A survey is given of three-valued paraconsistent propositionallogics connected with Jaśkowski’s criterion for constructing paraconsistentlogics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested.

Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common? The book adopts truth-functional approach to examine functional properties of finite-valued Łukasiewicz logics Łn+1. Prime numbers are defined in algebraic-logical terms and represented as rooted trees. The author designs an algorithm which for every prime number n constructs a rooted tree where nodes are natural numbers and n is a root. Finite-valued logics Kn+1 are specified that they have (...) tautologies if and only if n is a prime number. It is discovered that Kn+1 have the same functional properties as Łn+1 whenever n is a prime number. Thus, Kn+1 are 'logics' of prime numbers. Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. Along with characterization of prime numbers author also gives characterization, in terms of Łukasiewicz logical matrices, of powers of primes, odd numbers, and even numbers. (shrink)

The purpose of the study is to determine the key strategies of philosophical criticism of Heidegger’s Black Notebooks, whose achievement is realized in the following tasks: 1) to identify the body of texts that represent the discourse of philosophical criticism of Heidegger notes; 2) to reveal the typological features of the different strategies of interpreting Black Notebooks; 3) to reconstruct a thematic horizon of Heidegger studies, opened up by discussion on published notes. The methodology combines elements of discourse analysis with (...) traditional methods of historical and philosophical criticism. Scientific novelty is expressed in the following: 1) philosophical discourse of the Notebooks’ reception includes texts of narrowly specialized character, as well as reflections of key philosophers 2) basic strategies in philosophical critique of Black Notebooks convey the overall structure of the discourse of interpretation of Heidegger’s legacy, distributed between apologetics and ideological criticism; 3) Black Notebooks have exacerbated the problem of architectonics of Gesammtausgabe and formed the textual basis for the study of "silence" period in philosophical life of Heidegger. Conclusions. The discourse of philosophical critique of Heidegger’s notes proves evidence for ideological charge of philosophizing and justifies socially oriented approaches of historical and philosophical studies examining philosophizing as a special cultural practice, not as a form of sublime creativity. (shrink)

The purpose of the study is to determine the key strategies of philosophical criticism of Heidegger’s Black Notebooks, whose achievement is realized in the following tasks: 1) to identify the body of texts that represent the discourse of philosophical criticism of Heidegger notes; 2) to reveal the typological features of the different strategies of interpreting Black Notebooks; 3) to reconstruct a thematic horizon of Heidegger studies, opened up by discussion on published notes. The methodology combines elements of discourse analysis with (...) traditional methods of historical and philosophical criticism. Scientific novelty is expressed in the following: 1) philosophical discourse of the Notebooks’ reception includes texts of narrowly specialized character, as well as reflections of key philosophers 2) basic strategies in philosophical critique of Black Notebooks convey the overall structure of the discourse of interpretation of Heidegger’s legacy, distributed between apologetics and ideological criticism; 3) Black Notebooks have exacerbated the problem of architectonics of Gesammtausgabe and formed the textual basis for the study of "silence" period in philosophical life of Heidegger. Conclusions. The discourse of philosophical critique of Heidegger’s notes proves evidence for ideological charge of philosophizing and justifies socially oriented approaches of historical and philosophical studies examining philosophizing as a special cultural practice, not as a form of sublime creativity. (shrink)

The paper discusses functional properties of some four-valued logics which are the expansions of four-valued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by matrices having the same underlying algebra, but with a different choice of designated values, i.e. with one designated value. In the preceding literature both approaches were developed independently. Moreover, we present the lattices of the functional expansions of DM4.

The purpose is to identify common and distinctive features of concepts and methodology of the problem of subject within different discourses, implicitly or explicitly relevant to the definition of "clinical" mode of human existence. The research methodology combines techniques of discourse analysis and basic principles of historical and philosophical studies. Originality of the research lies in definition of the clinical philosophical discourse as a special communicative process, where utterances not only focus on disease syndromes, and reveal phenomenology of inner experience (...) of a pathological self, but also structure a certain type of sociality. Clinical discourse represents the space where the patient is treated not as a subject but as an object of disease. Ontology of clinical discourse prevails over ontology of disease, since its structures determine the notion of disease as such. Categorization of the disease, the idea of disease as a phenomenon subdued to professional authority leads to the idea of the need for patient’s isolation from the natural environment and removing him to special social institutions. The clinicist doctrines share the intention to reduce the patient’s self to its bodily dimension, while ignoring social determinants of psychological deviations. Conclusions of the study are summarized in the following positions: the current clinical discourse is based on the positivist-biological trend in humanitarian knowledge and it is the basis for the production and reproduction of medical and pharmaceutical repressive ideology; criticism of philosophical clinical discourse opens the possibility of overcoming the dominance of purely clinicist discourse; such a transformation is possible only after a paradigm shift in understanding the category of subject. (shrink)

