Separability is roughly the principle that, in comparing the value of two outcomes, one can ignore any people whose existence and welfare are unaffected. Separability is both antecedently plausible, at least as a principle of beneficence, and surprisingly powerful; it is the key to some of the best positive arguments in population ethics. This chapter surveys the motivations for and consequences of separability. In particular, it presents an ‘additivity theorem’ which explains how separability leads to total utilitarianism and closely related (...) axiological views. It then examines systematically how this family of views can avoid the Repugnant Conclusion by incorporating lexicality, a critical level, or a neutral range. (shrink)

Thick terms and concepts, such as honesty and cruelty, are at the heart of a variety of debates in philosophy of language and metaethics. Central to these debates is the question of how the descriptive and evaluative components of thick concepts are related and whether they can be separated from each other. So far, no empirical data on how thick terms are used in ordinary language has been collected to inform these debates. In this paper, we present the first empirical (...) study, designed to investigate whether the evaluative component of thick concepts is communicated as part of the semantic meaning or by means of conversational implicatures. While neither the semantic nor the pragmatic view can fully account for the use of thick terms in ordinary language, our results do favour the semanticist interpretation: the evaluation of a thick concept is only slightly easier to cancel than semantically entailed content. We further discovered a polarity effect, demonstrating that how easily an evaluation can be cancelled depends on whether the thick term is of positive or negative polarity. (shrink)

Dans le domaine du placement d’enfants, la loi de 1996 préconisant le maintien de la communauté de vie des frères et sœurs est souvent comprise comme une injonction sine qua non. Cet article se fait l’écho des observations d’une équipe pluridisciplinaire (éducateurs, psychologue, psychanalyste) engagée depuis de longues années dans l’accueil familial qui dévoilent, à travers une analyse à la fois quantitative et clinique, une réalité qui vient nuancer cet impératif. Les auteurs montrent que, dans un certain nombre de cas, (...) le maintien de la communauté de vie de la fratrie contribue à l’entretien de la pathologie des liens familiaux et à l’aliénation du sujet. Pourtant, il est possible d’imaginer des dispositifs où séparation de la fratrie n’est pas synonyme de rupture des liens fraternels. (shrink)

Ontological separation plays a key role in Aristotle’s metaphysical project: substances alone are ontologically χωριστόν. The standard view identifies Aristotelian ontological separation with ontological independence, so that ontological separation is a non-symmetric relation. I argue that there is strong textual evidence that Aristotle employs an asymmetric notion of separation in the Metaphysics—one that involves the dependence of other entities on the independent entity. I argue that this notion allows Aristotle to prevent the proliferation of substance-kinds and thus to secure the (...) unity of his metaphysical system. (shrink)

In this paper, I accomplish a conceptual task and a historical task. The conceptual task is to argue that (1) Einstein’s Principle of Separability (henceforth “separability”) is not a supervenience principle and that (2) separability and entanglement are compatible. I support (1) by showing that the conclusion of Einstein’s incompleteness argument would still follow even if one assumes that the state of a composite system does not supervene on the states of the subsystems, and by showing that what Einstein says (...) in “Quantum Mechanics and Reality” (1948) strongly suggests that separability is not a principle about how subsystem states relate to the state of composite systems. I support (2) by showing that if separability was incompatible with entanglement, then Einstein’s argument would be incoherent in a trivial way. Thus, by arguing for (1) and (2) I directly challenge what has been, and still is, a very common reading of separability. The historical task is to offer the first detailed review of the different ways in which separability has been defined by physicists and philosophers in the last 60 years. Among other things, such a review distinguishes three different definitions of the principle, and shows that since the 1990s and up until the present date, it became standard to take separability (as presented by Einstein) to be a supervenience principle. (shrink)

Separation of powers is one of the ideas with profound theoretical and practical significance, especially in the field of political science. The birth of the theory of separation of powers marked the transition from the barbaric use of power in authoritarian societies to the exercise of civilized power in democratic societies. Therefore, separation of powers is considered an objective necessity in democratic states, a condition to ensure the promotion of liberal values, and a criterion for assessing the existence and development (...) of the Rule of Law where people's sovereignty plays a paramount role. On the way to perfecting political thinking, the theory of separation of powers has developed into a complete system in the main philosophy of John Locke. Within the scope of the article, the author focuses on analyzing Locke's ideology of separation of powers in terms of the nature of separation of powers, the basis and some principles of power division, and the roles of the different parts of government power and the relationship between them. (shrink)

Certain separation problems in descriptive set theory correspond to a forcing preservation property, with a fusion type infinite game associated to it. As an application, it is consistent with the axioms of set theory that the circle.

For Max Weber, modernity is characterized by a tragic conflict among value spheres, each claiming to possess the ‘true meaning’ of human life. In particular, Weber argues that while the political sphere is dominated by the unifying, exclusionary, power-driven, and war-prone nation state, the ethical sphere is characterized by the universalization of individually based, deontological norms. For Weber, I argue, the modern separation between the ethical and political spheres originates in ancient Judaism. His work on Judaism, mostly neglected by political (...) theorists, describes the emergence of politics as an autonomous, naturalistic sphere with the establishment of kingship. Biblical prophets, simultaneously, were the inventors of an idealistic, mulish, universal ethics Weber termed the ‘ethics of ultimate ends’. Thus, against the Greek model harmonizing ethics and politics, Judaism invented an antagonistic model of the two. This Jewish imagination lay dormant for almost two millennia but returned to the stage in secularized modernity. (shrink)

The United States Constitution is arguably the greatest practical achievement of the Enlightenment. Yet most of the elements of the Constitution are borrowed from elsewhere. