Let P be the ω-orbit of a point under a unary function definable in an o-minimal expansion ℜ of a densely ordered group. If P is monotonically cofinal in the group, and the compositional iterates of the function are cofinal at +\infty in the unary functions definable in ℜ, then the expansion (ℜ, P) has a number of good properties, in particular, every unary set definable in any elementarily equivalent structure is a disjoint union of open intervals and finitely many (...) discrete sets. (shrink)

Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. But (...) it is well known that 〈ℝ, <, +, · ℚ 〉 defines every real Borel set, in particular, every open subset of any finite cartesian power of ℝ and every subset of any finite cartesian power of ℚ. To put this another way, the definable open sets in models ofTare essentially as simple as possible, whileT′ has a model where the definable open sets are as complicated as possible, as is the structure induced on the new predicate.In contrast to the preceding example, if ℝalgis the set of real algebraic numbers andT′ Th, then no model ofT′ defines any open set that is not definable in the underlying model ofT. (shrink)

Let ℜ be an o-minimal expansion of (ℝ, <+) and (φk)k∈ℕ be a sequence of positive real numbers such that limk→+∞f(φk)/φk+1=0 for every f:ℝ→ ℝ definable in ℜ. (Such sequences always exist under some reasonable extra assumptions on ℜ, in particular, if ℜ is exponentially bounded or if the language is countable.) Then (ℜ, (S)) is d-minimal, where S ranges over all subsets of cartesian powers of the range of φ.

We investigate expansions of the ordered field of real numbers equipped with a family of real power functions. We show in particular that the theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization. We derive that every function of one variable definable in this structure, not ultimately identically 0, is asymptotic at + ∞ to a real function of the form x (...) cxr, c ≠ 0; in particular, this structure is polynomially bounded. Furthermore, given any definable function f:U → with U open in n, if α ε U and f is infinitely differentiable at α, then f is real analytic in a neighborhood of α. (shrink)

Support vector machines are being used increasingly in affective science as a data-driven classification method and feature reduction technique. Whereas traditional statistical methods typically compare group averages on selected variables, SVMs use a predictive algorithm to learn multivariate patterns that optimally discriminate between groups. In this review, we provide a framework for understanding the methods of SVM-based analyses and summarize the findings of seminal studies that use SVMs for classification or data reduction in the behavioral and neural study of emotion (...) and affective disorders. We conclude by discussing promising directions and potential applications of SVMs in future research in affective science. (shrink)

We initiate an investigation of structures on the set of real numbers having the property that path components of definable sets are definable. All o-minimal structures on $(\mathbb {R},<)$ have the property, as do all expansions of $(\mathbb {R},+,\cdot,\mathbb {N})$. Our main analytic-geometric result is that any such expansion of $(\mathbb {R},<,+)$ by Boolean combinations of open sets (of any arities) either is o-minimal or defines an isomorph of $(\mathbb N,+,\cdot )$. We also show that any given expansion of $(\mathbb (...) {R}, <, +,\mathbb {N})$ by subsets of $\mathbb {N}^n$ (n allowed to vary) has the property if and only if it defines all arithmetic sets. Variations arise by considering connected components or quasicomponents instead of path components. (shrink)

An open U ⊆ ℝ is produced such that (ℝ, +, ·, U) defines a Borel isomorph of (ℝ, +, ·, ℕ) but does not define ℕ. It follows that (ℝ, +, ·, U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (ℝ, +, ·). In particular, there is a Cantor set E ⊆ ℝ (...) such that (ℝ, +, ·, E) defines a Borel isomorph of (ℝ, +, ·, ℕ) and, for every exponentially bounded o-minimal expansion $\germ{R}$ of (ℝ, +, ·), every subset of ℝ definable in ( $\germ{R}$ , E) either has interior or is Hausdorff null. (shrink)

We say that E is R-sparse if f(Ek) has no interior, for each k 2 N and f : Rk ! R de nable in R. (Throughout, \de nable" means \de nable without parameters".) In this note, we consider the extent to which basic metric and topological properties of subsets of R de nable in (R;E)# are determined by the corresponding properties of subsets of R de nable in (R;E), when R is an o-minimal expansion of (R;<;+;0;1) and E is (...) R-sparse. The precise statement of the main result is a bit complicated, but we can state some special cases now. (shrink)

