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)

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.

Interpretation of Wittgenstein’s statement ‘whereof one cannot speak, thereof one must be silent’ and consequences of rule-following paradox is the topic of this article. The revision of Wittgensteinian approach to the relations between speech and mind, and approaches to the speech by Vygotsky and Austin allow approving the disagreement with Wittgenstein and exhibit the cases when is necessary ‘to break silence and speak’. Argument is based on the hermeneutical approach to the skeptical image of Wittgenstein studies that disclose the meaning (...) of hypothetic relevance between performative utterances and impulses generated by inner speech. Wittgenstein’s ideas are demonstrated as the contemporary version of a Pyrrhonism. Classical skepticism intensifies procedures for justification of philosophical knowledge, because philosophy tries to disprove skeptical claims. Wittgenstein studies play approximately the same role. Interpretation of the proposition ‘whereof one cannot speak, thereof one must be silent’ in a view of performative utterance allow coordinating the inner philosophical speech made by Wittgenstein, and the speech made by his commentators and critics. (shrink)

The article defends the thesis that interpreting Plato’s natural philosophy it is useful to take the terms horatos and aoratos in two distinct meanings: “observable” and “unobservable”, and “visible” and “invisible”. This approach helps to perceive new sides of Plato’s ideas, implicitly present in the “Timaeus”, which allows interpreting it in both anthropomorphic and anti-anthropomorphic senses.

The paper defends the thesis that Proclus Diadochus’ ideas are still relevant in modern culture. It appears that the ideas of Neoplatonism as a whole and these of Proclus’ in particular matter at least in some aspects of modern culture, such as the foundations of politics, the basic characteristics of philosophy and the fundamental aspects of understanding of the human existence. In the sphere of politics, one can note the ideas useful for creating of the non-totalitarian forms of ideology. In (...) contemporary philosophy the Neoplatonic studies can be interpreted as one of the bases of understanding of rational knowledge. The ideals of material harmony are essential for understanding of the human existence. (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 present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.

The article analyzes the philosophical concept of the “porous self” of J. Rivera. The originality of this concept in the post-phenomenological project is determined by the role of theological constructions that modify the primal experience of self-consciousness. This modification allows us to interpret the phenomenological description of the human self as different from the classical — “porous” temporality, i.e., correlating through “two entrances”—the internal and external—with eternity. Within this approach, the primary phenomenon of the constitution of the "porous" self becomes (...) the inner word, which in the appeal to eternity turns out to be the original self-awareness of the self as a temporality. The secondary phenomenon of the constitution of the “porous” self is not the mundane temporality of M. Heidegger, but Epektasis as an intense striving towards the end of time in General. The worldly temporality of the self, transformed by faith, is phenomenologically revealed as open to eternity in each of its moments. The third phenomenon of the temporality of the self is Memoria, whose interpretation reveals how the structure of the inner consciousness of time by E. Husserl can be framed ontologically and harmoniously integrated into the theological concept. The article shows how, based on this understanding of both the internal and external openness of the “porous” self for eternity, the integral structure of its temporality is formed. The temporality of the porous self is a modification of Husserl’s time diagrams and the intertwining of two streams of temporality at the same time from past to future and from future to past, which itself constitutes a phenomenal field of events of self. This understanding of temporality sets new perspectives for the phenomenological analysis of subjectivity. (shrink)

In the article, I discuss the Heideggerian criticism of the Aristotelian concept of time. Heidegger thought that it was Aristotle who is to be blamed for so-called “ordinary” interpretation of time. Later on, Augustine developed this interpretation, while Kant and Hegel brought it to a logical end. The author observes that even if the post-Aristotelian thought and Hegel as its embodiment understood time in many respects naturalistically, we might trace both naturalistic and anti-naturalistic ways of interpretation of time in Aristotle. (...) It appears therefore that Aristotle had also laid the foundations of existential comprehension of time, having influenced thereby the formation of the European rationality in all variety of its forms and manifestations. (shrink)

In the article, we offer a model for actualization of the dialogue between the representatives of dramatic art and philosophy in Ancient Greece, having compared the notion of wisdom in Aristophanes and in Plato. In addition to his literary virtues, Aristophanes can be perceived as a philosopher of education. Extrapolation of these results on the modern situation opens prospective of dialogical ways of interactions between the representatives of different spheres of cultural life. Values on which such representatives are based can (...) differ, but the common idea to guide the analysis remains true regardless of these differences in their viewpoints: our opponents could well proceed from opposite philosophical principles but their position cannot be treated as necessarily mistaken. It demands efforts of all the participants of the dialogue, and ancient thought seems to offer general opportunities for this, which serves as a good example of the enduring value of the ancient ideals in the history of human culture. (shrink)

