Categorical Logic Research Articles

2º Capítulo

The self-subsistence of the measure, as a logical category, presents itself as free from external determinations, as would be the most diverse expedients, which operate the most diverse types of restrictions: commandments, external orders and strange laws. By enjoying this freedom of determination, the logical category of measurement presents itself in its different operations as capable of operating independently of criteria external to itself. Furthermore, it itself generates its own measurement criteria, without the need to use external parameters, which could be offered by another measurement criterion.

Os Descaminhos da Dialética Hegeliana entre Lógica e Natureza

The aim of this study is to investigate the relationship between Logic and Nature within the Hegelian system. Our focus lies on the status of the categories of nature: are they merely a redoubling of the equivalent logical categories or is there a substantial difference between them? First, we analyze the secondary literature on the subject and conclude that it falls short of the complexity of the problem. Secondly, we make a detailed comparison between the Philosophy of Nature and the Science of Logic and hypothesize that the natural categories presuppose logic as a standard, that is, a kind of ruler that determines what the ideal development would be; however, as nature fails to faithfully reproduce this standard, its categories deviate considerably from the logical categories.

Enhancing Healthcare Informatics: Integrating Category Theory Reasoning into OMOP-CDM Ontology Model.

The task of managing diverse electronic health records requires the consolidation of data from different sources to facilitate clinical research and decision-making support, with the emergence of the Observational Medical Outcomes Partnership - Common Data Model (OMOP-CDM) as a standard relational database schema for structuring health records from different sources. Working with ontologies is strongly associated with reasoners. Implementing them over expansive and intricate Ontologies can pose computational challenges, potentially resulting in slow performance. In this paper, we propose the implementation of a new reasoner based on categorical logic over a translation of OMOP-CDM into an ontology model. This enables enhancements to the efficiency and scalability of implementing such models.

Auditor's professional judgment and opinion

The paper is devoted to such an actual problem in the field of audit activity as professional judgment and an auditor's opinion. A proper clarification of the logical content of these concepts significantly affects the effectiveness of the audit according to requirements of International Standards on Auditing (ISA). To date, in scientific publications the various approaches to the interpretation of the given concepts are expressed. A significant part of the authors is limited to general definitions and only some of them make attempts to substantiate their research with the laws and categories of logic. At the same time, native authors in every possible way avoid a full-fledged logical definition of content of the concept "auditor's opinion". The main reason is that there is an unsuccessful translation from English terminology into Ukrainian. In some cases, the term "opinion" has been translated as "opinion", and in others it has been called "conclusion". Therefore, if the term "opinion" is preferred, it turns out that the audit begins with an auditor's opinion and ends with it. An auditor's opinion fully encompasses such forms of logical thinking as concepts, judgments and inferences. The paper not only shows the misinterpretation of the concepts of "professional judgment" and "auditor's opinion" in a number of scientific studies. Also it is proposed the own vision of the cognition process in the auditing field based on the laws of general and dialectical logic. A related scheme of an auditor's professional judgment is given. From this scheme it can be seen that the opinion of a professionally competent auditor from the very beginning of the audit is being transformed through rationale into the concepts and requirements of the ISA. Further, an auditor's rationale is being transformed into judgments and conclusions. Based on them, as a result of proving or proving and planning, the specific conclusions of an auditor are formed as a report. The paper states that an auditor's professional judgment, like the professional judgment of other specialists, is subordinated to the general laws of logic. Its specificity lies in the fact that it is carried out with professional skepticism in conditions of uncertainty and risk and is subject to the requirements of legislation and ISA.

Письмо Д.И. Чижевского Л.Я. Ганчикову (1953)

We publish the letter from the philosopher D.I. Chizhevsky (1894–1977), who lived in Germany, to his colleague and compatriot professor L.Ya. Ganchikov (1893–1968), who lived in Italy and worked on the history of Russian religious thought. Chizhevsky, apparently answering the addressee’s questions, essentially sets out his scientific curriculum vitae, with a brief biography and a list of main publications. The letter is an auto-interpretation of the creative heritage of D.I. Chizhevsky, in which the thinker defines his main interest as an attempt to substantiate some issues of logic and ethics by distinguishing those areas in which different types of logical categories are applicable, and also points to the philosophers closest to him – E. Husserl, H.W.F. Hegel, S.L. Frank, N.O. Lossky. The publication of the letter is accompanied by a thorough academic commentary, which fits the information given in it into the context of the life and creative path of D.I. Chizhevsky.