The derivation of a category of ‘environmental rights’ (as argued in this journal by Margaret DeMerieux) from certain cases heard in the European Court of Human Rights is examined. Opposing the majority judicial opinion of that court, there is emerging a dissenting view which is reluctant to extend a rights perspective to those nuisances which can, in theory, be avoided by relocation of the family home. This critique is then extended to Marcic v Thames Water Utilities in which the claimant (...) used the Human Rights Act 1998 (as well as common law) to secure damages for an environmental threat (flooding) to his home. It is further argued that any ‘rights’ dimension currently attached to environmental intrusion on private life will give way to policy imperatives once the effects of climate change come to be recognized. (shrink)

In this paper, we continue investigations into the asymptotic behavior of solutions of differential equations over o-minimal structures.Let ℜ be an expansion of the real field (ℝ, +, ·).A differentiable mapF= (F1,…,F1): (a, b) → ℝiisℜ-Pfaffianif there existsG: ℝ1+l→ ℝldefinable in ℜ such thatF′(t) =G(t, F(t)) for allt∈ (a, b) and each component functionGi: ℝ1+l→ ℝ is independent of the lastl−ivariables (i= 1, …,l). If ℜ is o-minimal andF: (a, b) → ℝlis ℜ-Pfaffian, then (ℜ,F) is o-minimal (Proposition 7). We (...) say thatF: ℝ → ℝlis ultimately ℜ-Pfaffian if there existsr∈ ℝ such that the restrictionF↾(r, ∞) is ℜ-Pfaffian. (In general,ultimatelyabbreviates “for all sufficiently large positive arguments”.)The structure ℜ isclosed under asymptotic integrationif for each ultimately non-zero unary (that is, ℝ → ℝ) functionfdefinable in ℜ there is an ultimately differentiable unary functiongdefinable in ℜ such that limt→+∞[g′(t)/f(t)] = 1- If ℜ is closed under asymptotic integration, then ℜ is o-minimal and definesex: ℝ → ℝ (Proposition 2).Note that the above definitions make sense for expansions of arbitrary ordered fields. (shrink)

A close scrutiny of a European Community directive on habitats and of the statutory instrument by which it is implemented in Britain reveals small but nevertheless significant concessions towards an ecocentric approach. Planning law now allows interference in the habitats of protected species only when human interests are demonstrably overriding. Recent decisions of the European Court of Justice have given a very restrictive interpretation of the circumstances in which such interference may be permitted. The implications for further ecocentric influence in (...) environmental law are discussed. (shrink)

This paper makes the case for a wider acceptance of a probabilistic approach to causation in negligence. This acceptance would help to remove much of the incoherence which has come to afflict the English law of personal injury law. This incoherence can also be found in other common law jurisdictions (notably those of the United States, Canada and Australia). Concentrating upon recent UK case law, the argument opposes the contention that ‘naked statistics’ can play no role in establishing causation. The (...) argument is controversial but it can be reduced to three unremarkable grounds: (1) With its acceptance (albeit in certain carefully prescribed circumstances) of liability for a negligently increased risk which has eventuated, the common law has already embraced a probabilistic conception of causation; (2) The English common law already employs a probabilistic (frequentist) approach to identifying coincidences; and (3) With the ‘balance of probabilities’ as the standard of proof in civil cases, the common law has long had a probabilistic (epistemic) concept at its core. Probabilistic approaches (at both the type and token level) are shown to be consistent with laypersons’ understanding of the concepts such as risk, chance, odds and likelihood. Moreover, a wider acceptance of a probabilistic perspective on causation would entail no major challenge to the fundamental aims of tort, viz. deterrence and corrective justice. (shrink)

We begin by proving that any Presburger-definable image of one or more sets of powers has zero natural density. Then, by adapting the proof of a dichotomy result on o-minimal structures by Friedman and Miller, we produce a similar dichotomy for expansions of Presburger arithmetic on the integers. Combining these two results, we obtain that the expansion of the ordered group of integers by any number of sets of powers does not define multiplication.

