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)

We identify two aspects of the problem of maintaining perceptual stability despite an observer's eye movements. The first, visual direction constancy, is the (egocentric) stability of apparent positions of objects in the visual world relative to the perceiver. The second, visual position constancy, is the (exocentric) stability of positions of objects relative to each other. We analyze the constancy of visual direction despite saccadic eye movements.Three information sources have been proposed to enable the visual system to achieve stability: the structure (...) of the visual field, proprioceptive inflow, and a copy of neural efference or outflow to the extraocular muscles. None of these sources by itself provides adequate information to achieve visual direction constancy; present evidence indicates that all three are used.Our final question concerns how information processing operations result in a stable world. The three traditionally suggested means have been elimination, translation, or evaluation. All are rejected. From a review of the physiological and psychological evidence we conclude that no subtraction, compensation, or evaluation need take place. The problem for which these solutions were developed turns out to be a false one. We propose a “calibration” solution: correct spatiotopic positions are calculated anew for each fixation. Inflow, outflow, and retinal sources are used in this calculation: saccadic suppression of displacement bridges the errors between these sources and the actual extent of movement. (shrink)

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)

This collective paper on radicalization and violent extremism part of the ‘Philosophy of education in a new key’ initiative by Educational Philosophy and Theory brings together some of the leading contemporary scholars writing on the most pressing epistemological, ethical, political and educational issues facing post-9/11 scholarship on radicalization and violent extremism. Its overall aim is to move beyond the ‘conventional wisdom’ associated with this area of scholarly research best represented by its many slogans, metaphors and other thought-terminating clichés. By providing (...) conceptual lenses on issues previously compartmentalized primarily [or even exclusively] in security and intelligence studies or at the fringes of scholarly interest, radicalization and violent extremism turn out to be much more complex than ‘radicalization studies’ has been eager to acknowledge. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

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)

Mindfulness-based interventions have proved effective in reducing various clinical symptoms and in improving general mental health and well-being. The investigation of the mechanisms of therapeutic change needs methods for assessment of mindfulness. Existing self-report measures have, however, been strongly criticized on various grounds, including distortion of the original concept, response bias, and other. We propose a psychophysiological method for the assessment of the mindfulness learned through time-limited mindfulness-based therapy by people who undergo meditation training for the first time. We use (...) the individual pre-post-therapy changes (dERPi) in the event-related brain potentials (ERPs) recorded in a passive meditation task as a measure of increased mindfulness. dERPi is computed through multivariate assessment of individual participant's ERPs. We tested the proposed method in a group of about 70 recurrently depressed participants, randomly assigned in 1.7:1 ratio to mindfulness-based cognitive therapy (MBCT) or cognitive therapy (CT). The therapy outcome was measured by the long-term change (dDS) relative to baseline in the depression symptoms (DS) assessed weekly, for 60 weeks, by an online self-report questionnaire. We found a strong, highly significant, negative correlation (r = -0.55) between dERPi (mean = 0.4) and dDS (mean = -0.7) in the MBCT group. Compared to this result, the relationship between dDS and the other (self-report) measures of mindfulness we used was substantially weaker and not significant. So was also the relationship between dERPi and dDS in the CT group. The interpretation of dERPi as a measure of increased mindfulness was further supported by positive correlations between dERPi and the other measures of mindfulness. In this study, we also replicated a previous result, namely, the increase (dLCNV) of the late contingent negative variation (LCNV) of the ERP in the MBCT group, but not in the control group (in this case, CT). We interpreted dLCNV as a measure of increased meditative concentration. The relationship between dLCNV and dDS was, however, very week, which suggests that concentration might be relatively unimportant for the therapeutic effect of mindfulness. The proposed psychophysiological method could become an important component of a "mindfulness test battery" together with self-report questionnaires and other newly developed instruments. (shrink)

We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II1factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

The Ukrainian photographer Sergey Bratkov started his career in 1987 with his first solo shows in Kharkiv, Cheb, and Tel Aviv. He has since enjoyed international recognition from solo and group exhibitions in Europe an.

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

The volume collects classics of Marxist historiography of science, including a new translation of Boris Hessen's “The Social and Economic Roots of Newton's ...

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.

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.

