In this paper, we study temporal logic for finite linear structures and surjective bounded morphisms between them. We give a characterisation of such structures by modal formulas and show that every pair of linear structures with a bounded morphism between them can be uniquely characterised by a temporal formula up to an isomorphism. As the main result, we prove Kripke completeness of the logic with respect to the class of finite linear structures with bounded morphisms between them.

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

Konstantin Pollok - Kant's Critical Concepts of Motion - Journal of the History of Philosophy 44:4 Journal of the History of Philosophy 44.4 559-575 Muse Search Journals This Journal Contents Kant's Critical Concepts of Motion Konstantin Pollok There are two significant places in Kant's Critical corpus where he discusses the concept of motion. The first is in the Critique of Pure Reason, where in the "Deduction of the Categories" Kant writes: Motion, as an act of the subject , (...) and therefore the synthesis of the manifold in space, first produces the concept of succession—if we abstract from this manifold and attend solely to the act through which we determine the inner sense according to its form. In this passage Kant simply refers to the concept of motion, and the immediate context in which this reference occurs reveals little about what he means by it. In the Metaphysical Foundations of Natural Science, however, motion plays a more significant role, and, concomitantly, it is in his writings on natural science that Kant most fully expresses his thoughts on the subject. For present purposes, the most relevant passage is paragraph 15 of the Preface of the Metaphysical Foundations, where Kant says that the concept of matter had … to be carried through all four of the indicated functions of the concepts of the understanding , where in each a new determination of this concept was added. The.. (shrink)

Konstantin Pollok offers the first book-length analysis of Kant's theory of normativity that covers foundational issues in theoretical and practical philosophy as well as aesthetics. Interpreting Kant's 'critical turn' as a normative turn, he argues that Kant's theory of normativity is both original and radical: it departs from the perfectionist ideal of early modern rationalism, and arrives at an unprecedented framework of synthetic a priori principles that determine the validity of our judgments. Pollok examines the hylomorphism in Kant's theory (...) of normativity and relates Kant's idea of our reason's self-legislation to the 'natural right' tradition, revealing Kant's debt to his predecessors as well as his relevance to contemporary debates on normativity. This book will appeal to academic researchers and advanced students of Kant, early modern philosophy and intellectual history. (shrink)

Various publications claim that medical AI systems perform as well, or better, than clinical experts. However, there have been very few controlled trials and the quality of existing studies has been called into question. There is growing concern that existing studies overestimate the clinical benefits of AI systems. This has led to calls for more, and higher-quality, randomized controlled trials of medical AI systems. While this a welcome development, AI RCTs raise novel methodological challenges that have seen little discussion. We (...) discuss some of the challenges arising in the context of AI RCTs and make some suggestions for how to meet them. (shrink)

PA is Peano Arithmetic. Pr(x) is the usual Σ1-formula representing provability in PA. A strong provability predicate is a formula which has the same properties as Pr(·) but is not Σ1. An example: Q is ω-provable if PA + ¬ Q is ω-inconsistent (Boolos [4]). In [5] Dzhaparidze introduced a joint provability logic for iterated ω-provability and obtained its arithmetical completeness. In this paper we prove some further modal properties of Dzhaparidze's logic, e.g., the fixed point property and the Craig (...) interpolation lemma. We also consider other examples of the strong provability predicates and their applications. (shrink)

Physical theories are complex and necessary tools for gaining new knowledge about their areas of application. A distinction is made between abstract and practical theories. The last are constantly being improved in the cognitive activity of professional physicists and studied by future physicists. A variant of the philosophy of physics based on a modified structural-nominative reconstruction of practical theories is proposed. Readers should decide whether this option is useful for their understanding of the philosophy of physics, as well as other (...) philosophies of particular sciences. (shrink)