In this article, the epistemological interpretation of the relationship between concepts of relativism, beliefs, and probability ensures a defense of two theses, namely, (i) epistemic relativism refers to attitudes that depend on the repetition and anchoring of probabilistic beliefs, and (ii) Popper’s propensity interpretation of probability discloses the connections between relativity, probability, and collective subjectivity. The propensity interpretation brings a framework for describing the role of collective subjectivity in epistemic systems. This approach, as an acceptable epistemological stance, is related to (...) the variability of anchored collective beliefs. The repetition and anchoring of subjective probabilistic beliefs becomes a relative reference frame for evaluating the elements of knowledge. With this in mind, each particular way of considering probability indicates a manner of distinguishing epistemic systems. In epistemic systems, the statements are collective points of view expressed in the form ‘p is justified when belief in p is probably reliable.’ The statements can be accurate in a particular epistemic system but inaccurate in other systems. As a result, by avoiding the ‘all statements must be true or false’ requirement, each proponent of a certain epistemic system can build a probabilistic picture of the world. In this picture, not every statement needs to be ‘true’ when and if the statement expresses a collective point of view that has a propensity to be reliable and justified. (shrink)

The paper defends the thesis that phenomenological methods can play key role in explications of the transformation reasons of philosophical images of science. It can be made by the comparative analysis among phenomenology and other approaches revealing strong and weaknesses of separate approaches. Such principles of an explication of the transformation reasons of philosophical images of science were allocated: 1) the science is a set of the idealizing consciousness attitudes which allow to build images of the world in borders of (...) regional ontologies (or «particular ways of understanding of reality»);2) idealizing attitudes correspond to the comprehension of intentionality experiences structures; 3) the general transformation reason of images of science is the change of consciousness attitudes. (shrink)

The theoretical gap with the action actually performed is one of the fundamental problems of anthropology and the theory of action. To understand it, it is worth turning to the antitheoretical and anti-formalist pathos of the "late" Wittgenstein, which opposes all attempts to describe action and language in terms of rules and abstract structures. A critical analysis of the assumptions of intellectualism borrowed from simple common sense allows us to show that the logical analysis of action and language deals not (...) with a real language, but with an artificially created abstraction. The article attempts to show the positive significance of this criticism. The main conclusion of the study is that a thinker is able to adequately understand action and language if he also makes his own scientific attitude to them the subject of his analysis. Only in this way can we hope to transform Wittgenstein's antitheoretical pathos into the basis of a constructive study of action and language. The tools of scientific analysis are often much more rigorous and logical than its subject. Wittgenstein's analysis of language games and the life form behind them is an attempt to avoid such too strict and too logical methods and constructions in anthropology, philosophy of action and philosophy of language. The novelty of the research lies in the application of Wittgenstein's ideas to clarify the weaknesses and difficulties faced by the humanities in the XX century and today, as well as to find a way out of these difficulties. The relevance of the work is connected with the great interest of modern logicians and philosophers in Wittgenstein's work, with the urgent need to identify new ways of developing philosophical anthropology. (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.

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.

The article analyzes the interpretation of Fr. Alexander Men of Buddhism as teaching of the “Axial Age”. It is based on his seven-volume work “History of Religion: In Search of the Way, Truth and Life”. First defines the methodology used by Fr. Alexander, which is comparative and hermeneutic in nature. At the same time, he proceeds from a theistic-Christian value position, which, nevertheless, allows him respectfully treats other religious-philosophical traditions. The originality of the author’s interpretation of Buddhism is determined, both (...) its adequate features and one-sided, set by the value orientation. The concepts of transcendence and transcendent are differentiated, which allows conducting a comparative analysis of Buddhism and Christianity, assessments given by Fr. Alexander. The denial of the transcendent in Buddhism does not mean the absence of transcendence, especially in understanding the status of nirvana, which is defined purely apophatically. In the Indian worldview, he finds five essential principles that make Buddhism and Christianity related, despite all the difference in their positions: apophaticism, denial of the highest value of earthly goods, recognition of the high dignity of personal asceticism in spiritual life, the concept of “karma” as retribution, the idea of salvation-liberation as the main goal of religion. These principles, in his opinion, “constitute a strong bridge connecting Eastern religious experience with the Gospel”. The work of A. Men contributes to the expansion of the cultural horizon, liberation from both nationalist and Eurocentric points of view, contributes to the development of a dialogue that is so necessary right now. It is noted that the “Axial Age” concept by K. Jaspers as a whole allows avoiding one-sided assessments, revealing the common source of all axial teachings, which can be defined as “a breakthrough to the transcendent”. (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.