У статті здійснено логічну реконструкцію інтердискурсивного поля між філософемами Мартіна Гайдеґґера і Теодора Адорно. На основі дослідження рефлексивної літератури визначено основні тенденції історико-філософської аналітики цього поля. Установлено, що ключовим концептуальним чинником напруження між досліджуваними дискурсами постає характер розуміння онтико-онтологічної відмінності. Визначено тактичні можливості застосування методологічних інструментів адорнівської ідеологічної критики в контексті історико-філософського освоєння творчості М. Гайдеґґера.

In this note we prove that some familiar systems of finitely many-valued logics havefactor semantics, and establish necessary conditions for a system of many-valued logic having semantics of this kind.

We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H of the intuitionistic propositional logic to an implicational fragment TV of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics (...) to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics. (shrink)

Heidegger proved to be one of the key thinkers of the last century. His philosophical legacy accompanied by affluent body of critical literature disclose the horizon for any local philosophical community, e. g. the Ukrainian one, to obtain its own language and problematic. To work out a appropriate receptive disposition towards Heidegger’s thought, we have to generalize the logics of some constituted histories of reading Heidegger in Continental, Anglo-Saxon, and Russian intellectual fields. Contemporary historico-philosophical discourse dominated by receptive disposition of (...) history of ideas omits social references of philosophical texts. This is symptomatic for ontological, existential, and lingual focuses on Heidegger, so characteristic for Ukrainian studies. We try to work out the interpretative disposition of situational analysis of Heidegger’s discourse on the methodological and conceptual basis provided by P. Bourdieu and R. Collins’s sociological views on Heidegger. Our goal here is to find a possibility to appropriate certain elements from sociology of knowledge to the apparatus of historico-philosophical analysis, although sociology of knowledge is suspected to be more valuable in explaining biasis than in accounting for correct opinions and adequate interpretations. This controversy between sociological and philosophical fields made us consider the critical reception of P. Bourdieu’s issues. What is really relevant to the tasks of historical and logical reconstructions of Heidegger’s thought, its contexts and evolution is Bourdieu’s claim to consider its polyphonic nature, its stylistics evolving from pragmatic force of Sein und Zeit to prophecies of the poetic thinking to come in the history of Being. We argue that such concepts of sociology of knowledge as structural homology, intellectual field, and symbolic capital can substantially enforce and enrich historico-philosophical studies, being framed in the disposition of situational analysis of philosophical texts. (shrink)

In the domain of the Ukrainian history of philosophy one can clearly observe symptoms of eclecticism, contamination, and corruption. Such situation is rooted in continuous insufficiency of the methodological framework of Ukrainian philosophy, split by the demise of Soviet ideological structures. Critical condition of humanitarian epistemology is aggravated by the urgent need to overtake foreign studies in the corresponding field, which constantly increase in number and evolve in character. All of the aforementioned symptoms are indicative for historical and philosophical reception (...) of Martin Heidegger's legacy by the Ukrainian academy. Heidegger studies have already formed a separate trend in the world philosophical discourse. We focus on critical assessment of certain reflexes, i.e. definite interpretative strategies providing different transcriptions of the same referents, i.e. definite philosophical forms, texts, or problems. In the general contour of Heidegger studies I differentiate the following reflexes: reflex of immanent hermeneutics, reflex of reductive interpretation, reflex of genetic historiography, and reflex of ideological historiography. In this paper I continue to identify transcriptions of "Heidegger's controversy" (the referent of historico-philosophical thought), provided by the reflex of ideological historiography. As I have recently identified the transcription of political implications of Heidegger's philosophy in the terms of sociology of knowledge, so now it comes to biographical transcription of Heidegger's political engagement, elaborated by Hugo Ott and Victor Farias. Critical assessment of their methodological approach revealed imposition of biographical objectivity on philosophy discourse, simplification of the complexity of philosophical form, and the pathos of elementary humanism as the ideological criterion of their research. (shrink)

