Let be a saturated model of inaccessible cardinality, and let be arbitrary. Let denote the expansion of with a new predicate for. Write for the collection of subsets such that ≡. We prove that if the VC-dimension of is finite then is externally definable.

We compute that the index set of PAC-learnable concept classes is m-complete Σ30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{0}_{3}}$$\end{document} within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^{0}_{1}}$$\end{document} classes, in a sense made precise here. This family of concept classes is sufficient to cover all standard examples, and also has the property that PAC learnability (...) is equivalent to finite VC dimension. (shrink)

We develop “local NIP group theory” in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure G expanding a group, and left invariant NIP formula δ...

In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VC-minimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion full (...) VC-minimality, show that this lies strictly between weak o-minimality and VC-minimality, and show that theories that are fully VC-minimal have low VC-density. (shrink)

We show that any formula with two free variables in a Vapnik–Chervonenkis (VC) minimal theory has VC-codensity at most 2. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acleq= dcleq, the VC-codensity of a formula is at most the number of free variables (from the work of Aschenbrenner et al., the author, and Laskowski).

We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory . Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.

A theory $T$ is shown to have an ICT pattern of depth $k$ in $n$ variables iff it interprets some $k$ -maximum VC class in $n$ parameters.

This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on $\mathrm {VC}_{\mathrm {ind}}$-density and use it to compute the exact $\mathrm {VC}_{\mathrm {ind}}$-density of polynomial inequalities and a variety of geometric set families. The main technical tool used is the notion of a maximum set system, which we juxtapose to indiscernibles. In the second part of (...) the paper we give a maximum set system analogue to Shelah’s characterization of stability using indiscernible sequences. (shrink)

We define a new type of “shatter function” for set systems that satisfies a Sauer–Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah’s two-rank instead of VC dimension. We identify the least exponent bounding the rate of growth of the shatter function, the quantity analogous to VC density, with Shelah’s $\omega $ -rank.

We generalise the concept of clique width to structures of arbitrary signature and cardinality. We present characterisations of clique width in terms of decompositions of a structure and via interpretations in trees. Several model-theoretic properties of clique width are investigated including VC-dimension and preservation of finite clique width under elementary extensions and compactness.

This essay demonstrates a previously unnoticed connection between formal and statistical learning theory with regard to Nelson Goodman’s new riddle of induction. Discussions of Goodman’s riddle in formal learning theory explain how conjecturing “all green” before “all grue” can enhance efficient convergence to the truth, where efficiency is understood in terms of minimizing the maximum number of retractions or “mind changes.” Vapnik-Chervonenkis (VC) dimension is a central concept in statistical learning theory and is similar to Popper’s notion of degrees (...) of testability. I show that for a class inductive problems of which Goodman’s riddle is one example, a reliable inductive method minimizes the maximum number of mind changes exactly if it always conjectures the hypothesis from the set with lowest VC dimension consistent with the data. I also discuss the relevance of these results to language invariance and curve fitting. (shrink)

It has consistently been shown that agents judge the intervals between their actions and outcomes as compressed in time, an effect named intentional binding. In the present work, we investigated whether this effect is result of prior bias volunteers have about the timing of the consequences of their actions, or if it is due to learning that occurs during the experimental session. Volunteers made temporal estimates of the interval between their action and target onset , or between two events . (...) Our results show that temporal estimates become shorter throughout each experimental block in both conditions. Moreover, we found that observers judged intervals between action and outcomes as shorter even in very early trials of each block. To quantify the decrease of temporal judgments in experimental blocks, exponential functions were fitted to participants’ temporal judgments. The fitted parameters suggest that observers had different prior biases as to intervals between events in which action was involved. These findings suggest that prior bias might play a more important role in this effect than calibration-type learning processes. (shrink)

That humans can categorize in different ways does not imply that there are qualitatively distinct underlying natural kinds or that the field of concepts splinters. Rather, it implies that the unitary goal of forming concepts is important enough that it receives redundant expression in cognition. Categorization science focuses on commonalities involved in concept learning. Eliminating makes this more difficult.