The article presents a conception of the end of history, developed on the basis of Giorgio Agamben’s critical engagement with Alexandre Kojève’s reading of Hegel. Departing from Agamben’s concept of inoperosity as an originary feature of the human condition, we argue that the proper or ‘second’ end of history consists not in the fulfilment of its dialectical process but rather in the radical interruption of the dialectic that terminates the teleological dimension of social praxis. Introducing the figure of the ‘workless (...) slave’ into the scenario of the Master—Slave dialectic, the article demonstrates how the dialectic of history may be ended in a non-dialectical fashion through inoperative praxis that subtracts itself from the struggle for recognition. In the conclusion, the implication of this reading of the end of history for the understanding of Agamben’s ‘coming politics’ is addressed. (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)

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.

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)

'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.

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)

The principle motivation of this work is to display the sense in which the epistemic reading of a Kripke model tacitly requires common knowledge of the model, CKM. This requirement significantly restricts the amount of epistemic situations we are able to consider. We explore possible worlds epistemic models in a general setting without CKM assumptions and show that such models can be identified with observable substructures of Kripke models. We argue that such observable models offer a new level of generality (...) and conceptual clarity in epistemic modeling. Similar analysis applies to intuitionistic models. (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.

Various features of the interpretation of these schools main positions, the reasons for their appearance and the consequences for the development of Mahayana Buddhism have been the subject of discussion in this research. Attention is drawn to the existence of various ideas of Buddhist authors about the interpretation of fundamental philosophical ideas of these schools. The influence of the peculiarities of translation into other languages for the adequate transmission of the author’s thought is discussed. It is noted that the possibility (...) of different interpretations was already established in the very methodology of the transmission of Buddhist doctrines, formed at the earliest stages of Buddhism. The opinions of a number of Tibetan authors are analyzed. The study presents the derivation of the existence of different interpretations of some categories central to Mahayana Buddhism due to the presence of different philosophical methodologies. A number of features were associated with the interpretation of the correlation of logical-critical knowledge, yogic methods and their priority in choosing ways to achieve an exit from the chain of rebirth. The factor of similarities in the positions of such authors as Nāgārjuna and Vasubandhu (traditionally attributed to different schools) makes it problematic to unambiguously interpret their philosophical positions; Some features of these schools were determined not only by theoretical backgrounds, but also by political struggle for a leading place in the Buddhist hierarchy of a certain country, as well as the desire to affect authorities. (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)

We start by giving a survey to the theory of $${\text {Borel}}^{*}$$ sets in the generalized Baire space $${\text {Baire}}=\kappa ^{\kappa }$$. In particular we look at the relation of this complexity class to other complexity classes which we denote by $${\text {Borel}}$$, $${\Delta _1^1}$$ and $${\Sigma _1^1}$$ and the connections between $${\text {Borel}}^*$$ sets and the infinitely deep language $$M_{\kappa ^+\kappa }$$. In the end of the paper we will prove the consistency of $${\text {Borel}}^{*}\ne \Sigma ^{1}_{1}$$.

The presented article compares the points of view on time developed in analytical philosophy and in phenomenology actively developed by B. Russell and L. Tengelyi. The objective of the study coincides with the identifying a common horizon for understanding time in analytical philosophy and phenomenology. This help to clarify the possibilities of productive interaction between analytical philosophy and phenomenology. The author of the article believes that a positive answer to this question can be ensured by a special thought experiment. The (...) experiment involves assessing the perception of time in extreme circumstances in terms of phenomenology and analytical philosophy. (shrink)

The action of social laws cannot be conceived of apart from the active role of the human subject, without the participation of the subjective factor in the historical process. This viewpoint seems to me to be the only correct one. It derives from the premise, postulated by Marxism, that people's social activity must be regarded as a mode of existence of social reality, the embodiment of the social form of movement of matter, and a mode of functioning of social laws (...) themselves. All social reality, considered as a whole, all so-called "humanized nature," preserves and reproduces itself only if it is embodied in living human activity and by means of it. For example, Marx observed that a machine taken out of the productive process ceases to be a productive force of society. He emphatically rejected the notion that the objective embodiments of the historical process could function and develop automatically, independently of people, and pointed out the dependence of their social functions on living human activity. All objective embodiments of the historical process are only intermediate links and aspects of a process in which individuals renew themselves as they renew the world created by them. (shrink)