Home – Home – Jornals – Philosophy of Sciences 2025 number S5

We take a look at the definition of a halting probability from logical and algorithmic information theoretical points of view.

The subject-matter of investigation is the nontrivial modal-logic problem of equivalence of de-dicto and de-re types of modalities. The target - explicating, exact formulating and adding the precisely formulated principle of equivalence of the modality-types as a new proper philosophy axiom scheme to the multimodal axiomatic system of formal philosophy Φ+∃. The scientific novelty : for realizing the target, the already published formal axiomatic theory Φ+∃ has been transformed into a qualitatively different logically formalized multimodal axiomatic system called Φ^DR due to manifest taking into an account and systematical dealing with the different modality types called de-dicto and de-re. For accomplishing the transformation, (1) definitions of the alphabets of artificial object-language and meta-language of Φ+∃ have been changed: new symbols Ω^D and Ω^R standing for perfection-modalities (belonging to the types D and R, respectively) have been included into the alphabet of metalanguage of Ф^DR; (2) in Φ^DR, one new axiom-scheme (containing the new symbols Ω^D and Ω^R) has been added to the set of axiom-schemes of Φ+∃; (3) by means of the artificial language of Φ^DR, a precise formulation of the principle of equivalence of the modality-types de-dicto and de-re is given, and the concrete epistemic condition, under which the equivalence principle is valid, is defined. For the first time, a nontrivial multimodal interpretation is given for the traditional formal logic square of opposition and hexagon. Also, for the first time, these geometric figures have been utilized for visual modeling a system of formal-axiological relations among qualitatively different de-re - perfection-modalities as evaluation-functions.

This paper examines the problem of semantics of intensional contexts from a special perspective related to the principles of operation of generative artificial intelligence (AI). Intensional contexts such as beliefs, desires, knowledge and convictions pose a particular challenge for modern language models, since they require taking into account the meanings of expressions in logical possible worlds or cognitive states of subjects. This paper is a kind of sketch for the formulation of a problem that has an engineering and philosophical dimension. Here, we analyze the mechanisms of operation of transformers that use contextual embeddings to model the meanings of words through self-attention. It was revealed that modern language models are able to effectively process anaphoric dependencies and contextual connections, but they face limitations when interpreting intensional constructions. Particular attention is paid to experiments with vector representations of objects in multidimensional space, during which difficulties arise when distinguishing between subjective beliefs and objective reality. The nature of the difficulties indicates that working with intensional contexts requires not only a simple analysis of probabilistic connections between words, but also a deeper understanding of the semantics of linguistic expressions.

We illustrate the functions of the concept of dispute in the formal theory of argumentation with the help of two well-known examples from the theory of argumentation: the example of Harry from Bermuda, used by S. Toulmin, and the example of Tweety the penguin, who does not fly, although it is a bird, used in non-monotonic logic. Reconstruction of these examples allows us to show the importance of the concept of dispute in the logic of argumentation for developing ways to solve the task of finding and selecting the strongest arguments with which the outcomes of argumentation between the parties can be identified. The solution of this task is a unification of the efforts of two leading areas of modern formal theory of argumentation - the argumentation logic and the dialectical theory of argumentation.

This article describes the language, semantics, and proof theory for firs t-order hybrid modal logic, which solves the problem of cross-world quantification.

The paper examines the logical representation of knowability in terms of the first-order hybrid epistemic logic proposed by C. Proietti. This logic contains alethic and epistemic modalities, and hybrid operators. Two drawbacks of Proietti’s formalization are shown and two modifications thereof are suggested.

We show that the description of the primary apperception in the Critique of Pure Reason (2^nd edition) - which is necessary for any synthesis by an act of judgement - contains a contradiction. According to Kant, in order to synthesise by an act of judgement a single representation from the elements of a given in intuition manifold, it is necessary to recognise the representations which are contained in this manifold as my own representations. In order to do this, it is necessary to carry out the synthesis of a certain representation. This synthesis, according to Kant, requires no further syntheses. But the latter synthesis requires a new synthesis. Therefore, a synthesis that does not have other syntheses as a prerequisite for its realisation is impossible. The argument makes use of the semantic analysis of representations (Vorstellungen) that are synthesised by judgments, so that in the present paper we intend to show a change in the understanding of Kant in the light of the “semantic turn”.

The article explores Michael Polanyi's concept of tacit knowledge and its relevance in contemporary scientific and technological contexts. It reviews the historical and epistemological background, the social dimension of collective tacit knowledge in science, and the challenges posed by the "black box" problem in artificial intelligence. Using the evolution of chess algorithms from Deep Blue to AlphaZero as a case study, the article illustrates the shift from explicit, formalized knowledge to opaque, tacit knowledge. It emphasizes the enduring importance of tacit knowledge for understanding the nature of scientific practice and modern cognitive systems.

