We consider the well-known provability logic GLP. We prove that the GLP-provability problem for polymodal formulas without variables is PSPACE-complete. For a number n, let L0n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^{n}_0}$$\end{document} denote the class of all polymodal variable-free formulas without modalities ⟨n⟩,⟨n+1⟩,...\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle n \rangle,\langle n+1\rangle,...}$$\end{document}. We show that, for every number n, the GLP-provability problem for formulas from L0n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^{n}_0}$$\end{document} (...) is in PTIME. (shrink)

Let Con↾x denote the finite consistency statement “there are no proofs of contradiction in T with ≤x symbols.” For a large class of natural theories T, Pudlák has shown that the lengths of the shortest proofs of Con↾n in the theory T itself are bounded by a polynomial in n. At the same time he conjectures that T does not have polynomial proofs of the finite consistency statements Con)↾n. In contrast, we show that Peano arithmetic has polynomial proofs of Con)↾n, (...) where Con∗ is the slow consistency statement for Peano arithmetic, introduced by S.-D. Friedman, Rathjen, and Weiermann. We also obtain a new proof of the result that the usual consistency statement Con is equivalent to ε0 iterations of slow consistency. Our argument is proof-theoretic, whereas previous investigations of slow consistency relied on nonstandard models of arithmetic. (shrink)

It is well-known that natural axiomatic theories are well-ordered by consistency strength. However, it is possible to construct descending chains of artificial theories with respect to consistency strength. We provide an explanation of this well-orderedness phenomenon by studying a coarsening of the consistency strength order, namely, the$\Pi ^1_1$reflection strength order. We prove that there are no descending sequences of$\Pi ^1_1$sound extensions of$\mathsf {ACA}_0$in this ordering. Accordingly, we can attach a rank in this order, which we call reflection rank, to any$\Pi (...) ^1_1$sound extension of$\mathsf {ACA}_0$. We prove that for any$\Pi ^1_1$sound theoryTextending$\mathsf {ACA}_0^+$, the reflection rank ofTequals the$\Pi ^1_1$proof-theoretic ordinal ofT. We also prove that the$\Pi ^1_1$proof-theoretic ordinal of$\alpha $iterated$\Pi ^1_1$reflection is$\varepsilon _\alpha $. Finally, we use our results to provide straightforward well-foundedness proofs of ordinal notation systems based on reflection principles. (shrink)

In this paper, we study finitely axiomatizable conservative extensions of a theoryUin the case whereUis recursively enumerable and not finitely axiomatizable. Stanisław Krajewski posed the question whether there are minimal conservative extensions of this sort. We answer this question negatively.Consider a finite expansion of the signature ofUthat contains at least one predicate symbol of arity ≥ 2. We show that, for any finite extensionαofUin the expanded language that is conservative overU, there is a conservative extensionβofUin the expanded language, such that$\alpha (...) \vdash \beta$and$\beta \not \vdash \alpha$. The result is preserved when we consider eitherextensionsormodel-conservative extensionsofUinstead ofconservative extensions. Moreover, the result is preserved when we replace$\dashv$as ordering on the finitely axiomatized extensions in the expanded language by a relevant kind of interpretability, to witinterpretability that identically translates the symbols of the U-language.We show that the result fails when we consider an expansion with only unary predicate symbols for conservative extensions ofUordered by interpretability that preserves the symbols ofU. (shrink)

By a well-known result of Kotlarski et al., first-order Peano arithmetic \ can be conservatively extended to the theory \ of a truth predicate satisfying compositional axioms, i.e., axioms stating that the truth predicate is correct on atomic formulae and commutes with all the propositional connectives and quantifiers. This result motivates the general question of determining natural axioms concerning the truth predicate that can be added to \ while maintaining conservativity over \. Our main result shows that conservativity fails even (...) for the extension of \ obtained by the seemingly weak axiom of disjunctive correctness \ that asserts that the truth predicate commutes with disjunctions of arbitrary finite size. In particular, \ implies \\). Our main result states that the theory \ coincides with the theory \ obtained by adding \-induction in the language with the truth predicate. This result strengthens earlier work by Kotlarski and Cieśliński. For our proof we develop a new general form of Visser’s theorem on non-existence of infinite descending chains of truth definitions and prove it by reduction to Gödel’s second incompleteness theorem, rather than by using the Visser–Yablo paradox, as in Visser’s original proof. (shrink)

We fix a gap in a proof in our paper Reducing ω-model reflection to iterated syntactic reflection.

