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)

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)

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)

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)

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)

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)

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)

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)

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)

This Introduction introduces readers to the concepts of political philosophy: authority, democracy, freedom and its limits, justice, feminism, multiculturalism, and nationality. Accessibly written and assuming no previous knowledge of the subject, it encourages the reader to think clearly and critically about the leading political questions of our time. THe book first investigates how politcial philosophy tackles basic ethical questions such as 'how should we live together in society?' It furthermore looks at political authority, discusses the reasons society needs politics in (...) the first place, explores the limitations of politics, and asks if there are areas of life that shouldn't be governed by politics. Moreover, the book explores the connections between political authority and justice, a constant theme in political philosophy, and the ways in which social justice can be used to regulate rather than destroy a market economy. In his travels through this realm, Miller covers why nations ar the natural units of government and wonders if the rise of multiculturalism and transnational co-operation will change all this, and asks in the end if we will ever see the formation of a world government. (shrink)

The Neo-Moorean Deduction (I have a hand, so I am not a brain-in-a-vat) and the Zebra Deduction (the creature is a zebra, so isn’t a cleverly disguised mule) are notorious. Crispin Wright, Martin Davies, Fred Dretske, and Brian McLaughlin, among others, argue that these deductions are instances of transmission failure. That is, they argue that these deductions cannot transmit justification to their conclusions. I contend, however, that the notoriety of these deductions is undeserved. My strategy is to clarify, attack, defend, (...) and apply. I clarify what transmission and transmission failure really are, thereby exposing two questionable but quotidian assumptions. I attack existing views of transmission failure, especially those of Crispin Wright. I defend a permissive view of transmission failure, one which holds that deductions of a certain kind fail to transmit only because of premise circularity. Finally, I apply this account to the Neo-Moorean and Zebra Deductions and show that, given my permissive view, these deductions transmit in an intuitively acceptable way—at least if either a certain type of circularity is benign or a certain view of perceptual justification is false. (shrink)

Looking out the window, I see that it's raining outside. Do I know that it’s raining outside? According to proponents of the Entailment Thesis, I do. If I see that p, I know that p. In general, the Entailment Thesis is the thesis that if S perceives that p, S knows that p. But recently, some philosophers (McDowell 2002, Turri 2010, Pritchard 2011, 2012) have argued that the Entailment Thesis is false. On their view, we can see p and not (...) know that p. In this paper, I argue that their arguments are unsuccessful. (shrink)

Platonists and nominalists disagree about whether mathematical objects exist. But they almost uniformly agree about one thing: whatever the status of the existence of mathematical objects, that status is modally necessary. Two notable dissenters from this orthodoxy are Hartry Field, who defends contingent nominalism, and Mark Colyvan, who defends contingent Platonism. The source of their dissent is their view that the indispensability argument provides our justification for believing in the existence, or not, of mathematical objects. This paper considers whether commitment (...) to the indispensability argument gives one grounds to be a contingentist about mathematical objects. (shrink)

This chapter outlines the main ideas of my book National responsibility and global justice. It begins with two widely held but conflicting intuitions about what global justice might mean on the one hand, and what it means to be a member of a national community on the other. The first intuition tells us that global inequalities of the magnitude that currently exist are radically unjust, while the second intuition tells us that inequalities are both unavoidable and fair once national responsibility (...) is allowed to operate. This conflict might be resolved either by adopting a cosmopolitan theory of justice (which leaves no room for national responsibility) or by adopting a ?political? theory of justice (which denies that questions of distributive justice can arise beyond the walls of the sovereign state). Since neither resolution is satisfactory, the chapter defends the idea of national responsibility and proposes a new theory of global justice, whose main elements are the protection of basic human rights worldwide, and fair terms of interaction between independent political communities. (shrink)

The metaphor of weighing reasons brings to mind a single (double-pan balance) scale. The reasons for φ go in one pan and the reasons for ~φ go in the other. The relative weights, as indicated by the relative heights of the two pans of the scale, determine the deontic status of φ. This model is simple and intuitive, but it cannot capture what it is to weigh reasons correctly. A reason pushes the φ pan down toward permissibility (has justifying weight) (...) only insofar as it pushes the ~φ pan up toward impermissibility (has requiring weight). Thus, Single Scale is committed to Single Proportion (first pass): all reasons have the same proportion of justifying and requiring weight. Many normative theories reject Single Proportion, and they are not thereby confused about how to weigh reasons. One can be mistaken about the weight of a reason without being confused about how reasons are to be weighed. Single Scale is problematic, not because it appeals to the image of a scale, but because it appeals to the image of a single scale. We need two scales to capture what it is to weigh reasons correctly. (shrink)