The articles examines the teleofunctional solution to the problem of mental causation, presented by Dmitry Volkov in his recently published book Free Will. An Illusion or an Opportunity. D.B. Volkov proposes solutions to three big metaphysical problems – mental causation, personal identity, and free will. Solving the first problem, Volkov creatively combines the advantages of Dennett’s teleofunctional model and Vasilyev’s local interactionism. Volkov’s teleofunctional model of mental causation seeks to prove the causal relevance of mental properties as non-local higher order (...) properties. In my view, its substantiation is based on three points: (a) critics of the exclusion problem and Kim’s model of mental causation, (b) “Library of first editions” argument, (c) reduction of the causal trajectories argument (CTA 1) by Vasilyev to the counterpart argument (CTA 2) by Volkov. Each of these points faces objections. Kim’s criticism is based on an implicit confusion of two types of reduction – reduction from supervenience and from multiple realizability. The latter type does not threaten Kim’s ideas, but Volkov uses this very type in his criticism. The “Library of first editions” argument does not achieve its goal due to compositional features and because non-local relational properties are a type of external properties that cannot be causally relevant. The reduction of CTA 1 to CTA 2 is unsuccessful since, in the case of this reduction, important features of CTA 1 are lost – these are local mental properties, due to which the influence of non-local physical factors occurs. My main objection is that the concept of causally relevant non-local properties is incompatible with the very concept of cause. The set of causally relevant properties of cause can only be local. (shrink)

The English Synopsis is after the text of the book. The book presents an original and generalizing substantive vision of the philosophy of science through the prism of a detailed analysis of the polysystem structure of scientific theories. Theories are considered, firstly, as complex specialized forms of developed scientific thinking about the realities studied by natural science, secondly, as constantly improving tools for producing new knowledge in interaction with experimental research, and thirdly, as carriers of ordered and verified knowledge. Emphasis (...) is placed on their nominal and ontic subsystems. The book develops personal and joint research of the authors (theoretical physicist and philosopher), the experience of teaching philosophy of physics at NaUKMA, philosophy of science at the Higher School of Philosophy at the H. Skovoroda Institute of Philosophy of the National Academy of Sciences of Ukraine and theoretical physics at the National Technical University "Ihor Sikorsky Kyiv Polytechnic Institute". The research is based on a significant source base covering works of modern Western researchers in natural science and philosophy of science. For students, teachers, and scientists who are interested in the problems of modern philosophy of science and have a certain amount of scientific knowledge. It will also be useful for high school students who are eager to become scientists. (shrink)

An application of diagrams for separating modes of theory development.

This article is a commentary on ChatGPT and LLMs (Large Language Models) in general. It argues that this technology has matured to the point where calling systems such as ChatGPT “stochastic parrots” is no longer warranted. But it also argues that these systems continue to have serious limitations when it comes to reasoning. These limitations are much more severe than commonly thought. A large array of examples are given to support these claims.

When it comes to invasive manipulation of animals on the biological level, reactions of disgust are common and often influential on people’s moral judgments. As a case in point, the Belgian Blue, a breed of hyper-enhanced cattle which will serve as a case study for the present article, has historically been met with revulsion. Traditionally, in bio- and animal ethics, this ‘yuck factor,’ has been denied any productive role in proper moral justification, since rationalism is still a dominant paradigm in (...) those disciplines. This is not surprising since rationalism offers the fulfilment of certain expectations we have of morality, like universality, intersubjective communicability, and objectivity. Increasingly, however, the preconceptions of rationalism have been brought into question, both through empirical as well as philosophical insights. In this paper, we will explore a way in which researchers who are, accordingly, critical of rationalism, and who wish to take seriously the role disgust plays in the formation of moral judgments when it comes to biological manipulation of animals, can do so without abandoning those virtues of rationalism which make it such an appealing position. We will do so by offering what we call a ‘tempered’ kind of rationalism, that is, one which conceives of rationality in the terms of Mary Midgley, not as distinct from, but as a possible function of, well-ordered emotion. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

ArgumentPost-Stalinist reforms resulted in dramatic changes in the ways of operation of Soviet science: one can say that they altered the very understanding of what science was, or should be, in the socialist society. A new vision came about as a result of political and rhetorical efforts of scientists, who pushed forward their various, often conflicting, agendas acting in accordance with specific rules of Soviet polity. The most visible part of the reform came with the 1961 administrative reorganization of the (...) USSR Academy of Sciences. The related series of changes, however, was much broader and comprehensive, modifying the relationships between science and ideology, politicians and academic researchers, and establishing the very division between fundamental and applied research, which had been strongly rejected during the preceding Stalinist period. (shrink)