Journal of Mathematical Logic, Volume 23, Issue 02, August 2023. In mathematical logic there are two seemingly distinct kinds of principles called “reflection principles.” Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic reflection principles assert that every provable sentence from some complexity class is true. In this paper, we study connections between these two kinds of reflection principles in the setting of second-order arithmetic. We prove that, for (...) a large swathe of theories, [math]-model reflection is equivalent to the claim that arbitrary iterations of uniform [math] reflection along countable well-orderings are [math]-sound. This result yields uniform ordinal analyzes of theories with strength between [math] and [math]. The main technical novelty of our analysis is the introduction of the notion of the proof-theoretic dilator of a theory [math], which is the operator on countable ordinals that maps the order-type of [math] to the proof-theoretic ordinal of [math]. We obtain precise results about the growth of proof-theoretic dilators as a function of provable [math]-model reflection. This approach enables us to simultaneously obtain not only [math], [math] and [math] ordinals but also reverse-mathematical theorems for well-ordering principles. (shrink)

Changes in the productive forces and, consequently, in the economic structure of socialist society as a whole are being prepared by the current relationships of production. We refer particularly to the influence of socioeconomic processes under the conditions of the revolution in science and technology on the development of the individual as a factor in the productive forces and as subject in production relationships.

RésuméQuels sont les objets de la perception? Deux réponses célèbres à cette question soutiennent que ce sont soit les images des objets extramentaux, c'est-à-dire la façon dont ils nous apparaissent, soit les objets eux-mêmes. Dans cet article, je présente une analyse de cette question par Abū l-Barakāt al-Baġdādī, un savant post-avicennien dont l'impact sur l'histoire de la philosophie islamique a été largement négligé. Abū l-Barakāt s'est opposé au dualisme épistémologique traditionnel aristotélicien-avicennien, qui établit une distinction entre la perception sensorielle des (...) particuliers matériels et la conception des universaux immatériels, notamment en ce qui concerne le percevant et/ou la structure de la perception. Selon la théorie d'Abū l-Barakāt, tous les actes épistémiques ont la structure unifiée d'une relation directe entre un même percevant et les objets eux-mêmes – matériels et immatériels. Sa thèse principale consiste à dire qu'avoir des organes corporels n'est pas nécessaire pour la perception sensorielle. Dans la dernière section de cet article, je montre que la critique d'Abū l-Barakāt de la tradition aristotélicienne-avicennienne fut considérée comme une innovation révolutionnaire en épistémologie. Cela peut avoir déterminé les théories épistémologiques de deux des philosophes arabes postavicenniens les plus importants : Faḫr al-Dīn al-Rāzī et Šihāb al-Dīn al-Suhrawardī. (shrink)

Niels Bohr was born on October 7, 1885. He was one of the great innovators in physical science in the twentieth century. It so happens that 1985 also marks fifty years since the long discussions, which had begun in the 1920s between Albert Einstein and Bohr on the philosophical problems of quantum physics, attained their apogee. An article co-authored by Einstein, B. Podolsky, and N. Rosen, "Can Quantum Mechanics Be Considered a Complete Description of Physical Reality?," was published in 1935 (...) in the journal Physical Review. According to Bohr, "by virtue of its clarity and, it would seem, flawless argumentation, the work of Einstein, Podolsky, and Rosen has created excitement among physicists and played a great role in the discussion of general philosophical questions of physics." Precisely as a result of the publication of this article, the critical position of Einstein concerning quantum mechanics became known to a broader circle of physicists. In the same year, Bohr responded to Einstein and his co-authors with an article under the same title. (shrink)

The concept of retroactive apparent occurrence, the main ingredient of Wheeler's delayed-choice thought experiments, is systematically incorporated into the quantum theory of measurement (in the framework of the recent review of Busch, Lahti, and Mittelstaedt). Besides, the (general) notion of individual-system measurement is introduced, and, due to it, premeasurement is defined by a truly minimal condition. Finally, retroactive apparent occurrence is made use of to derive apparent objectification in measurement. The derivation is discussed in the framework of the quantum mechanical (...) approach to the objectification problem. (shrink)