This article surveys the exponential increase in Rand references in scholarly and popular sources to illustrate her cultural ascendancy as an iconic figure. Special attention is paid to Rand's impact on popular literature, television, cartoons, and illustrated media, including comics. Rand's own involvement in illustrated presentations of her ideas is explored, as is her influence on such comic artists as Steve Ditko, Frank Miller, and others. Nathaniel Branden's insights on the role of comics in projecting heroic values are also (...) addressed. (shrink)

Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one (on the other hand, it is known via [10, 3, 7] that every real of strictly positive effective Hausdorff dimension computes (...) reals whose effective packing dimensions are arbitrarily close to, but not necessarily equal to, one). (shrink)

The importance of mate choice and sexual selection has been emphasized by the majority of evolutionary psychologists. This paper assesses three cases of work on mate choice and sexual selection in evolutionary psychology: David Buss on cross-cultural human mate preferences, Randy Thornhill and Steve Gangestad on the link between mate preferences and fluctuating asymmetry, and Geoffrey Miller on the role of Fisher’s runaway process in human evolution. A mixture of conceptual and empirical problems in each case highlights the general (...) weakness of work in evolutionary psychology on these issues. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Wandering at Ease in the ZhuangziJames MillerWandering at Ease in the Zhuangzi. Edited by Roger T. Ames. Albany: State University of New York Press, 1998. Pp. viii + 239."Good grief!" exclaimed the reviewer as he greedily tore open the package from Philosophy East and West. "Not another book on Zhuangzi!"As it turns out, Wandering at Ease in the Zhuangzi, edited by Roger T. Ames, was found to be (...) not just "another book on Zhuangzi" but, instead, a wonderful collection of creative essays that genuinely wanders on Zhuangzi's vast spirit and that should appeal to a broad academic audience. Do not be deceived by the publisher's blurb on the back cover: "an excellent balance of philological and philosophical analysis." This summary of the book's contents proves to be fortunately misleading.The common thread running through this book is that it is dedicated to Yang Yu-wei, who taught many of the contributors while they were graduate students at Taiwan Normal University. Randall P. Peerenboom hilariously describes his first encounter with Professor Yang in a coda to his essay "Living Beyond the Bounds:Henry Miller and the Quest for Daoist Realization":He darted across the busy main street, dodging traffic, all the while calling out my name in a booming voice sure to attract the attention of the wandering undead and waving his arms in whirlwind fashion, managing somehow to evoke simultaneously images of Don Quixote and Sancho Panza, Jack Nicholson in One Flew over the Cuckoo's Nest, and the Bodhidharma. Welcome, I thought, to the wonderful world of Oz.(p. 139) [End Page 125]This description sets the tone for the essays here, which concentrate on the Zhuangzi's humor, character, and personality, unafraid to stride out across the busy, one-way streets of traditional academic disciplines. While remaining rigorously within the bounds of academic probity, this volume steadfastly resists the dangerous encroachment of desiccating intellectualism upon the wit, intelligence, and charm of one of the world's greatest works of literature.All of the essays "live beyond the bounds" in some fashion or other. Chris Jochim's "Just Say No to 'No Self' in Zhuangzi" reviews recent writing on self and personhood in the Zhuangzi, and includes the treatment of Zhuangzi in the theories of flow and happiness by the noted psychologist Mihalyi Csikszentmihalyi. Daniel Coyle's study of the zhenren (authentic person), lurks tentatively in the shadows of comparative mysticism. A comparison such as "Theocentrism aside, Zhuangzi's language is Eckhart-like in that it cancels itself out, short-circuiting the intellect so as to open one up to spontaneity and the omnipresence of Heaven" deserves greater exploration than a short essay can afford. James D. Sellmann's essay on the transformative effects of humor is briefly illuminated by a reference to Milan Kundera's The Book of Laughter and Forgetting (1986),1 but this worthy literary intersection is only pursued in a footnote. The question of philosophy and literature is also raised in William Callahan's study of action and decision making in the story of Cook Ding. Callahan, again in footnotes, acknowledges the influence of Kundera, Barthes, and Derrida in his quest to understand what it means to "read" literary philosophy or philosophical literature. His essay, however, owes its chief debt to the linguistic analysis of Chad Hansen and A. C. Graham, and we can only hope that he will soon furnish us with the full fruits of his literary education.One group of essays deals with particular characters in the Zhuangzi. Kirill Ole Thompson's inventive study of fishermen in the Zhuangzi wades into the waters of Tang poetry, incorporating translations of Zhang Zhihe, Liu Zongyuan, Wang Wei, and Sikong Shu. The literary connection is only in a coda, but it is there nonetheless. A future study would perhaps do well to broaden this research to include works of art. One thinks of Wang Meng's masterpiece of around 1360, Fisherman of Huaxi or the Yuan literatus Wu Zhen's Fisherman Recluse on Lake Dongting, both in the collection of the National Palace Museum, T'aipei.2Zhuangzi's close companion, Hui Shi, is the subject of... (shrink)