There are no universally adopted answers to the natural questions about scientific concepts: What are they? What is their structure? What are their functions? How many kinds of them are there? Do they change? Ironically, most if not all scientific monographs or articles mention concepts, but the scientific studies of scientific concepts are rare in occurrence. It is well known that the necessary stage of any scientific study is constructing the model of objects in question. Many years logical modeling was (...) dominant in the concept studies. Last decades, concepts came to be regarded as the subject of mathematical modeling. However, different authors take different features of concepts as independent variables of their models. Our objective is to characterize informally the spectra of relevant variables for the modeling of scientific concepts. (shrink)

In this paper, we tackle the widely held view that practice-oriented approaches to ethics are conservative, preserving the moral status quo, and, in particular, that they do not promote any change in our dealings with animals or formulate clear principles that help us to achieve such change. We shall challenge this view with reference to Wittgensteinian ethics. As a first step, we show that moral thought and action rest on basic moral certainties like: equals are to be treated equally and (...) unequals unequally. We then explore the relations between this insight and the notion of the difficulty of reality elaborated by Cora Diamond. Our goal is to show that a Wittgensteinian-Diamondian approach to animal ethics is not necessarily morally conservative. Indeed, it offers a profound practice-oriented approach to animal ethics that is capable of promoting change in human dealings with animals because it is compatible with radical critique. (shrink)

In den Kant-Forschungen werden sowohl historisch als auch systematisch orientierte Arbeiten zur Philosophie Immanuel Kants veröffentlicht. Die Bände stellen Funde unbekannter oder verschollen geglaubter Kantischer Autographen und Vorlesungsskripte vor und erörtern Editionsprobleme der Kantischen Vorlesungen und Werke. Sie enthalten darüber hinaus Studien zu Kants Umfeld und zur Kant-Rezeption im 18. Jahrhundert sowie systematisch angelegte Arbeiten zu Architektonik und System der Philosophie Kants.

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

Against the well-established critical rejection of rights a growing literature in the tradition of agonistic democracy asserts their emancipatory role in the struggles for social change. However, agonistic theorists, invested as they are in the idea of democratic innovation as a process of gradual ‘augmentation’ of existing rules, institutions and practices, fail to account for the ruptural capacity, and hence for the full radical potential, of rights. Using the performative approach, I develop a conception of rights claiming as a defiant (...) practice to express the ruptural dimension of certain forms of rights politics. I demonstrate how defiant rights claiming articulates immanent critique by declaring the incapacity of putative duty-bearer institutions and governments to uphold the claimed right due to structural constraints, thereby generating inevitable contradictions within the extant order and creating the necessity for an alternative one. Moreover, in order to fully capture the emancipatory potential and creative capacity of rights, this article argues for understanding certain forms of rights politics both as augmentation and rupture, taking the two to be different dimensions of the same radical democratic practice. I present the creative use of rights discourse by the Landless Workers’ Movement in Brazil and the transnational network of agrarian movements, La Via Campesina, as precisely such a combination of the practice of augmentation and defiant claims, which has led to the transformation of the right to food and land into the right to food sovereignty, demonstration of the structural embeddedness of rights violations in the existing global regime of food production and distribution, and authorisation of an alternative vision of the future. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 105 Heft: 4 Seiten: 509-530.

Against the standard interpretation of Kant's ‘Copernican revolution’ as the prioritization of epistemology over ontology, I argue in this paper that his critique of traditional metaphysics must be seen as a farewell to the perfectionism on which early modern rationalist ontology and epistemology are built. However, Kant does not simply replace ‘perfection’ with another fundamental concept of normativity. More radically, Kant realizes that it is not simply ideas but only the relation of ideas that can be subject to norms, and (...) thus he shifts the focus from the reality of ideas to the validity of judgments. Section 1 of this paper clarifies the pre-Kantian role of the concept of perfection and examines Kant's critical response to that concept. Section 2 identifies Kant's point of departure from the Cartesian ‘way of ideas.’ Section 3 explains the key problem of his novel account of epistemic normativity. I conclude that Kant's anti-perfectionism must be seen as the driving force behind his ‘Copernican revolution’ in order to fully appreciate his mature account of epistemic normativity. (shrink)