Starting from two observations regarding nursing ethics research in the past two decades, namely, the dominant influence of both the empirical methods and the principles approach, we present the cornerstones of a foundational argument-based nursing ethics framework. First, we briefly outline the general philosophical–ethical background from which we develop our framework. This is based on three aspects: lived experience, interpretative dialogue, and normative standard. Against this background, we identify and explore three key concepts—vulnerability, care, and dignity—that must be observed in (...) an ethical approach to nursing. Based on these concepts, we argue that the ethical essence of nursing is the provision of care in response to the vulnerability of a human being in order to maintain, protect, and promote his or her dignity as much as possible. (shrink)

States claim the right to choose who can come to their country. They put up barriers and expose migrants to deadly journeys. Those who survive are labelled ‘illegal’ and find themselves vulnerable and unrepresented. The international state system advantages the lucky few born in rich countries and locks others into poor and often repressive ones. In this book, Christopher Bertram skilfully weaves a lucid exposition of the debates in political philosophy with original insights to argue that migration controls must be (...) justifiable to everyone, including would-be and actual immigrants. Until justice prevails, states have no credible right to exclude and no-one is obliged to obey their immigration rules. Bertram’s analysis powerfully cuts through the fog of political rhetoric that obscures this controversial topic. It will be essential reading for anyone interested in the politics and ethics of migration. (shrink)

Scientific consensus is widely deferred to in public debates as a social indicator of the existence of knowledge. However, it is far from clear that such deference to consensus is always justified. The existence of agreement in a community of researchers is a contingent fact, and researchers may reach a consensus for all kinds of reasons, such as fighting a common foe or sharing a common bias. Scientific consensus, by itself, does not necessarily indicate the existence of shared knowledge among (...) the members of the consensus community. I address the question of under what conditions it is likely that a consensus is in fact knowledge based. I argue that a consensus is likely to be knowledge based when knowledge is the best explanation of the consensus, and I identify three conditions—social calibration, apparent consilience of evidence, and social diversity, for knowledge being the best explanation of a consensus. (shrink)

In a recent paper, Barry Loewer attempts to defend Humeanism about laws of nature from a charge that Humean laws are not adequately explanatory. Central to his defense is a distinction between metaphysical and scientific explanations: even if Humeans cannot offer further metaphysical explanations of particular features of their “mosaic,” that does not preclude them from offering scientific explanations of these features. According to Marc Lange, however, Loewer’s distinction is of no avail. Defending a transitivity principle linking scientific explanantia to (...) their metaphysical grounds, Lange argues that a charge of explanatory inadequacy resurfaces once this intuitive principle is in place. This paper surveys, on behalf of the Humean, three strategies for responding to Lange’s criticism. The ready availability of these strategies suggests that Lange’s argument may not bolster anti-Humean convictions, since the argument rests on premises that those not antecedently sharing these convictions may well reject. The three strategies also correspond to three interesting ways of thinking about relations of grounding linking Humean laws and their instances, all of which are consistent with theses of Humean supervenience, and some of which have been heretofore overlooked. (shrink)

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of denying (...) each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive. (shrink)

Just as theory of representation is deficient if it can’t explain how misrepresentation is possible, a theory of computation is deficient if it can’t explain how miscomputation is possible. Nonetheless, philosophers have generally ignored miscomputation. My primary goal in this paper is to clarify both what miscomputation is and how to adequately explain it. Miscomputation is a special kind of malfunction: a system miscomputes when it computes in a way that it shouldn’t. To explain miscomputation, you must provide accounts of (...) computational behavior, computational norms, and how computational behavior can deviate from computational norms. A secondary goal of this paper is to defend an (quasi-)individualist, mechanistic theory of miscomputation. Computational behavior is narrowly individuated. Computational norms are widely individuated. A system miscomputes when its behavior manifests a narrow computational structure that the widely individuated norms say that it should not have. (shrink)

Philosophers have recently argued, against a prevailing orthodoxy, that standards of knowledge partly depend on a subject’s interests; the more is at stake for the subject, the less she is in a position to know. This view, which is dubbed “Pragmatic Encroachment” has historical and conceptual connections to arguments in philosophy of science against the received model of science as value free. I bring the two debates together. I argue that Pragmatic Encroachment and the model of value-laden science reinforce each (...) other. Drawing on Douglas’ argument about the indispensability of value judgments in science, and psychological evidence about people’s inability to objectively reason about what they care about, I introduce a novel argument for Pragmatic Encroachment. (shrink)