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.

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)

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.

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.

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)

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)

The author first argues against the view that an agent is morally blameworthy for performing an action only if it is morally wrong for that agent to perform that action. The author then proposes a replacement for this view whose gist is summarized in the principle: an agent S is morally blameworthy for performing action A only if S has the belief that it is wrong for her to do A and this belief plays an appropriate role in S’s Aing. (...) He focuses on explicating the role an agent’s belief that a prospective action, A, of hers is wrong must play in the production of her A-ing in order that she be blameworthy for A-ing. Towards this end, the author makes use of cases involving akrasia and self-deception. (shrink)

The scholarship on meaningful work has approached the topic mostly from the perspective of the subjective experience of the individual worker. This has led the literature to under-theorize, if not outright ignore, the cultural and normative dimension of meaningful work. In particular, it has obscured that a person’s ability to find meaning in her life in general, and her work in particular, is typically anchored and dependent on shared institutions and cultural aspirations. Reflecting on the future of work, particularly (...) on the dangers posed by the threat of technological unemployment, helps us recognize this cultural and normative dimension of meaningful work. I argue that a world with few work opportunities is a world devoid of a core structuring ideal around which our society has organized itself and, as such, will strain our ability to make sense of what it means to find life meaningful. To make this case I show that work operates as a central organizing _telos_ around which our contemporary lives gravitate. Work touches everyone and everything, defining the rhythms of our days and weeks and providing a center of gravity around which our lives are structured. Work constitutes a central dimension of human flourishing. Through work we provide for our material needs, develop our skills and virtues, build community, and contribute to the common good. As such, work constitutes a central organizing ideal in contemporary Western societies, a fact has significant normative force and plays an important role in our finding work meaningful. (shrink)

Many of us today are all too willing to accept a humanist and scientific account of the universe which considers human existence as a fleeting accident. The triumph of John Hick’s gripping work is his exposure of the radical insufficiency of this view. Drawing on mystical and religious traditions ancient and modern, and spiritual thinkers as diverse as Julian of Norwich and Mahatma Ghandi, he has produced a tightly argued and thoroughly readable case for a bigger, more complete, picture of (...) reality in which a fifth, spiritual dimension, plays a central role. ‘Essential reading for anyone concerned with spirituality in the modern world’ Professor Keith Ward, University of Oxford Erudite, provocative and deeply moving, Hick’s persuasive narrative will prompt all curious readers to re-examine their own spiritual horizons.‘This stimulating book opens up many fundamental issues that must concern everyone. It deserves to be widely read. ‘ Expository Times ‘Learned, lucid and engaging, easy to read and easy to applaud for its sheer clarity of style and its breadth of interest, even when one disagrees with it!’ Anvil. (shrink)

How are justified belief and rational belief related? Some philosophers think that justified belief and rational belief come to the same thing. Others take it that justification is a matter of how well a particular belief is supported by the evidence, while rational belief is a matter of how well a belief coheres with a person’s other beliefs. In this paper, I defend the view that justification is a dimension of rationality, a view that can make sense of both (...) of these conflicting accounts. When it modifies belief, ‘rational’ is a multidimensional adjective, as there are multiple dimensions along which a belief can be rational. I will argue that one of these dimensions is justification, an account that can not only explain why philosophers give diverging theories of the relationship between justified belief and rational belief, but can also reveal why rational belief and justified belief are closely related despite being distinct. (shrink)

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 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)

The current report presents results of the qualitative analysis of the usage of the key math terms in the content of the reviewed websites in the current sample, with emphasis on the necessary distinctions for the word and concept of ‘odds’. Patterns, motivations, conceptual and contextual aspects of the usage are discussed. The theoretical norms of adequacy of this usage in the context of gambling are briefly presented. -/- Technical report of the research project 'Reflection of the mathematical dimension (...) of gambling in iGaming online content - A qualitative analysis'. (shrink)

Expressives like damn and bastard have, when uttered, an immediate and powerful impact on the context. They are performative, often destructively so. They are revealing of the perspective from which the utterance is made, and they can have a dramatic impact on how current and future utterances are perceived. This, despite the fact that speakers are invariably hard-pressed to articulate what they mean. I develop a general theory of these volatile, indispensable meanings. The theory is built around a class of (...) expressive indices. These determine the expressive setting of the context of interpretation. Expressives morphemes act on that context, actively changing its expressive setting. The theory is multidimensional in the sense that descriptives and expressives are fundamentally different but receive a unified logical treatment. (shrink)

Looks at the ways people soothe or console themselves when faced with suffering and studies the psychological use of transitional objects.

I distinguish between the classical Gricean approach to conversational implicatures , which I call the action-theoretic approach, and the approach to CIs taken in contemporary cognitive science. Once we free ourselves from the AT account, and see implicating as a form of what I call “conversational tailoring”, we can more easily see the many different ways that CIs arise in conversation. I will show that they arise not only on the basis of a speaker’s utterance of complete sentences but also (...) on the basis of sub-sentential clauses—cases of so-called embedded implicatures—as well as from discourse segments containing several sentences—cases that Geurts calls ‘multiplicatures’. I will argue that they arise also from contents that are themselves implicit, such as presupposed contents or other implicatures. All but the first sort of case are difficult for the traditional Gricean AT account to handle, whereas they fall naturally out of an account that sees conversational participants as engaged in conversational tailoring—i.e., as engaged in a process of shaping informational and discourse structural properties of utterances in their successive conversational turns, and hence shaping their interlocutors’ cognitive environments. (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 (professional challenges and moral dilemmas, dominating considerations, perception of a moral role, and experiences of the ethical effects of rationing). 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 aesthetic transformation becomes a vehicle of recognition and indictment. Herbert Marcuse, 1978, p. 9 In his ‘Reflections on Reclamation through Art’, Thomas Heyd poses the question: Can art ef...