No argument from the Arabic philosophical tradition has received more scholarly attention than Avicenna's ‘flying man’ thought experiment, in which a human is created out of thin air and is able to grasp his existence without grasping that he has a body. This paper offers a new interpretation of the version of this thought experiment found at the end of the first chapter of Avicenna's treatment of soul in theHealing. We argue that it needs to be understood in light of (...) an epistemological theory set out elsewhere by Avicenna, which allows that all the constitutive properties of an essence will be clear to someone who understands and considers that essence. On our reading, this theory is put to work in the ‘flying man’: because the flying man would grasp that his own essence has existence without grasping that he has a body, connection to body cannot be constitutive of the essence. (shrink)

This is a translation of an article which appeared in 1928 in the journal Red Virgin Soil (Krasnaya nov) founded by Aleksandr Voronsky. Its author, the Russian Marxist Fedor Kapelusz, makes use of the now largely-ignored book of Algie Simons, Social Forces in American History (1911). In comparing America’s past to its present, Kapelusz offers a sharp political assessment and at the same time a contribution to the materialist conception of American history.

The article attempts to explain the difficulty of systematization of philosophical categories. Philosophical categories are defined as common forms of cognitive and world view attitude of the man to the nature, society and his own existence. The article also analyses basic approaches to the process of creating the system of philosophical categories in the history of philosophical thought. The review of the major historical phases of philosophical interpretation of categories allows to state the existence of the problematic issue connected with (...) forming the system of categories. A lot of attempts have been undertaken on this subject. All of them were found controversial. It can be explained by the fact that all the attempts to systematize categories contradict the following principles - if categories are universal reflection forms of objective characteristics of existence, then their hierarchy must be the reflection of these characteristics’ hierarchy. But it is impossible to imagine that the "hierarchy" principle operates in the system of being, because the objective world is organized rather on the principle of "equality" than "subordination". The article addresses functional and developmental characteristics of philosophical categories. The article gives the author`s understanding of the concept of "philosophical categories". (shrink)

In this article the author holds that progress in philosophy is a vague concept. Its criteria are not universally acknowledged. All that is clear is that philosophy does not develop in a linear way. Philosophy is polydiscoursive. As for the past fifty years, the author believes three important things happened in philosophy. (1) It has been shown that consciousness exists not within one individual but spreads within a community of people; (2) philosophy has discovered autism, a result that helps us (...) to understand a human being as neither a biological nor a social individual but a third thing—a dreaming being who is not only asocial but also tongueless, where speech and consciousness are separated; and (3) contemporary philosophy has learned to distinguish between sign and symbol. And it has been realized that the human mind is neither an instinct nor a computer but an objectified suffering, a transformed emotion. (shrink)

В сборник включены ранее не публиковавшиеся религиозно-философские произведения Ф. Н. Глинки.

Essentialism can be defined as a metaphysical theory according to which things have essential and accidental properties. In this paper, I will address Avicennian essentialism, that is, essentialism...

ABSTRACTScholarship on medieval philosophy has rightfully acknowledged the historical and systematical merit of Avicenna’s thought in all divisions of philosophy. Avicenna however did not...

One of the most widespread claims combining epistemology and metaphysics in post-Avicennian Islamic philosophy was that every object of thought is real. In Muʿtazilite reading, it was endorsed due to a theory of knowledge which states that knowledge is a connection or relation between the knower and the object known. Avicennists accepted it due to the rule that in a proposition “s is p” if p is something positive s has to be positive and real too. Hence, insofar as one (...) can conceptually distinguish between two non-existent items, they have to be real. In this article, the author presents significant consequences of this theory: the acceptance and denial of non-existent yet real extramental objects; the concept of mental existence as an alternative solution; the conceivability of paraconsistent ideas and their reality or reducibility to some real objects. (shrink)

This book constitutes the refereed proceedings of the 13th International Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012, held in Helsinki, Finland, in July 2012, co-located with the 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012. The 34 papers were carefully reviewed and selected from a total of 127 submissions. The papers present original research and cover a wide range of topics in the field of design and analysis of algorithms and data structures.

