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)

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 article is devoted to the philosophy of industrial design as the most important area of aesthetic and engineering activity of people, shaping the appearance of modern society. The object of the study is industrial design, and its subject is the philosophical foundations of industrial design. The goal of the study is to identify the philosophical essence of industrial design in epistemological, ontological and anthropological dimensions. Attention is paid to the historical aspects of industrial design, which allows us to more (...) accurately understand the essence of this phenomenon. The author’ also considered modern industrial design, which in its philosophy is characterized by a strong anti-globalist orientation. It is noted that the philosophical understanding of industrial design contributes to the understanding of the features of its historical development. The main conclusion of the study is that industrial design has a certain philosophical content associated not only with the aesthetic side of reality, but also with its axiological and ethical structure. The epistemological problems of industrial design are important: products act as carriers of certain knowledge and concepts and accumulate the cultural experience of mankind. Anthropological problems of design are associated with the model of a human creator and a human recipient of activity. The scientific novelty of the research lies in the understanding of industrial design, which is a systemic object, developing in space and time. In its existence, this object combines presence and “service”, independent givenness and significance for a person. (shrink)

The subject of this study is a set of alleged contradictions in the development of artificial intelligence, pursued in order to achieve their overcoming. Philosophical anthropology contains the potential to analyze complex interactions, to articulate the problems that arise between artificial intelligence and humans. The philosophical and anthropological analysis of artificial intelligence is aimed at understanding this human phenomenon, human presence and its experience. The article is an attempt to identify and outline the trajectories for the possible resolution of the (...) contradiction in the development of artificial intelligence, the analysis of the parameters proposed by philosophical anthropology to solve their problems in the modern socio-cultural situation. The relevance of the proposed problem arises in the fact that artificial intelligence qualitatively changes the existence of a person, and in philosophical anthropology there is a potential to outline the prospects for the development of artificial intelligence, while preserving the languid human in a person. To study this perspective is very important in society. The novelty of the topic raised in the article is the analysis of solving the problems of artificial intelligence from the standpoint of philosophical anthropology, in the articulation of contradictions in the development of artificial intelligence, in the search for solutions to overcome these contradictions. Philosophical anthropology provides tools for a balanced decision on the development of artificial intelligence, the degree of its impact on human existence. (shrink)

The purpose of the study is to identify the needs of bachelor students of various areas in the field of fine arts in the skills of mastering computer graphics and using its various types in professional activities. The Federal State Educational Standard in the areas of education, general and professional competencies associated with the possession of computer graphics, methods and techniques of work necessary for organizing a holistic process in this discipline are analyzed.

This publication aims to analyze the economic, social, and cultural phenomena that first appeared in the "era of revolutions" that occurred in the nineteenth to early twentieth centuries. The modern European trend toward tolerance, which is the basis of current social and cultural changes, including in our country, has specific intellectual grounds. The subject of the study was the ideosphere of the nineteenth and early twentieth centuries, including philosophical, economic, and psychological concepts that gave rise to modern trends in these (...) areas. The result of this study was the determination of the reasons that caused the change of the ideological paradigm in Europe. The novelty of the research lies in the fact that, for the first time, the intellectual foundations of the formation of tolerance as an actual socio-cultural phenomenon are analyzed. This article consistently proves that among the first such grounds, it is possible to determine the emergence of machine production and, as a result, the appearance of a mass person with a culture corresponding to them, performing a compensatory and entertaining function. The most important cultural foundation is mainly the intellectual "background" created by the teachings of Friedrich Nietzsche, Karl Marx, and Sigmund Freud. The ideas of Anglo-American pragmatism played a significant role in forming a new morality, which included the denial of religion and its values, giving it a utilitarian character. During the subsequent historical period and at present, these views have become the basis for the creation of the so-called "individual faith," in which religion ceases to be the guide of human life but only serves the needs of the individual. The desacralization of religion leads to the study of different aspects of sexuality, which opens up the possibility for modern thinking about gender. The concept of "natural law" should also be attributed to the intellectual factors of the formation of modern European tolerance. (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.

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 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)

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)

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)

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.

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 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 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)

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)

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)

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)

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.

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.