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (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)

In this paper we develop a general theory of algorithmic fairness. Drawing on Johnson King and Babic’s work on moral encroachment, on Gary Becker’s work on labor market discrimination, and on Strawson’s idea of resentment and indignation as responses to violations of the demand for goodwill toward oneself and others, we locate attitudes to fairness in an agent’s utility function. In particular, we first argue that fairness is a matter of a decision-maker’s relative concern for the plight of people from (...) different groups, rather than of the outcomes produced for different groups. We then show how an agent’s preferences, including in particular their attitudes to error, give rise to their decision thresholds. Tying these points together, we argue that the agent’s relative degrees of concern for different groups manifest in a difference in decision thresholds applied to these groups. (shrink)

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

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)

This volume brings together the religious and philosophical writings of the founders of Russian religious philosophy, Aleksei Khomiakov and Ivan Kireevsky. Both began their intellectual careers in the literary world of the 1820s. The texts collected here make the philosophical concepts of Sobornost (community, universality, wholeness, ecumenicity) and integral knowledge, available to western readers. Based on the primacy of the heart, the spiritual wholeness of the human being and the cognitive will, integral knowing moves beyond rationality to union with the (...) object of knowledge in knowing. This book provides an introduction to Russian religious philosophy, and a profound, meditative text for anyone concerned with human and spiritual unity. Also included are two responses to Slavophile ideas by the prominent Russian philosophers Pavel Florensky and Nikolai Berdiaev. (shrink)

La quatrième de couverture indique : "Ils souffrent comme nous. Comme nous aussi, ils jouissent du bien-être. Mieux que nous parfois, ils s'imposent par la ruse et l'intelligence. Comment continuer à les traiter comme des " choses " dont on se contenterait de condamner l'abus? Mais faut-il pour autant leur accorder des droits, et si oui lesquels? Et qui veillera à leur application? Pour répondre à ces questions et à tant d'autres, Boris Cyrulnik l'éthologue, Elisabeth de Fontenay la philosophe, (...) Peter Singer le bioéthicien croisent leurs regards et confrontent leurs savoirs sur la question animale. Trois sensibilités, trois parcours, trois formes d'engagement : la voie est tracée, au-delà des divergences et des contradictions, et en partie grâce à elles, pour que le législateur s'attelle à la rédaction du contrat qu'il nous faut maintenant passer sans délai avec nos frères en animalité, au nom de la dignité humaine.". (shrink)

Im 2009 erschienenen Buch "Philosophie des Leidens" versucht Boris Wandruszka, jene immanente Lebensstruktur und Lebensdynamik aufzudecken, die zu den einfachsten und fundamentalen Strukturmomenten des Leidens vorstosst; diese erste "Wissenschaft vom Leiden" transzendierte daher nicht die Grenzen der Anschaubarkeit, sondern verblieb in der "Immanenz des 'inneren Lebens' bzw. des Erlebens". Im aktuellen Buch "Metaphysik des Leidens" werden die "realen Bedingungen der Moglichkeit von Leiden" ermittelt: Wie muss eine Welt beschaffen sein, damit darin ein leidendes Wesen erscheinen konne? Welche Rolle hat (...) das Leiden in Bezug zum fundamentalen Widerfahrnis-, Resonanz- und Responsivitatscharakter des Lebens? Es wird gezeigt, dass menschliches Leben, das einer plural-agonalen Welt ausgesetzt ist, nicht leidfrei moglich ist, dass aber andererseits das Leid nicht das letzte Wort sein kann, sondern notwendig auf Ganzheit, Reifung, Erlosung und Harmonie bezogen ist. Nur auf dem Hintergrund der Spannung zwischen absoluter Seins-, Sinn- und Lebensfulle und der stets problematischen und fragilen Teilhabe von Menschen am "absoluten und leiduberwindenden Urleben" kann Leiden entstehen, durchlitten, verstanden, aber auch uberwunden werden. Hier erreicht der "Opfergedanke", in dem das unvermeidliche Leid frei angenommen und dadurch transformiert wird, seine reinste und hochste Ausformung. Erst nach Klarung dieser Verhaltnisse wird die "Theodizeefrage" als "das Problem der Probleme" angegangen und am Leitfaden der Hiob-Erzahlung diskutiert. Letztlich erweist sich, dass trotz allem Schmerz, Mangel, Unrecht und Unsinn ein "Potential des Unendlichen" im Leiden verborgen liegt, das auf seine Uberwindung durch Sein-, Sinn- und Werterfullung, durch Tat, Erkenntnis und Liebe verweist und dass diese drei "Machte" der Leidensherausforderung bedurfen, um ihre Weite, Tiefe und Hohe auszuloten. (shrink)

Merleau-Ponty's «Phenomenology of Perception» suggests perception to be the primary level of the giveness of the world. Perception appears as always an incomplete synthesis of the plural, bringing together bodily and material aspects. Such the simplest interpretation of perception as rendering a contact within the dyad «body-world» is a preliminary axiom for explaining the rest of the process of noematic sense formation. At the same time, Merleau-Ponty’s theoretical intuitions clearly presuppose more, and perception is also thought of as the final (...) point where sense is already given by some way. Thus, in Phenomenology, the second interpretation of perception presumes it to be sense-giving accompanied by the tacit cogito. Merleau-Ponty suggests that these interpretations are compatible with each other, but the transition between them seems really problematic. In the research author shos that the limit of the initial synthesis of perception - some sense of the perceived (exemplyfing meanings as «this horse», «the green density that rushed towards me») - is unattainable from within perception itself and by its means. Perception is itself mediated by other faculties, such as memory, reflection, and imagination. Argumentation for this thesis is carried out in several ways; the relations in the perception/imagination pair show us the most characteristic case, where Merleau-Ponty, judging by later works, himself comes close to recognizing the limitations of the hypothesis of «the world of perception», to the need for a phenomenological development of the topic of faculties. Based on the application of the phenomenological method and the analysis of the conceptual constructions of Merleau-Ponty, we can conclude the following: «the world of perception» does not exist, but the phenomenology of faculties is demanded. (shrink)