This essay is an examination of the perception during the Song dynasty of moral life and human nature as reflected in the moral thought of Zhu Xi 朱熹. It is based on the assumption that for every historical period there is a corresponding particular type of morality.1 The thesis that this analysis defends is the existence of an immanent transmoral dimension within Neo-Confucian morality. This dimension is fully immanent as a constantly present grounding of the individual. It is (...) also fully transmoral as a capacity that enables the individual to surpass conventional notions of morality or moral norms and practices, and to reach the ultimate source of morality. The latter is inward but anchored in a higher... (shrink)

The right to conscientious objection in the provision of healthcare is the subject of a lengthy, heated and controversial debate. Recently, a new dimension was added to this debate by the US Supreme Court's decision in Burwell vs. Hobby Lobby et al. which effectively granted rights to freedom of conscience to private, for-profit corporations. In light of this paradigm shift, we examine one of the most contentious points within this debate, the impact of granting conscience exemptions to healthcare providers (...) on the ability of women to enjoy their rights to reproductive autonomy. We argue that the exemptions demanded by objecting healthcare providers cannot be justified on the liberal, pluralist grounds on which they are based, and impose unjustifiable costs on both individual persons, and society as a whole. In doing so, we draw attention to a worrying trend in healthcare policy in Europe and the United States to undermine women's rights to reproductive autonomy by prioritizing the rights of ideologically motivated service providers to an unjustifiably broad form of freedom of conscience. (shrink)

This paper argues that an adequate conception of a good life should recognize, in addition to happiness and morality, a third dimension of meaningfulness. It further proposes that we understand meaningfulness as involving both a subjective and an objective condition, suitably linked. Meaning arises when subjective attraction meets objective attractiveness. In other words one’s life is meaningful insofar as one is gripped or excited by things worthy of one’s love, and one is able to do something positive about it. (...) The paper concludes with some speculations about how this conception of meaningfulness might help to explain the conditions under which social volunteering can be especially rewarding. (shrink)

Emotion Review, Volume 14, Issue 4, Page 264-269, October 2022. Müller's position-taking view of emotions takes issue with the widely endorsed philosophical notion that emotional feelings are a form of consciousness in which we become acquainted with the evaluative properties of objects and events. Müller rejects this perceptual theory of emotions and casts doubt on the idea that it is through emotional feeling that we develop an awareness of value. In so doing, his proposal amounts to a denial of any (...) epistemic function of emotional feeling. Challenging such a radical move, in my commentary, I discuss several affective phenomena in which feelings do seem to serve an epistemic function. These cases pose problems for Müller's version of the position-taking view of emotion, at least in its current form. (shrink)

The current technical report presents the partial results of the quantitative analysis of the research project, after the review of 247 gambling websites. It is focused on and discusses the usage of the math terms specific to gambling in the reviewed sample. In particular, the fifth technical report discusses the usage of math terms associated with the game of slots, as found in the reviewed sample.

The purpose of the article is the analysis of the causes of the systemic crisis that hit modern civilization through the description of its main structures, identifying the relationship between its elements, assessments of their heuristic potential. This will open up opportunities for finding ways to resolve this crisis, new directions of civilizational development. Theoretical basis of the research are the systems analysis, socio-philosophical and philosophical-anthropological approaches as well as the analysis of scientific developments in the field of global studies. (...) Originality lies in the fact that this article is the first to show the connection between the main structural elements of human civilization as a system. Change in one of the parameters leads to a change in all the others, together with a change in civilization as a whole. Conclusions. The reason for the deep crisis that hit modern civilization is its imbalance as a system. The most important elements of this system are population size, resources and technology, and the core is consciousness in its individual and collective forms. The perception, processing, and use of information, which is a defining civilizational resource, as well as the stability of the entire system depend on the state of consciousness. Consciousness, based on old, obsolete principles and stereotypes, is unable to cope with the most acute challenges of time. New consciousness, since it is formed, will mark the transition to a new theoretical picture of the world and a model of human behavior, in which people will act, driven by proven knowledge, and not willfulness and prejudice. The idea of forming a productive information environment where the ideas of constructiveness and creative work will dominate rather than consumerism and destruction, as is the case at present, must become the categorical imperative of the new consciousness. (shrink)