This paper offers a critical analysis of the commensurability between two foundational questions in the philosophy of artificial intelligence: “Can a machine think?” and “Can a machine win the imitation game?” It is argued that, despite Alan Turing’s pragmatic substitution proposed in 1950, these questions differ in ontological status and conceptual framework. Drawing on the works of D. Dennett, J. Searle, D. Chalmers, and others, the paper demonstrates that commensurability is possible only in an epistemologically limited, inductive sense-but not in a logical or ontological one. The study emphasizes the necessity of distinguishing behavioral simulation from genuine thinking, thereby avoiding the category mistake often associated with interpreting the Turing Test as proof of machine consciousness.

This article examines the opposition between the practice-oriented and classical approaches in the philosophy of logic. It analyzes the critique of the classical tradition by proponents of the practice-oriented approach. The prospects for a practical turn in the philosophy of logic are explored.

In the first part of the article, I showed that an interfering factor for the development of science and philosophy of science is the lack of consensus in the philosophical community about the philosophical status of the methodology of science, and, as a consequence, inadequate attention to research in this discipline. I have considered two well-known sets of arguments against the methodology of science. The first group is based on the recognition by the philosophical community of the relativistic nature of physical knowledge after the discoveries of the theory of relativity and quantum physics. The second group of arguments is based on the attitude of the classics of the philosophy of science towards science. Thus, P. Feyerabend denied the universal nature of scientific methods, and T. Kuhn often denied the objective development of science. I have formulated the following counterarguments. First, despite a certain relativism in contemporary science, philosophers’ аbstrаction from scientific achievements leads to a decline in the quality of research in the philosophy of science. Secondly, in his autobiography, Feyerabend acknowledged the ironic nature of his famous argument for scientific relativism. In the second part of the article, I described certain prospects for the participation of philosophers with knowledge of specialized sciences in scientific activity, mainly as critics of the imperfections of science and the incorrect use of philosophical ideas by scientists. However, there are certain prospects for the participation of the philosophical community in projects of a non-critical nature, for example, the construction of new criteria of explanation and understanding for the natural sciences and formal disciplines.

The paper aims to show that the example given by J. Fantle and M. McGrath (2002) (pragmatic considerations regarding the risk of attributing the desired epistemic status to a given belief in a given situation affects the very concept of «epistemic fact» and, as a consequence, we must abandon evidentialism as the idea that necessary and sufficient conditions of justification are determined exclusively by available epistemic data) does not achieve its goal. The idea of B. Weatherson’s example (2005) is to show that J. Fantle and M. McGrath do not distinguish between «the degree of confidence in the truth of a proposition» (pragmatic conditions on justification) and «the degree of confidence in a belief» (pragmatic conditions on belief). We want to use the logic of an adequate epistemic basing relation, i.e. «meta-beliefs that explain why these reasons are precisely the reasons by virtue of which the belief is held» (G. Harman, K. Korcz, etc.), connecting the corresponding belief and its reasons. B. Weatherson points out on only one possible option for assessing the basing relation - through the «analogy with lotteries», - but in a more general case, the logic of looking for an adequate epistemic basing relation allows us to more thorougthfully indicate that we can justify the «practical nature of reasoning» without resorting to assumptions that already suggest that we are obliged to interpret justification in terms of «pragmatic encroachment».

This article explores the problem of measurement in quantum mechanics, closely related to the Heisenberg uncertainty principle and philosophical debates about the ontological or epistemological nature of quantum uncertainty. The author traces the evolution of views on this problem-from Einstein's concept of hidden variables to modern interpretations that view measurement as a violation of the closed nature of a quantum system and a process of obtaining information. The goal of the study is to connect modern interpretations of the observation problem with Max Planck's understanding of fundamental thermodynamic quantities (in particular, entropy) and compare it with the modern information approach to the problem of quantum measurements, which is based on Shannon's concept of entropy.The paper presents the meaning of the Heisenberg uncertainty principle and its interpretations (the ontological interpretation of Bohr and Heisenberg, and the epistemological interpretation of Einstein). The connection between the thermodynamic interpretation of the measurement process (based on the ideas of M. Planck) and information theory (K. Shannon's approach) is demonstrated. A comparative analysis of the concepts of entropy in Planck and Shannon is provided: their physical and informational interpretations, areas of application, and semantic emphases. Specific examples illustrating the change in a system's entropy upon the removal of a particle (an ideal gas, a crystal at a temperature close to absolute zero, a system with bound states) are considered.The main conclusions of the article are that entropy in thermodynamics (Planck) and information theory (Shannon) have a common statistical nature, but differ in context and the direction of "uncertainty": for Planck, it is a property of the system for the observer, while for Shannon, it is a property of the source for the receiver. The comparison of the thermodynamic and information approaches opens up prospects for a new understanding of the problem of measurements in quantum mechanics through the prism of information theory. The significance of this work lies in its interdisciplinary synthesis of ideas from thermodynamics, quantum mechanics, and information theory, which allows for a deeper understanding of the nature of quantum uncertainty and the measurement process as an information exchange.