This paper explores the use of new scientific techniques to examine collections of historic scientific apparatus and other technological artefacts. One project under discussion uses interferometry to examine the history of lens development, while another uses X-ray fluorescence to discover the kinds of materials used to make early mathematical and astronomical instruments. These methods lead to surprising findings: instruments turn out to be fake, and lens makers turn out to have been adept at solving the riddle of aperture. Although exciting, (...) in some ways this is neither novel nor particularly unusual. After all, lab techniques have been used in art and archaeological collections for a very long time. In fact, scientific instruments themselves have been examined in this way since at least the 1950s. What, then, is special about the use of new instruments to examine old instruments? We argue that the answer has less to do with measuring historical innovation or establishing priority, and more to do with networks of craft know-how that, typically, have left no other historical traces than those embodied in surviving instruments themselves. We show, in particular, how collections of objects can be mobilised within wider histories of knowledge, placing instruments within a dynamic interplay of craft knowledge, expertise, labour, commerce, and material exchange, over the longue durée. Finally, we suggest that these kinds of lab analyses can be given an extra dimension through the use of computational modelling, and we introduce the “Tools of Knowledge” project, which is designed to bring together XRF with techniques from the digital humanities, in order to tell a new story about the development of scientific instruments from the 16th to the 20th century. (shrink)

Regular musical activity as a complex multimodal lifestyle activity is proposed to be protective against age-related cognitive decline and Alzheimer’s disease. This cross-sectional study investigated the association and interplay between musical instrument playing during life, multi-domain cognitive abilities and brain morphology in older adults from the DZNE-Longitudinal Cognitive Impairment and Dementia Study study. Participants reporting having played a musical instrument across three life periods were compared to controls without a history of musical instrument playing, well-matched for reserve proxies of education, (...) intelligence, socioeconomic status and physical activity. Participants with musical activity outperformed controls in global cognition, working memory, executive functions, language, and visuospatial abilities, with no effects seen for learning and memory. The musically active group had greater gray matter volume in the somatosensory area, but did not differ from controls in higher-order frontal, temporal, or hippocampal volumes. However, the association between gray matter volume in distributed frontal-to-temporal regions and cognitive abilities was enhanced in participants with musical activity compared to controls. We show that playing a musical instrument during life relates to better late-life cognitive abilities and greater brain capacities in OA. Musical activity may serve as a multimodal enrichment strategy that could help preserve cognitive and brain health in late life. Longitudinal and interventional studies are needed to support this notion. (shrink)

There is a growing trend in European countries for childbearing to occur later in women’s lives. The recent increase in the use of ART, together with the long-term trend towards later childbearing, raises questions as to the acceptable age of childbearing in contemporary society. ART legislation varies considerably across Europe and age limits for access to fertility treatment are rarely defined. The legislation takes into account the preferences of potential parents; children’s preferences, however, are not ascertained. The article discusses a (...) research method used in a survey of older children and young adults. The objective of the survey was to answer the following questions: What age would children prefer their parents to be if they could choose? What are their reasons? Respondents were asked the following question: “How old would you like your mother and father to be when you are 20 (version for respondents younger than 16) or 25 (version for those older than 16) if you could wave a magic wand?” Furthermore, their reasons for wishing a change were identified through an open question, “Why would you like to change the age of your parents?”. (shrink)

The notion of “projective aesthetics” is considered in this paper for the first time as a variant of the recourse to praxis that characterizes contemporary aesthetics and its “aesthetic involvement”. Projective aesthetics involves the use of methodologies of a new type: “schizoanalysis”, “conceptivism” and “projectivism”. The emphasis is put on the principle of “rhizome” and on the features of so-called “culturonics”, a way of thinking “through projects” in the cultural sphere. Projective aesthetics implies a way of philosophizing about art and (...) aesthetics which is defined by a functional orientation in terms of a process of aestheticization and artification, and, accordingly, of projectivity. The connection between projective aesthetics and the peculiarities of modern communicative aesthetics is also examined, together with the need for creating a philosophical glossary of artistry and modern art, meant as a relevant project for aesthetics. In the text, a special place is also given to a number of projects implemented in the process of teaching philosophical aesthetics, as related to beauty as well as with the direct participation of students in filling out the contents of the above-mentioned glossary. (shrink)