In the article the trends of national industrial enterprises development are investigated. The problems of innovative development of domestic industry are identified based on state industrial development concept. Particular attention is paid to the analysis of the management policy of industrial enterprises personnel quantity and quality dates. The processes of the personnel decreases invariably accompanied by a number of organizational and technical issues that will determine new requirements for the organization of internal management model of enterprise environment. Considered and analyzed (...) organizational and administrative activities of increasing professional and technical potential of personnel stuff. The paper proposes the ways to improve effectiveness of personnel stuff policy based on the current terms of international industrial market. The author refined the professional competences model structure of industrial enterprises staff. Consider the structure of complex events management personnel structure and the ways of their further development and implementation. (shrink)

A short report on the trip to India.--Philosophical doctrine of Buddhism.--Logic in ancient India.--The doctrine of categorical imperative in the Brāhmaṇas.

A central question in the history of metaphysics concerns the ontological status of such notions as 'redness,' 'humanity,' or 'animality,' which one calls 'universals.' Since one uses these notions to describe objects in the real world, it may seem intuitive that they exist in extramental reality: one says that universals are 'real'. Famously, though, several problems arise from this view. A central problem known both to medieval and contemporary scholars goes as follows: I look at a red rose and recognize (...) that there is 'redness' in it. Then, I look at a red apple and recognize that there is 'redness' in it, too. Does this mean that one and the same 'redness' appears in both the rose and the... (shrink)

Avicenna's analysis of the definition of substance and accident repeatedly emphasizes two points: one and the same essence cannot be substance in one instance and accident in another; whetherxis extrinsic or intrinsic for an underlying subject,ydoes not tell us anything as to whetherxis substance or not. Both points are development in an argument against certain unnamed people who claimed the opposite. In this article I will show that Avicenna's opponents are to be identified with the mainstream Baghdad Peripatetic School which (...) based itself on the Late Antique rule that “parts of substances are substances”. As for Avicenna's own position, it was developed on the basis of the heterodox position of Yaḥyā b. ʿAdī, who anticipated Avicenna's first point. This is a further piece of evidence for something that has only recently begun to be appreciated: the influence of Ibn ʿAdī on Avicenna.RésuméL’analyse d’Avicenne portant sur les définitions de la substance et de l’accident met en exergue les deux propositions suivantes: 1) la même essence ne peut être à la fois une substance dans un cas et un accident dans un autre; 2) le fait quexsoit extrinsèque ou intrinsèque à unysous-jacent ne nous permet pas de conclure quexest une substance. Ces deux propositions sont articulées dans un débat avec d’autres personnes ayant un point de vue opposé dont on ne connaît pas l’identité. Dans cet article, nous verrons que ces adversaires font partie de l’école péripatétique de Bagdad, qui elle-même s’appuie sur une proposition datant de l’Antiquité tardive et selon laquelle les parties de substances sont elles-mêmes des substances. La position d’Avicenne fut développée à partir de celle de Yaḥyā b. ʿAdī. Cet article apporte ainsi un argument nouveau qui met en évidence l’influence, remarquée seulement depuis peu, d’Ibn ʿAdī sur Avicenne. (shrink)

Central among the complex philosophical problems created by the development of contemporary physics is the problem of the objectivity of physical knowledge, the problem of the reflection of objective reality in our knowledge.

The specificity of tantric soteriology consists of a combination of three basic principles - unity, salvation, and bliss. This article explores the principle of salvation. Spiritual liberation implies the final overcoming of obstacles hindering the new worldview. Unlike the principle of unity, the principle of salvation focuses on difference, not on identity, drawing a sharp line between the desired state of liberation and the present state of dependence. The main obstacles to spiritual liberation are expressed in the well-known triad “avidyā (...) - karma - saṃsāra”. The principle of salvation appears in Tantrism in two interrelated forms, the ascetic and śaktic ones. Both of them agree with each other in rejection of spiritual ignorance. Spiritual ignorance is the main “negative goal”; without deliverance from it there is no freedom. The state of ignorance is existential one and endowed with powerful protective “forces”. The principle of salvation implies the deliverance not only from everything that is usually considered negative, but also of “positive” things. In the śaktic mode of the principle of salvation, it is assumed that an incorrect view of reality is eliminated by a correct view of it. Due to the fact that, according to the tantric adepts, the energies of the divine Śakti act in the world, the understanding of this fact leads the adept to stop perceiving himself as a dependent being even in the midst of an infinite variety of processes and events of the world. Life is then perceived as an unconditioned, spontaneous “divine play”, a stream of divine pleasure. Ascetic form can be reduced to an ontological interpretation of the principle of salvation, and śaktic form to a cognitive one. (shrink)