The paper analyzes the problem of interdisciplinarity on the example of T. Fuchs’ neurophenomenology. The author reconstructs the history of the dialogue the philosophy and psychiatry as the history of antinomianism of scientific approaches, reveals the foundations of enactivism as the basis for the cessation of antinomianism in the philosophy of psychiatry, discovers two waves of enactivism in psychiatry. Enactivist attitudes of modern neurophenomenology are clarified. The significance of neurophenomenology for discussions on the “hard problem of consciousness” is shown. The paper includes the consistent analysis of the project of Thomas Fuchs’ neurophenomenology and its serious attitudes: criticism of neurobiologism, reductionism and representationism. The structure of neurophenomenology is reconstructed and the central problem of embodiment is posed. The paper discusses the main pathological transformations of consciousness as a field of intentionality: changes in corporeality, temporality and social relations. It is shown that Fuchs’ ideas on relational psychiatry and polydisciplinarity is especially productive. The author studies the interaction of neurobiology and philosophy, psychotherapy in their analysis and the correction of mental illnesses. The productivity of Fuchs’ model for international specialists and the possibilities of its development in the Russian tradition of neuropsychology and psychotherapy is emphasized.

In this report a history of the emergence of various concepts of possible worlds that have entered science in different ways - as discovery in quantum mechanics, as well as in the course of solving semantic problems in mathematical logic, or through the desire of mathematicians to introduce into physics a categorical apparatus that is alternative to the apparatus based on set theory is provided. According to the author, the criterion of the reality of possible worlds in theoretical terms may be the development of the same physics applied to them as in the case of theoretical physics known to us, the progenitors of which were Newton and Leibniz.

The article examines the philosophical foundations and limits of artificial intelligence rationality within the context of decision-making. The author analyzes the distinction between epistemic and practical rationality, emphasizing the latter as the fundamental basis for rational agent functioning. Central to the discussion is the concept of bounded rationality, according to which decision-making occurs under conditions of incomplete information, cognitive constraints, and limited computational resources. The article argues that ideal rationality is unattainable, making bounded rationality the most appropriate model for artificial intelligence. Four types of rationality are explored: ideal, computational, bounded rationality, and bounded optimality. The study concludes that bounded rationality is practically most applicable in developing intelligent systems. Furthermore, it highlights the necessity of considering these limitations when designing adaptive algorithms and underscores the significance of human involvement in the decision-making process to enhance reliability. The «human-in-the-loop» model is interpreted not merely as a technical mode of interaction, but as an embodiment of situational rationality, taking into account context, moral implications, and the uniqueness of each specific situation. Human participation adds a value-based and interpretative dimension to algorithmic reasoning, restoring the connection between rationality and phronesis. Given that algorithms are limited by resources and prone to errors, it is precisely the human who is capable of identifying contextual nuances and providing meaningful corrections. Thus, human inclusion in the loop emerges as a critical factor in enhancing the reliability of artificial intelligence-driven decisions.

The article examines the metaphysical foundations of naturalism in relation to consciousness. Naturalism is the most natural and widespread, but not devoid of contradictions, philosophical position. Its weak points are the assertion of the priority of scientific knowledge, while the criteria of scientificity often turn out to be vague; the proclamation of reduction as the main principle, adherence to which can deprive the subject of study of its specificity; denial of the significance of ontological foundations in solving epistemological issues. Naturalism in relation to consciousness, in turn, is faced with the need to assert the ontological status of consciousness: it is a separate ontological entity and then all laws known to science must apply to it, or it is not a separate ontological entity and must be considered as a property of the brain or something similar. Non-reductive naturalism regarding consciousness appears as an internally contradictory philosophical position: by refusing to reduce consciousness to the brain in an attempt to defend the uniqueness of the qualitative qualities of mental states, we thereby violate one of the main postulates of naturalism. It turns out that the ontological status of consciousness cannot be ignored when considering consciousness as a special phenomenon; any of our theories of consciousness directly depend on the definition of this status.

The article offers methodological recommendations for the most accurate tracking of the scientometric index of publication activity and demand for publications of a scientist known in science as the Hirsch index(h-index). The author introduces the developed formula for finding the growth of the scientist's citations added over a certain period of time that affect the increase in the Hirsch index, talks about the parameters of its dependence, gives advice on practical non-automated and automated calculation of the index, describes the scope of its application. The annual, or semi-annual, monitoring of the growth index of active citations, according to the author, is intended to stimulate scientists to further publication activities.