Письмо Д.И. Чижевского Л.Я. Ганчикову (1953)

We publish the letter from the philosopher D.I. Chizhevsky (1894–1977), who lived in Germany, to his colleague and compatriot professor L.Ya. Ganchikov (1893–1968), who lived in Italy and worked on the history of Russian religious thought. Chizhevsky, apparently answering the addressee’s questions, essentially sets out his scientific curriculum vitae, with a brief biography and a list of main publications. The letter is an auto-interpretation of the creative heritage of D.I. Chizhevsky, in which the thinker defines his main interest as an attempt to substantiate some issues of logic and ethics by distinguishing those areas in which different types of logical categories are applicable, and also points to the philosophers closest to him – E. Husserl, H.W.F. Hegel, S.L. Frank, N.O. Lossky. The publication of the letter is accompanied by a thorough academic commentary, which fits the information given in it into the context of the life and creative path of D.I. Chizhevsky.

Marx’s Dissertation in Light of the Value-Form

Abstract My article investigates Marx’s dissertation from the perspective of the categories of Hegelian logic employed in the writings on the critique of political economy and, in particular, in the analysis of the value-form (Wertform) in Capital. The aim of my contribution is to show how Marx’s early writing is not intended as a mere ‘exercice encore scolaire’ (Althusser), but as the first documented confrontation with Hegel’s logic. Marx’s early writing displays a moment of elaboration and acquisition of Hegel’s method. I argue that the Epicurean atom represents a developing contradiction, and that the dissertation follows a precise Darstellung, which extends from the metaphysical and physical principle to the abstract subjectivity of Epicurean atomism.

Correlation of evaluativeness, expressiveness and emotionality

The linguistic category of evaluation is a reflection of the logical category of evaluation, which expresses the subject's attitude to some object or phenomenon. The category of evaluation has points of contact with such phenomena as comparison, as in the evaluative act there is always a correlation with a certain standard, and modality, which, like evaluation, contains such elements as objectivity, subjectivity, and attitude. The distinctive features of the two mentioned categories from the category of evaluation are the absence of an axiological conclusion in the comparison and the limitation of the expression of modality to the level of the sentence, while evaluation can be expressed by elements of all linguistic levels. The obligatory elements of the evaluation frame are the subject, object and basis of evaluation. In literary texts, the source of all evaluative judgements is the author, who can put them into the mouth of the observer, narrator or characters. The object can be any element of reality, but most often people’s actions and qualities are subject to evaluation. Depending on the basis, there are axiological, intellectual, emotional, etc. evaluations. Although there is a notion of subjective and objective evaluation, we can only speak of relative objectivity. In connection with this criterion, we distinguish between evaluation in the narrow sense, associated with the subjective opposition between good and bad, and in the broad sense, where the object is correlated with the norms accepted in society. The evaluative semantics is revealed most fully by means of lexical-phraseological and syntactic levels. Lexical evaluative predicates are divided into general evaluative predicates, in which the evaluative meaning constitutes the denotation, and particular evaluative predicates, where the evaluative component of the meaning is included in its connotation along with expressive and emotional components. In most cases, these three components are co-present in a word, on the basis of which many linguists do not distinguish between evaluativeness, emotionality and expressiveness. However, there are differences: expressivity consists in the purposeful influence on the listener by increasing the impressive power of the utterance without changing the semantics of the unit, emotionality expresses the subject’s own impressions, while the evaluative component is associated with the reflection of the measure of conformity of the object to a standard in some quality.

Methodological arsenal of Aristotle and Kant. Categories

The classical toolkit of philosophy includes, as a necessary basic “set”, certain general concepts, extremely abstract and deeply essential, which are called in Greek categories, and in Latin predicabiles, but more often — universals.
 Initially, Aristotle introduces the first ten such categories into his texts that further became canonic, in a small but very complex work of the same name. Up to the era of Modernity, his methodological arsenal served European philosophy with unfailing success.
 However, in the XVIII century, Immanuel Kant, sharply and definitely distinguishing rationality and reason unlike Aristotle, introduces the categories of logic not as abstractions, but as propositions systematically developed from a general principle: the ability, or faculty, of judgment. These approaches are very different: for example, in relation to concepts, — and Aristotle’s categories are precisely concepts, — the question of truth does not arise at all: it concerns only judgments.
 On the other hand, these approaches have something in common. Both philosophical systems in the field of gnoseology are formal-logical.
 Kant’s approach, dialectical in the study and explanation of the objective world, in terms of the theory of knowledge was not yet dialectical; or, it is believed rather, that this was negative-dialectical. In fact, this approach is intermediate, syntagmatic.

Особенности синтаксиса немецких фронтовых (архивных) документов

The aim of the study is to identify the syntactic characteristics of the structure of German frontline texts as a separate kind of military discourse with its specificity of expression of logical categories associated with them. The paper examines military frontline texts from the perspective of their functional purpose (orders, reports, summary messages, etc.) and also identifies and describes the syntactic means that form the structure of discourse types of speech, i.e., narration, description, reasoning. Frontline texts make up a significant part of the materials in numerous archives and museums in Germany and Russia, but their role and status in military discourse remain open. The study is novel in that it substantiates the identification of a special type functioning on the basis of written communication during hostilities within the framework of military discourse, as opposed to the status discourse form (orders, formal regulations, codes, etc.) and the personal discourse form (communication through field mail) by conducting a comprehensive analysis of the syntactic structure of frontline texts. As a result of the study, it has been found that the texts of frontline discourse are characterized by the following logical links: attribution, conjunction, implication, which possess the appropriate syntactic means of expression. The analysis of the functional and semantic organization of German military frontline documents has shown that syntax can be considered as the basis of the structural organization of both military discourse as a whole and its varieties in the form of frontline texts.

Special vocabulary of the Russian sublanguage of social work in the stratification aspect

The article examines the vocabulary of the Russian sublanguage of social work from the standpoint of stratification terminology, identifies and characterizes the varieties of terminological vocabulary, as well as special names functioning in the lower case of the sublanguage. The object of the study is the sublanguage of social work employees. The subject of the study is the lexical composition of a special sublanguage of social work. The following methods were used in the course of the study: the method of selective receipt of special texts, the sociolinguistic method, the functional-semantic method and the method of linguistic description. The author considers the studied vocabulary from the standpoint of genesis, formal-structural criterion, motivation, on the basis of correlation with logical categories. The results of the study identified stratification categories of special vocabulary of the Russian sublanguage of social work, carried out the classification of special units by genesis, from the standpoint of formal structural criteria, on the basis of motivation and correlation with logical categories. It is revealed that the key functions of the special vocabulary in the studied sublanguage are nominative and cognitive. In the course of the research, the conclusion is made about the "maturity" of the special vocabulary of the sublanguage of social work and its high linguistic informativeness. The scientific novelty of the research lies in the fact that for the first time (within the framework of the problems of modern linguistics) a comprehensive analysis of the vocabulary of the Russian sublanguage of special work was carried out, stratification categories of professional vocabulary of the sublanguage of social work were identified.

On duality and model theory for polyadic spaces

This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove completeness, omitting types, and Craig interpolation theorems for coherent or intuitionistic logic. Our approach emphasizes the role of interpolation and openness properties, and allows for a modular, syntax-free treatment of these model-theoretic results. As further applications of the same method, we prove completeness theorems for constant domain and Gödel-Dummett intuitionistic predicate logics.

Hegel and the Paradox of Presence

Abstract This essay evaluates Hegel's claim that the phenomenon of time exhibits a quantitative logic in the context of a paradox concerning temporal presence. On the one hand, in time, the present always is. It seems that the very nature of time, assuming that it is really passing, requires us to assent to the continuous being of the present. If time is always passing, there must always be a present when the passing actually occurs and thus when beings actually exist. On the other hand, any particular moment of presence, as a point or an interval, immediately ceases to be or has not yet come to be. And, because of this, no delineated moment can be purely self-present. Conceived as an unextended point, presence would be nothing enduring of its own against time's passing, while, conceived as an interval, presence contains before and after within itself, meaning as an interval that is not actually present at once. The paradox is therefore that time's passing demands we think being present and presence as being, while being present, strictly speaking, seems impossible due precisely to that passing. Hegel claims to reconcile the self-same form of presence, a presence that always is, with continuous change under the category of quantity. However, I argue that the non-identity between the logical category and the phenomenon of time renders this reconciliation ineffective against the paradox, breaking down, more specifically, as it concerns the formation of a temporal magnitude. I evaluate alternative Hegelian interpretations for determining whether the irresolvability of the paradox proves problematic after all, arguing that the paradox in fact presents a significant problem for the conceivability of temporal existence.

