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...

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).

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 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.

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)

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.

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.

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)

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)

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)

Personal values have long been associated with individual decision behavior. The role played by personal values in decision making within an organization is less clear. Past research has found that managers tend to respond to ethical dilemmas situationally. This study examines the relationship between personal values and the ethical dimension of decision making using Partial Least Squares (PLS) analysis. The study examines personal values as they relate to five types of ethical dilemmas. We found a significant positive contribution of (...) altruistic values to ethical decision making and a significant negative contribution of self-enhancement values to ethical decision making. (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)

We draw on the behavioral agency model to explore the ethical consequences of CEO equity incentives. We argue that CEOs are more concerned with funding pension plans when they have more to gain from their stock options yet will increasingly underfund employee pension funds as their current option wealth increases. Our findings reveal that both effects hold when the CEO has greater power (also occupying board chair) over firm decision making. Our study suggests that there is an ethical dimension (...) to equity incentives, given they are intended to align CEO interests with shareholders, yet potentially incentivize CEO behaviors with adverse consequences for employees. Insights from our findings provide boards and regulators with behavioral levers to protect employee well-being in the context of pension funding. (shrink)

Die These, dass neben dem Wohlergehen und der Moral der Sinn eine dritte, irreduzibel eigenständige und fundamentale Dimension des guten Lebens darstellt, hat im Zuge des erneuten Interesses an der Kategorie des Sinns breite Beachtung gefunden. Das Ziel dieses Beitrags besteht erstens darin zu erkunden, was diese These eigentlich beinhaltet. Bei näherer Prüfung zeigt sich nämlich, dass die These auch und gerade von ihren Vertretern bisher überwiegend durch Appelle an Intuitionen und durch Abgrenzung zu alternativen Positionen, aber eben nur (...) unzureichend positiv motiviert und konturiert wurde. Insbesondere wird vorgeschlagen, zwischen einer axiologischen und einer rationalitätstheoretischen Variante der These zu unterscheiden. Während Sinn gemäß der axiologischen Eigenständigkeitsthese eine irreduzibel eigenständige, fundamentale Wertdimension bildet, entlang derer ein Leben als mehr oder weniger gut qualifiziert werden kann, behauptet die rationalitätstheoretische Eigenständigkeitsthese, dass Sinn eine irreduzibel eigenständige, fundamentale Quelle praktischer Gründe bildet. Diese Unterscheidung ist nicht zuletzt deshalb bedeutsam, weil die zweite These die erste vorauszusetzen scheint, während das Umgekehrte nicht gilt: Selbst Hauptvertreter der axiologischen Eigenständigkeitsthese machen sich die rationalitätstheoretische Variante nur mit großen Einschränkungen zu eigen, die wiederum zu kritischen Fragen auch an die axiologische Fassung Anlass geben. Zweitens soll im Zuge einer Erkundung des durch die axiologische wie auch durch die rationalitätstheoretische Version der Eigenständigkeitsthese aufgespannten Problemfeldes gezeigt werden, dass bisher keine überzeugenden Argumente für die Eigenständigkeitsthese vorgebracht und auch keine plausiblen inhaltlichen Kandidaten für eine Theorie des Sinns, die die Anforderungen an eine solche eigenständige Dimension des guten Lebens und Quelle praktischer Gründe sui generis erfüllen würden, identifiziert werden konnten. Des Weiteren sprechen auch allgemeine wert- und rationalitätstheoretische Erwägungen gegen die Annahme einer solchen Dimension. (shrink)

Planetary protection is not just a matter of science. It is also a matter of value. This is so independently of whether we only include the protection of science or if we also include other goals. Excluding other values than the protection of science is thus a value statement, not a scientific statement and it does not make planetary protection value neutral. It just makes the axiological basis (that is, the value basis) for planetary protection more limited in a way (...) that is inconsistent with the axiological grounds for back contamination, ethically questionable and strategically unwise. However we look at it, we cannot get away from the conclusion that the axiological dimension of planetary protection is a task that needs to involve experts on value theory as well as experts from a range of different sciences and also include opinions from outside the academic community. (shrink)

Hersch’s objective in his paper was to “illustrate how an existential ontology has a great deal to offer psychotherapists”. The first of three sections addresses existential themes such as guilt and anxiety and explores the notion of bad faith; the second focuses on why existential ontology provides a more suitable grounding for psychotherapy than traditional models; and the third offers the author’s invention of a mental status examination that is derived from existential ontology. To illustrate how existential ontology may be (...) useful to psychotherapists, Hersch directs our attention to those existential themes that are crucial to understanding the role ontology plays, existential.. (shrink)

PART I The superpower and asymmetry PART II Jus ad bellum, jus in bello, jus post bellum PART III Leadership and accountability PART IV Soldiersa (TM) ...

