a sequence of cognitive syntheses), which could be used in modern research in cognitive science, neuroscience and artificial intelligence. At the same time, there is currently a question (task), on the one hand, (...) about the transition of transcendentalism to neurotranscendentalism, i.e. the development of neurocognitological research aimed at identifying the neural correlates of the components/structures of the Kant’s mind (the transition from Kant’s mind to the Kantian brain)), and, on the other hand, the creation of intelligent computer programs (systems) that implement the cognitive model of the Kant’s mind. This article outlines ways to solve both the first and second of these problems. (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)

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)

The article deals with the problem of compatibility of the extended mind thesis with the concept of epistemic responsibility. This compatibility problem lies at the intersection of two current trends in Virtue Epistemology (VE): the study of extended cognition, and the return of VE to the topic of epistemic responsibility. I give objections to two seemingly independent positions; their acceptance makes it difficult or even impossible to make the concept of epistemic responsibility applicable to the agents of digital society whose (...) cognition is extended. The core of both positions can be illustrated by the following thesis: “Since the subject cannot voluntarily change his/her beliefs, we cannot ascribe to him/her either epistemic responsibility or intellectual virtues that allow him/her to take responsibility”. The counter-arguments to this thesis are based on the distinction between the causal (responsibility-in) and normative (responsibility-for) components of responsibility. The absence of the former allows us to characterize the subject as not responsible, the absence of the latter as irresponsible. I propose two conceptual foundations that can make possible the consistent talk about the epistemic responsibility of an extended subject. 1) The subject may not be responsible for the beliefs taken from the epistemic environment, but the subject bears significant responsibility for what environment he finds himself in. 2) Being epistemically responsible means deliberately reducing the number of possible causal excuses – excuses based on agent’s unresponsibiity due to his causal dependence on his epistemic environment (‘cognitive extensions’). (shrink)

The topic of this article is the problem of World and Infinity. The concepts “Weltanschauung,” (I. Kant) and “Umgreifende” (K. Jaspers) are introduced. A transcendental analysis of the concepts "World" and "Infinite" as ideas of reason is carried out. The theory of the world by L. Tengely is analyzed. Metaphysical and mathematical interpretations of the infinite are compared (actual and potential infinity, openness, horizon).

The paper discusses the Strawsonian concept of descriptive metaphysics and its various implementations in conceptions of I. Kant, R.G. Collingwood and P.F. Strawson, their similarities and differences. Particular attention is paid to the analysis of Kant's transcendental philosophy (resp. transcendental idealism), or its metaphysics of appearance as a pioneer version of descriptive metaphysics and its comparison with the version of descriptive metaphysics of P. Strawson himself.

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

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)

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)

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)

In the “Critique of Pure Reason” and subsequent “Prolegomena to Any Future Metaphysics...”, “Metaphysical Principles of Natural Science”, “Opus Postumum” Kant develops one of the modes of his transcendentalism, the metaphysics of possible experience, whose task is to study the transcendental conditions for the possibility of our (cognition), which, according to Kant, has a priori character. P. Strawson calls this mode of metaphysics ‘ descriptive metaphysics ’ and connects it with the analyzing the ‘conceptual structure’ of our thinking about the (...) world. The contemporary realistic trend (primarily within the framework of the analytical philosophical tradition) in the interpretation of Kant’s transcendental philosophy is associated with the modern theory of “two aspects” (80s of the 20th century), which replaced the classical theory of “two objects/worlds” (compare also with the opposition “ theory of appearance vs. theory of appearances ”). Within the framework of this theory, the Kantian ‘appearance’ receives an objectified status, it is not our mental representation, but corresponds (as its signs) to really existing things, or Kantian ‘objects of experience’. The article traces the formation of the historical and conceptual background of the ‘ metaphysics of experience ’ (H. Paton's original expression). Historically, the metaphysics of experience inherits the neo-Kantian approach to interpreting Kant's transcendentalism as a ‘theory of experience’ (H. Cohen, E. Cassirer), then it develops in logical positivism/empiricism (H. Reichenbach, R. Carnap; further in post-posivivism: the theory of I. Lakatos and T. Kuhn), analytical philosophy of science (W. Sellars, G. Buchdal, H. Putnam), and at present the metaphysics of experience is developing in a number of contemporary works of an analytical orientation (P. Strawson, K. Ameriks, L. Allais and etc.). (shrink)

The article addresses the ongoing debate about the origins of biopolitics. While Foucault’s analysis of biopolitics approached it as a modern rationality of government, Agamben’s Homo Sacer series presented biopolitics as having a longer provenance, dating back to the antiquity. These polar positions are not mutually exclusive but coexist in these and other theories of biopolitics, which approach its object as both modern and ancient, having its chronological origin in the eighteenth to nineteenth centuries yet also possessing a prehistory of (...) precursors. The article interprets this dual origin in terms of Paolo Virno’s theory of historical temporality, which distinguishes between the chronological past of historical events and their potential past, which accompanies and is negated in them. Coexisting with its own unrealized potential, every historical event remains incomplete and extends itself both backwards and forwards, positing its precursors and prefiguring its future outcomes. While modern in the chronological sense, biopolitics is retrospectively inscribed in a longer historical lineage, its antecedents easily identifiable in the history of political thought. Finally, we apply this approach to Virno’s own account of the history of biopolitics, questioning his identification of past potential with labour-power. (shrink)

Kant’s transcendental philosophy of Kant is the metaphysics of possible experience related to the solution of the [semantic] problem set in his famous letter to M. Hertz (02.21.1772): “What is the ground of the relation of that in us which we call 'representation' to the object?” There are two possible ways to solve it: empiricism and apriorism, – and Kant chooses the second of them, thus making his “Copernican Revolution”. In the Preface to the 2nd ed. Critique Kant correlates his (...) Copernican turn/revolution with "altered method of our way of thinking [in metaphysics]" [BXVIII] and considers it as an analogue of the hypothetico-deductive scientific method of Copernicus – Galileo – Newton. The analysis of structure of the Copernican Revolution shows that it is possible to pick out two vectors: the empirical (from the thing-in-itself to representations) and the noumenal ones (from the transcendental unity of apperception [or transcendental object] to objects of experience). The introduction of an a priori vector (resp. a priori forms) means that Kant's conception is not empirical, but Kant’s keeping empirical vector says that it is compatible with empirical realism [A370–1]. Thus, Kantian transcendentalism is a synthesis of realism (basic level) and transcendental idealism (as a meta-level superstructure above it), whose task is to find out and analyze the transcendental conditions [possibility] of our knowledge of objects. (shrink)