El campo de intereses de la Antropología es basto. Cubre todas las épocas, todos los espacios, incorporando en las últimas décadas estudios en sociedades complejas, antropología política, económica, estudios de parentesco, etc. Cubre tanto la dimensión biológica -estudio de hominización, clasificación de las variedades raciales- como la dimensión cultural. Pretende explicar tanto las diferencias como las semejanzas entre los distintos grupos humanos. Pretende dar, también, razón tanto de la continuidad como del cambio de las sociedades. Algunos quieren ver las variaciones (...) de las sociedades y las culturas como una evolución semejante a la de las especies. Cuando la biología pretende responder todas las preguntas que el hombre se formula desde una teoría general de los viviente se transforma en una ciencia universal, proponiendo que los comportamientos de los social pasen a lo biológico, algo que hay que criticar. (shrink)

Developing a concept briefly introduced in Counterrevolution and Revolt, Marcuse here addresses the shortcomings of a Marxist aesthetic theory and explores a dialectical aesthetic in which art functions as the conscience of society. Marcuse argues that art is the only form of expression that can take up where religion and philosophy fail and contends that aesthetic offers the last refuge for two-dimensional criticism in a one-dimensional society.

Cost, expected benefits, and risks are paramount in grant agencies' decisions to fund scientific research. In _Cognitive Economy,_ Nicholas Rescher outlines a general theory for the cost-effective use of intellectual resources, amplifying the theories of Charles Sanders Pierce, who stressed an “economy of research.” Rescher discusses the requirements of cooperation, communication, cognitive importance, cognitive economy, as well as the economic factors bearing on induction and simplicity. He then applies his model to several case studies and to clarifying the limits imposed (...) on science by economic considerations. (shrink)

This article utilizes recent Western approaches to the ethical inquiry into human activities of forgetting, especially the approach represented by Ricoeur’s work on memory and forgetting and their ethical functioning. The three areas of Ricoeur’s investigation includes the therapeutic/pathological area; pragmatic area, which deals with the issue of individual and group’s self-identity in relation to time and otherness; and the more explicitly ethical area. These three divisions are useful to start with, but Ricoeur’s work shows some narrowness in neglect of (...) positive, productive and healthy forgetting, which has been deemed significant by the Zhuangzi. This paper is the first of the author’s serial writings to apply Ricoeur’s three areas of forgetting to investigate the forgetfulness of the Zhuangzi, and examines therapeutic forgetting and its ethical dimension only. (shrink)

It has typically been assumed that affective and social components of disagreement, such as trust and fair treatment, can be handled separately from substantive components, such as beliefs and logical principles. This has freed us to count as “deep” disagreements only those which persist even between people who have no animosity towards each other, feel equal to one another, and are willing to argue indefinitely in search of truth. A reliance on such ideal participants diverts us from the question of (...) whether we have swept away the opportunity for some real arguers to have their voices heard, and for those voices to determine the real substance of the disagreement. If affective and social issues need to be assessed side by side with belief differences and reasoning paradigms, investigating trust may assist us to understand and make progress on the affective and social components that are involved in disagreement. (shrink)

A brief survey of the development of some techniques from antiquity to recent times reveals that their initial phase was stimulated not by perspectives of exploiting their outcome, as is usually expected for technology, but by the valorization of the process itself. This initial phase, defined here as technopoiesis, is conceptually and practically distinct from what subsequently becomes technology in respect of inventiveness, standardization, technical skill, level of ornamentation, practical use, integration into systems of exchange, and ritualized versus secular uses. (...) It is shown that technopoiesis may profoundly modify the cultural environment by shaping the universe of beliefs, rituals, and values and that this influence may persist even after the transition to technology. It makes the distinction between technology and technopoiesis essential for evaluating the cultural influence of techniques, from the Paleolithic era to modern times. (shrink)

Spanish has a series of evidential discourse markers that combine the lexical semantics of visual perception with reference to inference or hearsay, for example, evidentemente ‘evidently’, por lo visto ‘visibly, seemingly’, al parecer ‘seemingly’ and se ve ‘one sees that, apparently’. The main aim of this article is to examine the grammatical, semantic and interactional properties of these four evidential discourse markers in informal and formal spoken Spanish. From a semantic point of view, we study the evidential values expressed by (...) these markers and discuss the correlations between them. From a functional point of view, we analyse the evidential markers on the basis of discourse-interactional criteria such as illocutionary force, position in the turn and kind of turn. From a grammatical point of view, we address the preferences in terms of person and Tense/aspect/modality experienced by these evidential markers in discourse. The main result of our analysis is that, as far as the semantic and discourse properties are concerned, evidentemente differs from por lo visto, al parecer and se ve que. The former seems to refer primarily to shared thoughts, developing a reading that goes beyond any of the traditionally distinguished evidential values. The three other markers, by contrast, refer to indirect evidence, often combining the evidential values of reported knowledge and inference. In talk-in-interaction, the two types of markers behave differently: evidentemente does not enhance turn-taking, whereas the other markers leave room for the co-participant to give his or her view of the state of affairs. (shrink)