In Locke’s economic and politic thinking is possible appraise some articulations that connect the teological, the economic and the politic. The humans work for divine decree and the labor is an economic concept inasmuch as it is the activity that yields private ownership, whose possession entails a natural right for all individuals. Safeguarding this right is liability of the government and of the state institutions. For Locke the market is previous to the civilian society, trade’s regulative structure sets the guidelines (...) of the governmental action, so that money’s circulation should not be interfered directly by the sovereign power neither leading it under particular politic interests. Thus, it is can find out an ontology of market in lockean thought, insomuch as trade space’s existence takes up the natural laws and project them in the space`s political. (shrink)

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

My aim in this article is to investigate the epistemic dimension of reasonableness. In the last decades, the concept of reasonableness has been deeply analysed, and yet, I maintain that a strictly epistemic analysis of reasonableness is still lacking. The goal of this article is to clarify which epistemic features characterize reasonableness as one of the fundamental virtues in the political domain. In order to justify political liberalism through a public justification that averts the risk of falling into a (...) dilemma, it is important to establish in advance which are the epistemic constraints that should be respected. My proposal is that a moderate approach in moral epistemology expresses the best scheme available to us – as moral agents constrained by the limit of our rationality – for establishing a normatively binding, and yet realistic, procedure of justification for political institutions and practices. (shrink)

In light of the observations and research design presented in the previous reports, the current technical report is focused on the relationship between the quality and specificity of the content of the gambling sites and the site’s SEO and marketing policy. This relationship is dependent upon the category of the gambling site and the difference in content quality, and the degree to which the mathematical dimension of gambling is reflected in this content is explained by this dependence.

My purpose in this dissertation is to show that a wide-ranging investigation of Michael Polanyi's epistemology and ontology taken together with his social-political writings reveals the possibility of explicating an ethical language which can be seen, in Polanyi's terms, to be tacit within these works. The work naturally divides into two parts: the first deals with Polanyi's epistemology and ontology; the second deals with the social and political writings. ;The first part consists in two major arguments: the epistemological and the (...) ontological arguments. The epistemological argument consists in lifting out the fundamental dynamic of the knowing act in order to show that this dynamic might apply as well to the knowlede of values, if, as is pointed out, Polanyi includes many other objects of knowledge than those of science in his epistemology. The key point here is that value knowledge, like all forms of knowledge for Polanyi, must be seen as personal knowledge, i.e. value knowledge is rooted in a commitment to believe that some aspect of reality is touched in it, though the standard of correctness is neither a subjective standard nor a claim to complete objectivity but rather an obedience to a commitment to which we expect all persons, including ourselves, to submit. Value knowledge is personal knowledge. ;The second major argument of the first part is the ontological argument. I lift out the ontological structure of the knowing person to demonstrate that a right knowledge of values implies a commitment to the right action involved in attaining such knowledge. This intimate link between knowing and being is essentially the link between values and right actions. ;The first part of the dissertation establishes the possibility of a Polanyian ethic. After taking detailed exception to Harry Prosch's analysis of the possibility of a Polanyian ethic based upon his notion of symbols, an analysis which claimed that ethics must be grounded in a Polanyian understanding of symbols, I push forward the notion of personal ethical knowledge. . . . UMI. (shrink)

The puzzle of the self-torturer raises intriguing questions concerning rationality, cyclic preferences, and resoluteness. Interestingly, what makes the case puzzling has not been clearly pinpointed. The puzzle, it seems, is that a series of rational choices foreseeably leads the self-torturer to an option that serves his preferences worse than the one with which he started. But this is a very misleading way of casting the puzzle. I pinpoint the real puzzle of the self-torturer and, in the process, reveal a neglected (...) but crucial dimension of instrumental rationality. (shrink)