The primary aim of this book is to understand how seemings relate to justification and whether some version of dogmatism or phenomenal conservatism can be sustained. It also addresses a number of other issues, including the nature of seemings, cognitive penetration, Bayesianism, and the epistemology of morality and disagreement.

Open-minded people should endorse dogmatism because of its explanatory power. Dogmatism holds that, in the absence of defeaters, a seeming that P necessarily provides non-inferential justification for P. I show that dogmatism provides an intuitive explanation of four issues concerning non-inferential justification. It is particularly impressive that dogmatism can explain these issues because prominent epistemologists have argued that it can’t address at least two of them. Prominent epistemologists also object that dogmatism is absurdly permissive because it allows a seeming to (...) provide justification even if the seeming was caused in some apparently inappropriate way. I conclude by disarming this objection. (shrink)

It is natural to think that many of our beliefs are rational because they are based on seemings, or on the way things seem. This is especially clear in the case of perception. Many of our mathematical, moral, and memory beliefs also appear to be based on seemings. In each of these cases, it is natural to think that our beliefs are not only based on a seeming, but also that they are rationally based on these seemings—at least assuming there (...) is no relevant counterevidence. This piece is an introduction to a volume dedicated to the question of what the connection is between seemings and justified belief: under what conditions, if any, can a seeming justify its content? (shrink)

The second edition of Doing Ethics in Media continues its mission of providing an accessible but comprehensive introduction to media ethics, with a theoretical grounding in moral philosophy, to help students think clearly and systematically about dilemmas in the rapidly changing media environment. Each chapter highlights specific considerations, cases, and practical applications for the fields of journalism, advertising, digital media, entertainment, public relations, and social media. Six fundamental decision-making questions - the "5Ws and H" around which the book is organized (...) - provide a path for students to articulate the issues; understand applicable law and ethics codes; consider the needs of stakeholders; work through conflicting values; integrate philosophic principles; and pose a "test of publicity." Students are challenged to be active ethical thinkers through the authors' reader-friendly style and use of critical early-career examples. While most people will change careers several times during their lives, all of us are life-long media consumers, and Doing Ethics in Media prepares readers for that task. Doing Ethics in Media is aimed at undergraduate and graduate students studying media ethics in mass media, journalism, and media studies. It also serves students in rhetoric, popular culture, communication studies, and interdisciplinary social sciences. The book's companion website-doingethicsin.media, or www.doingmediaethics.com-provides continuously updated real-world media ethics examples and collections of essays from experts and students. The site also hosts ancillary materials for students and for instructors, including a test bank and instructor's manual. (shrink)

It is often assumed that it seems to each of us as though time flows, or passes. On that assumption it follows either that time does in fact pass, and then, pretty plausibly, we have mechanisms that detect its passage, or that time does not pass, and we are subject to a pervasive phenomenal illusion. If the former is the case, we are faced with the explanatory task of spelling out which perceptual or cognitive mechanism (or combination thereof) allows us (...) to detect and track time’s passage (§2.1) If the latter, then we are faced with the task of explaining how, and why, we are subject to a pervasive phenomenal illusion (§2.2). There is, however, a third, somewhat less discussed, explanatory project. Rather than assuming that it seems to each of us as though time passes, and then attempting to explain why it seems that way, we jettison that assumption. According to these views it does not seem to us as though time passes; instead, we come to falsely believe that it seems to us as though time passes (§3). This view requires that we explain how we come to have systematically false beliefs about the way our experiences seem to us. This paper aims to motivate this third explanatory strategy and say something about what kind of cognitive mechanisms might be responsible for our having a false belief that it seems as though time passes, (§3.1) and why we might have evolved (some of) those mechanisms (§3.2). In particular, the paper does not aim to argue for this view: rather, it aims to present it as a viable contender alongside other more common views. (shrink)