In this paper, I examine recent phenomenological research on both depressive and manic episodes, with the intention of showing how phenomenologically oriented studies can help us overcome the apparently paradoxical nature of mixed states. First, I argue that some of the symptoms included in the diagnostic criteria for depressive and manic episodes in the DSM-5 are not actually essential features of these episodes. Second, I reconsider the category of major depressive disorder (MDD) from the perspective of phenomenological psychopathology, arguing that (...) severe depressive episodes should not be characterized by any particular moods (such as sadness, hopelessness, or guilt), and should instead be characterized by a diminished capacity for finding ourselves situated in and attuned to the world at all. In other words, the affective dimension of depression should be characterized as a change in the way we have moods, not as a change from one kind of mood to another. Third, I turn to mania, arguing that manic episodes, taken as the opposite of depressive episodes, should be characterized not by any particular moods (such as euphoria, grandiosity, or even irritability), but should instead be characterized by an enhanced or heightened capacity for finding ourselves situated in and attuned to the world. In other words, the affective dimension of mania, like the affective dimension of depression, should be understood as a change in the way we have moods, not as a change from one kind of mood to another. Fourth, I return to the phenomenon of mixed states and argue that the affective dimension of depression and mania, when conceived along the phenomenological lines I set forth in the previous sections, dissolves the paradox of mixed states by showing that the essential characteristics of depression and mania cannot and do not coincide. Many cases of mixed states are diagnosed because moods that we take to be essential features of either depression or mania arise within the context of what is considered to be the opposite kind of episode (e.g. dysphoria, typically associated with depression, often arises in what is otherwise considered a manic state). However, if we conceive of the affective dimension of depression as a decrease in the degree to which one is situated in and attune to the world through moods, and the affective dimension of mania as an increase in the degree to which one is situated in and attuned to the world through moods, then the particular mood one finds oneself in is simply irrelevant to the diagnosis of either depression or mania. As a result, the manifestation of any particular moods in what otherwise seems to be a pure manic or depressive episode does not constitute a mixed state. (shrink)

Background:In the face of scarcity, nurses may inevitably delay or omit some nursing interventions and give priority to others. This increases the risk of adverse patient outcomes and threatens safety, quality, and dignity in care. However, it is not clear if there is an ethical element in nursing care rationing and how nurses experience the phenomenon in its ethical perspective.Objectives:The purpose was to synthesize studies that relate care rationing with the ethical perspectives of nursing, and find the deeper, moral meaning (...) of this phenomenon.Research design:A systematic review and thematic synthesis of qualitative studies was used. Searching was based on guidelines suggested by Joana Brigs Institute, while the synthesis has drawn from the methodology described. Primary studies were sought from nine electronic databases and manual searches. The explicitness of reporting was assed using consolidated criteria for reporting qualitative research. Nine studies involving 167 nurse participants were included. Synthesis resulted in 35 preliminary themes, 14 descriptive themes, and four analytical themes. Discussion of relationships between themes revealed a new thematic framework.Ethical consideration:Every effort has been taken, for the thoroughness in searching and retrieving the primary studies of this synthesis, and in order for them to be treated accurately, fairly and honestly and without intentional misinterpretations of their findings.Discussion:Within limitations of scarcity, nurses face moral challenges and their decisions may jeopardize professional values, leading to role conflict, feelings of guilt, distress and difficulty in fulfilling a morally acceptable role. However, more research is needed to support certain relationships.Conclusions:Related literature is limited. The few studies found highlighted the essence of justice, equality in care and in values when prioritizing care—with little support to the ethical effects of rationing on nurses. Further research on ethical dimension of care rationing may illuminate other important aspects of this phenomenon. (shrink)