We say that two arithmetical formulas A, B have the Σ1-interpolation property if they have an ‘interpolant’ σ, i.e., a Σ1 formula such that the formulas A→σ and σ→B are provable in Peano Arithmetic PA. The Σ1-interpolability predicate is just a formalization of this property in the language of arithmetic.Using a standard idea of Gödel, we can associate with this predicate its provability logic, which is the set of all formulas that express arithmetically valid principles in the modal language with (...) two modal operators, □ for provability in PA and for Σ1-interpolability. In this paper we determine this provability logic .It turns out that this problem appears to be quite similar to the problem of such modal description of relative interpretability, a problem, solved by Berarducci and Shavrukov. However, the present case is sometimes easier. In particular, we prove in this paper the fixed point property and the Craig interpolation property for our modal system ELH. (shrink)

Nowadays the answer to the question “what is logic?” seems very simple and obvious—“logic is a science,” and after that usually one says what is this science about. As for the expressions “logic is an art” or “the art of logic,” then they are only metaphors or some kind of “façon de parler” used in serious scientific discourse. One of my aims here is to trace the line of development of dichotomy “logic as an art—logic as a science” and to (...) demonstrate that both these feat uses of logic have fundamental historical roots and play very important conceptual role in any theorizing about logic. Despite the fact that logic is undoubtedly a science, it can be interpreted as an art, moreover, the analysis of logic from this point of view expands, it seems to me, the researching possibilities in the field of the philosophy of logic at least in better understanding what is logic, what creates its unity independently from the historical period of its development, topics, and methods. (shrink)

For philosophers of German idealism and early German Romanticism, the imagination is central to issues ranging from hermeneutics to transcendental logic and from ethics to aesthetics. This volume of new essays brings together, for the first time, comprehensive and critical reflections on the significances of the imagination during this period, with essays on Kant and the imagination, the imagination in post-Kantian German idealism, and the imagination in early German romanticism. The essays explore the many and varied uses of the imagination (...) and discuss whether they form a coherent or shared notion or whether they embody points of philosophical divergence within these traditions. They shed new light on one of the most important and enigmatic aspects of human nature, as understood in the context of a profoundly influential era of western thought. (shrink)

Varieties of modern philosophies of mathematical and natural sciences are represented. Specific features of those sciences are analyzed on the basis of graph classifications of the respective philosophies. The importance of reconstructions of practical theories is emphasized for all kinds of philosophies of science used by them. The first part outlines the purpose of the article and considers subject and theoretical, the se- cond — evaluative, nominal, theoretical-reconstructive and linguistic-reconstructive classifica- tions of philosophies of science. The conclusions are made about (...) the problematic application of these classifications to the philosophies of social sciences and humanities. (shrink)

In this paper I discuss the ways in which the early Christian writer Arnobius of Sicca used rhetoric to shape religious identity inAduersus nationes. I raise questions about the reliability of his rhetorical work as a historical source for understanding conflict between Christians and pagans. The paper is intended as an addition to the growing literature in the following current areas of study: the role of local religion and identity in the Roman Empire; the presence of pagan elements in Christian (...) religious practices; the question of how to approach rhetorical works as historical evidence. (shrink)

Philosophy of Science; Ukraine; Polysytemic nature of theories; Practical theories; Subsystems of a theory.

The short exposition of the triplet model of concepts and some definitions connected with it are given. In this model any concept may be depicted as having three characteristics: a base, a representing part and the linkage between them. The paper introduces the fuzzification of concepts in terms of the triplet model.

By taking into account some texts published between the first and the second edition of the Critique of Pure Reason that have been neglected by most of those who have dealt with the deduction of the categories, I argue that the core of the deduction is to be identified as the ‘almost single inference from the precisely determined definition of a judgment in general’, which Kant adumbrates in the Metaphysical Foundations in order to ‘make up for the deficiency’ of the (...) A-deduction. Whereas the first step of the B-deduction is an attempt to show that the manifold of an intuition belongs to the ‘necessary unity of self-consciousness’ by means of the synthesis of the understanding, the second step has the task of showing that the very same synthesis is responsible for the spatio-temporal unity of the manifold. Thus, Kant's ‘answer to Hume’ is that no spatio-temporal objects of experience at all are merely ‘given’, independently of the conceptual activities of the understanding. Against the established view I substantiate the claim that with this ‘almost single inference’ of the second proof step the distinction between judgments of perception and judgments of experience consequently vanished from Kant's thinking. (shrink)