Ecological Implications of the Logic of Non-Duality

This paper explores the relationship between language and reality and the ecological implications of dualism, categorical logic, and the Aristotelian three laws of logic, on humans’ attitude toward the natural world. The paper engages in a comparative analysis of two traditions: one from the West (Neo-Platonism) and one from the East (Daoism). It argues that while both Neo-Platonism (as represented by Plotinus’ Enneads) and Classic Daoism (as represented by the Daodejing and the Zhuangzi) are successful in debunking rigid dualistic logic, Plotinus’s Oneness emanation theory in the end falls short of supporting an inclusive ecological ethics in a comprehensive manner. Still mired in dualism, Plotinian Neo-Platonism treats nature and the physical world as recalcitrant matter—an evil best to be avoided rather than embraced. By contrast, Classic Daoism’s non-dual multi-universe perspective of the world has much to offer with regard to creating a new eco-philosophy and ethics that supports a healthy, sustainable, ecology.

Limits, colimits, and spectra of modelled spaces

It is well-known that the construction of Zariski spectra of (commutative) rings yields a dual adjunction between the category of rings and the category of locally ringed spaces. There are many constructions of spectra of algebras in various contexts giving such adjunctions. Michel Coste unified them in the language of categorical logic by showing that, for an appropriate triple (T0,T,Λ) (which we call a spatial Coste context), each T0-model can be associated with a T-modelled space and that this yields a dual adjunction between the category of T0-models and the category of T-modelled spaces and “admissible” morphisms. However, most of his proofs remain unpublished. In this paper, we introduce an alternative construction of spectra of T0-models, which is reminiscent of Zariski spectra, and give a new proof of Coste adjunction. Moreover, we also extend spectra of T0-models to relative spectra of T0-modelled spaces and prove the existence of limits and colimits in the involved categories of modelled spaces. We can deduce, for instance, that the category of ringed spaces whose stalks are fields is complete and cocomplete.

The use of special knowledge in the investigation of violent crimes

The article is devoted to highlighting the issue of the use of special knowledge in the way of conducting an examination during the investigation of crimes committed with the use of violence. The study illustrates that the proposition that the expert’s participation in the evidence in criminal proceedings is based on the laws and categories of dialectics and formal logic and, moreover, is carried out by combining practical and intellectual activity. Also, the main and atypical types of examinations are distinguished: forensic medical; forensic psychiatric; forensic psychological; forensic biological; ballistics; cold weapons examination; trans- and dactyloscopic. Depending on the investigative situation at the time of the forensic examination and the available evidence, a list of issues to be resolved by the expert is indicated, such as: forensic chemistry during the investigation of violent crimes; forensic and orological; soil science; molecular and other genetic examinations, depending on the type of crime, the situation under investigation and the physical objects available. It was concluded that the theoretical and methodological foundations of such examinations need to be updated and adapted to the latest technology and the best state-of-the-art world experience.

Metaphorical Shift as a Way of Forming Professional Jargonisms of Lawyers in the Countries of the Anglo-Saxon Legal Family

The article is aimed at a study of the process of metaphorization involved in the formation of professional jargonisms in the field of Anglo-American jurisprudence. Distinction is made between motivated and unmotivated metaphorical jargonisms. The author highlighted the main source domains of anthropomorphic, socio-morphic, artefactual, and natural-morphic models of formation of jargonisms of English-speaking lawyers. Professionally significant slang names of subjects, objects, substances, places, actions, quantities, qualities are described in accordance with logical categories. Professionally significant slang names of subjects, objects, substances, places, actions, quantities, qualities are described in accordance with logical categories. In accordance with the part of speech of the lexeme that takes on a metaphorical meaning, legal jargonisms are grouped into the following subgroups: substantive, adjectival, verbal, verbal-substantive, and interjectional. Taking into account the semantic structure of the word, monosemantic and polysemantic metaphorical jargonisms are designated. The paper notes the abundance of synonymic relations in the considered layer of non-standard vocabulary.