Nowadays the Ukrainian historical and philosophical science is going through a harsh crisis of methodology, caused by distortion of universal coordinates of scientific thinking allegedly providing the condition of the so-called methodological pluralism. Numerous discussions focus on the question about the very scientific nature of history of philosophy as a branch of knowledge. The tendency which appears to prevail in such disputes defines history of philosophy as philosophy in contrast to the opinion that history of philosophy should be rather seen (...) as approximate to social history. This paper aims at revealing relevant methodological instruments of historical reconstruction of philosophical forms in the concreteness of their existence, conditioned by lives of real people with their real ends and drives. Thus we address Herbert Marcuse's critique of Martin Heidegger's philosophy, since once being a Heidegger's assistant he adopted a highly critical position towards his master's philosophy. Heidegger's Being and Time attracted Marcuse by existential analytics of Being-in-the-world of Dasein and the perspective on historicity of humane condition. In Marcuse's eye Heidegger had come close to the breakthrough towards maintaining of concrete philosophy, providing possibilities of philosophical approach to social realities. By 1932 Marcuse's attempts to reconcile categories of Heideggerian paradigm with strategies of Marxism proved to be a failure. After 1932 Marcuse finds the resources of theoretical enrichment in Marx's Economical and Political Manuscripts of 1844 and distances himself from Heidegger. Nevertheless Heideggerian moments appear to be employed further on in his thinking. Marcuse's critique provides us with an efficient assessment of Heidegger's key concepts as neutralized terms, unable of reaching out to the very reality of human existence, being ideological doubles of sociologicaly valid terminology. (shrink)

У статті розглянуто проблему методологічного оновлення української історико-філософської науки засобами філософської історіографії. Перехід від історії філософії до філософської історіографії уможливлює актуальні узагальнення щодо світового філософського процесу навіть у випадку дослідження таких різних філософських проектів, як критична теорія Теодора Адорно й фундаментальна онтологія Мартіна Гайдеґґера.

Research into the history of understanding Heidegger's ideas allows to reveal how different thinkers were likely to grasp the specific subjective positions that defined the meaning of philosophizing as a cultural practice posited by modern era of intellectual history. The figure of Heidegger is crucial because it shed light on the more general context of the evolution of philosophizing within the system of scientific knowledge. A clear contrast between scientific rationalism and philosophical thinking, inherent for Heidegger's philosophy, is now hardly (...) perceived within general coordinates of scientific philosophy of the last century, combining directions of phenomenology, Neo-Kantian tradition and positivism. Understanding the nature of synthesis of phenomenological method with the principles of the philosophy of life that formed the core of Heidegger's thought was the point of reference of such thinkers like Edmund Husserl and Ernst Cassirer. The problem of how to reconstruct the contours of delineation between the aforementioned philosophical trends remains relevant today and, as the latter define the contours of contemporary philosophy so that the barriers between different traditions of philosophy only intensified. Heidegger's desire to find premises of philosophizing, deeper than principles for a positivist and phenomenological science, would find support from Neo-Kantian thinkers, who also stood for autonomy of philosophy. But radical ontologism of Heidegger refused any possibility of dialogue. Husserl and Cassirer made critical remarks on ontologization as the leading motive of Heidegger's thought, which gave starting intention to further reception of Heidegger's work. It is ontology of time that has a threat of all consuming relativism and opportunism, since it deprives ethics from opportunities that would not fit the immanent structure of Dasein. Ontology of language fell prey to similar criticism, as Heidegger suggested lingual turn of existential analytics of Dasein. Cassirer in his own philosophy of symbolic forms forsaw the opportunity of linguistic totalization of being and developed his theory of generic symbolic forms. (shrink)

This paper is an abstract of the report which was presented on the Polish-Soviet meeting on logic . It is shown that one can consider a lineary-ordered Heyting’s and Brouwer’s algebras as truth-values for Lukasiewicz’s infinite-valued logic’s Lω.

In this paper we define n+1-valued matrix logic Kn+1 whose class of tautologies is non-empty iff n is a prime number. This result amounts to a new definition of a prime number. We prove that if n is prime, then the functional properties of Kn+1 are the same as those of ukasiewicz's n +1-valued matrix logic n+1. In an indirect way, the proof we provide reflects the complexity of the distribution of prime numbers in the natural series. Further, we introduce (...) a generalization K n+1 * of Kn+1 such that the set of tautologies of Kn+1 is not empty iff n is of the form p , where p is prime and is natural. Also in this case we prove the equivalence of functional properties of the introduced logic and those of n+1. In the concluding part, we discuss briefly a partition of the natural series into equivalence classes such that each class contains exactly one prime number. We conjecture that for each prime number the corresponding equivalence class is finite. (shrink)

In the paper the following questions are discussed: What is logical consequence? What are logical constants? What is a logical system? What is logical pluralism? What is logic? In the conclusion, the main tendencies of development of modern logic are pointed out.

This paper is a survey of V.A. Smirnovs main results in modern logic.