Does inferential justification require the subject to be aware that her premises support her conclusion? Externalists tend to answer “no” and internalists tend to answer “yes”. In fact, internalists often hold the strong higher-level requirement that an argument justifies its conclusion only if the subject justifiably believes that her premises support her conclusion. I argue for a middle ground. Against most externalists, I argue that inferential justification requires that one be aware that her premises support her conclusion. Against many internalists, (...) I argue that this higher-level awareness needn’t be doxastic or justified. I also argue that the required higher-level awareness needn’t be caused in some appropriate way, e.g. by a reliable or properly functioning faculty. I suspect that this weaker higher-level requirement is overlooked because, at first glance, it seems absurd to allow nondoxastic, unjustified, and unreliably-caused higher-level awareness to contribute to inferential justification. One of the central goals of this paper is to explain how such weak awareness can make an essential contribution to inferential justification. (shrink)

"Feminism, Theory and the Politics of Difference" looks at the question of difference across the full spectrum of feminist theory from liberal, radical, lesbian ...

The chapter introduces and characterizes the notion of fittingness. It charts the history of the relation and its relevance to contemporary debates in normative and metanormative philosophy and proceeds to survey issues to do with fittingness covered in the volume’s chapters, including the nature and epistemology of fittingness, the relations between fittingness and reasons, the normativity of fittingness, fittingness and value theory, and the role of fittingness in theorizing about responsibility. The chapter concludes with a brief discussion of issues to (...) do with fittingness that aren’t covered extensively by the volume’s chapters in order to indicate avenues for further research. (shrink)

Used as the basis of the program at the Equinox Holistic Alternative School in Toronto, The Holistic Curriculum advocates for an integrative approach to teaching and learning with a focus on developing a deep connection between mind and body.

After offering an opening consideration of the hazards of neoliberalism, I address the general shape of the crisis of care that has evolved under its auspices. Two aspects of this crisis require greater attention: the moral precarity of caregivers and the relational harms of neoliberal capitalism. Thus, I first consider the moral precarity that caregivers experience by drawing on a concept that originates in scholarly work on the experiences of healthcare workers and combat veterans, namely, moral injury. Through this concept, (...) we can see how caregivers in late-stage capitalism face a seemingly unavoidable violation of their own significant moral beliefs. Second, I examine how the crisis of care results not only in individual harms of moral injury but also in harms to relationships themselves, as I continue to track the impact of moral injury on our intrapersonal and interpersonal lives. Ultimately, I argue that an important facet of the crisis of care is how it operates as a crisis of relationality in which our intrapersonal and interpersonal connections are placed under practical and moral strain. In taking a broader view, we can see how the fraying of particular intrapersonal and interpersonal connections can accumulate, resulting in the unraveling of wider webs of interdependency, just when we need them most. Throughout the paper, I zero in on the moral implications of the crisis of care driven by neoliberalism, featuring the damages that caregivers and their relationships sustain when situated in morally precarious ways. In doing so, I drive home the point that the crisis of care under neoliberalism is as much a moral and relational crisis as it is a political and economic one. (shrink)

Classical acquaintance theory is any version of classical foundationalism that appeals to acquaintance in order to account for non-inferential justification. Such theories are well suited to account for a kind of infallible non-inferential justification. Why am I justified in believing that I’m in pain? An initially attractive (partial) answer is that I’m acquainted with my pain. But since I can’t be acquainted with what isn’t there, acquaintance with my pain guarantees that I’m in pain. What’s less clear is whether, given (...) classical acquaintance theory, it’s possible to have non-inferential justification to believe something false. Classical acquaintance theorists try to make room for such a possibility, but I argue that the attempts of Richard Fumerton, Ali Hasan, and Evan Fales are inadequate. I’ll focus on introspective justification, but similar issues arise for a priori justification as well. (shrink)

This chapter explores whether and when experience can be evidence. It argues that experiences can be evidence, and that this claim is compatible with just about any epistemological theory. It evaluates the most promising argument for the conclusion that certain experiences (e.g., seeming to see) are always evidence for believing what the experiences represent. While the argument is very promising, one premise needs further defense. The argument also depends on a certain connection between reasonable belief and the first person perspective.