Modality from the Cross-cultural Studies Perspective: a Practical Approach to Intersemiotic Translation

Any scientific question should be understood as a process of dynamic semiosis in search of truth. The revelatory web is goal-oriented (teleological), but with no stable outcome, static method, redefinition, or fixed agent. All outcomes, methods, and agents are temporary and are temporary “trends” in translation studies that can be abandoned for new ones. The translation can be categorized as a fragmented record or metaphorically as a mosaic, whose components allow the construction of a figurative, diegetic, dramatic world in intersemiotic translation, to be inscribed in the diagram of the narrative. The translation adopts the repetitive and non-repeating behavior patterns of a particular culture, rejecting trendy or outdated translation tools. The same applies to intersemiotic translation with interpretive and reinterpretive meaning. The ideas of the classics about a global approach to semiolinguistics have turned the whole traditional approach to translation studies upside down. The traditional view of the question of intercultural, intersemiotic translation focused on untested dichotomies labeled as dogmatic forms of double self-reflection. Intersemiotic translation offers experimental and temporal responses of a skeptical and evolutionary nature at the boundaries of the translated and untranslatable, correspondence and non-correspondence, conformity and unconformity, the starring role and purpose of intelligence, the dynamism and emotionality of the Falabilist spirit and the Falabilist heart of the translator. It focuses on the concepts of translation and retranslation, the fate of the intercultural text, the fate of the target text, and other semiotic issues of translation in the broadest sense, in the sense of an encoded phenomenon rather than an intersemiotic code. This paper analyzes cultural and linguistic transsemiosis from the perspective of translation and transduction to reveal the essence of intersemiosis. One considers the extrapolarity and complexity phenomenon of modality in terms of cognitive-discursive and semiotic features of its manifestation during translation. In the contemporary scientific pattern, the linguistic category of modality is considered as a functional-semantic, semantic-pragmatic, semantic- syntactic, syntactic, grammatical or logical category. One defines it as the inner attitude of the narrator to the content. The essence of modality in intersemiotic translatin is related to the inner linguistic thinking. Accordingly, intersemiotic translation is the recoding of the original text by means of another sign (semiotic) system.

THE CONCEPT OF «LANGUAGE AWARENESS» IN THE MODERN LINGUISTIC TERMINOLOGY

The article analyzes the historiography and historiosophy of the concept of linguistic consciousness in the projection onto the term system of modern linguistics. The definition of the term is proposed, its integrative connections, generic-species correlations in synchrony and diachrony are clarified. In the historical aspect, the formation of national and social linguistic consciousness and their textual implementation is established. Linguistic, sociocultural, cognitive, communicative factors are taken into account for the comprehensive disclosure of the content of the concept of linguistic consciousness and the differentiation of linguistic concepts related to it. A comprehensive analysis of the concept of language consciousness justifies its status as a psycholinguistic category that covers the results of mental activity, perception and assimilation of information verbalized by means of the national language. Its units are concepts (ethnocentrisms), which are realized in language with the help of an associative-verbal thesaurus: words, phrases, expressions, grammatical and logical categories, grammatical and textual forms, functioning of the intentional-motivational mechanism. In the language, two types of verbal manifestations of linguistic consciousness constantly interact: 1) associated with the formation of a stable mechanism of functional structures of associative-verbal thesauri, the developed core of networks, words, grammatical and logical categories, which is a manifestation of the durability of national memory; 2) connected with dynamic, primarily evaluative, processes in verbal networks, verbal structures, intentional images. Linguistic consciousness in all its varieties (folk, social and ethnocentric, communicative) is a dynamic, culturally and socially conditioned and integral element of the history of the literary language. It changes along with the development of the nation, acquires new forms and manifestations, improves synchronously with the formation of a conscious, intellectual society.

What should a generic object be?

AbstractJacobs has proposed definitions for (weak, strong, split) generic objects for a fibered category; building on his definition of (split) generic objects, Jacobs develops a menagerie of important fibrational structures with applications to categorical logic and computer science, including higher order fibrations, polymorphic fibrations, $\lambda2$ -fibrations, triposes, and others. We observe that a split generic object need not in particular be a generic object under the given definitions, and that the definitions of polymorphic fibrations, triposes, etc. are strict enough to rule out some fundamental examples: for instance, the fibered preorder induced by a partial combinatory algebra in realizability is not a tripos in this sense. We propose a new alignment of terminology that emphasizes the forms of generic object appearing most commonly in nature, i.e. in the study of internal categories, triposes, and the denotational semantics of polymorphism. In addition, we propose a new class of acyclic generic objects inspired by recent developments in higher category theory and the semantics of homotopy type theory, generalizing the realignment property of universes to the setting of an arbitrary fibration.