The current study evaluates qualitatively how the mathematical dimension of gambling is reflected in the content of gambling websites. A number of gambling websites have been reviewed for their content in that respect. A statistical analysis recorded the presence of the mathematical dimension of gambling and its forms in the content of the participating websites, and a qualitative research study analyzed and assessed the quality of the content with respect to that dimension. The technical reports associated with (...) this study describe the methods used in the processes of review and content analysis, details of the processes, and the specific challenges and difficulties that they posed. (shrink)

The 1948 Universal Declaration of Human Rights recognized that “everyone has the right freely to participate in the cultural life of the community, to enjoy the arts and to share in scientific advancement and its benefits”. As a result, cultural rights have been understood as inseparable from human rights and require protection mechanisms within particular international legal systems. The European continent is proud to have developed one of the most effective mechanisms of the human rights protection by establishing the Council (...) of Europe and adopting the European Court of Human Rights. The recent outbreak of the COVID-19 reformulated many concepts of access to human rights and possibilities to enjoy freedoms. Even if access to culture has been available online for many years, it is the time of globally occurring lockdowns that forced people to stay home and found themselves in a situation when all of a sudden online access to culture became the only way of access to culture. The article aims to analyze the current situation in Europe by asking questions if and how online access to culture is recognized and protected under the Council of Europe’s mechanisms with special emphasis on the case-law of the European Court of Human Rights in this field. (shrink)

This article sets out to improve our analytical understanding of the concept of “linking social capital.” Concretely, the article focuses on disaster contexts where the importance of linking social capital intensifies both for the vulnerable communities and for the local authorities concerned. Through an analysis of existing analytical practices, the article concludes that linking social capital is often subordinated to the two related social capital concepts of bonding and bridging, and that linking social capital is often exclusively defined and operationalized (...) based on expressions of organizational trust and participation. The article proposes a recalibration to encompass the political dynamics, and political survival theory is recommended as a way to address the hitherto underexplored governance dimension. Rather than using trust as the analytical pivot, this analytical entry point may facilitate a more nuanced understanding of the potential risks inherent in the relationships between local authorities and communities in disaster settings. (shrink)

The current technical report of the research project investigating how the mathematical dimension of gambling is reflected in the communication and texts associated with the gambling industry raises the problem of the adequacy of sampling and proposes a new approach in this respect. The qualitative analysis of the reviewed websites is extended to a deeper analysis of language and also to the organization and structure of websites’ content. Although not stated as a goal of the initial project, the research (...) will also try to identify relationships between the specificity of content relative to the mathematical dimension of gambling, and the management and marketing of the website. An overview of the results of the statistical analysis of the current sample is also presented. (shrink)

We prove various results connected together by the common thread of computability theory.First, we investigate a new notion of algorithmic dimension, the inescapable dimension, which lies between the effective Hausdorff and packing dimensions. We also study its generalizations, obtaining an embedding of the Turing degrees into notions of dimension.We then investigate a new notion of computability theoretic immunity that arose in the course of the previous study, that of a set of natural numbers with no co-enumerable subsets. (...) We demonstrate how this notion of $\Pi ^0_1$ -immunity is connected to other immunity notions, and construct $\Pi ^0_1$ -immune reals throughout the high/low and Ershov hierarchies. We also study those degrees that cannot compute or cannot co-enumerate a $\Pi ^0_1$ -immune set.Finally, we discuss a recently discovered truth-table reduction for transforming a Kolmogorov–Loveland random input into a Martin-Löf random output by exploiting the fact that at least one half of such a KL-random is itself ML-random. We show that there is no better algorithm relying on this fact, in the sense that there is no positive, linear, or bounded truth-table reduction which does this. We also generalize these results to the problem of outputting randomness from infinitely many inputs, only some of which are random.Abstract prepared by David J. Webb.E-mail: [email protected]: https://arxiv.org/pdf/2209.05659.pdf. (shrink)

In this paper I offer an account of the normative dimension implicit in D. Bernoulli’s expected utility functions by means of an analysis of the juridical metaphors upon which the concept of mathematical expectation was moulded. Following a suggestion by the late E. Coumet, I show how this concept incorporated a certain standard of justice which was put in question by the St. Petersburg paradox. I contend that Bernoulli would have solved it by introducing an alternative normative criterion rather (...) than a positive model of decision making processes. (shrink)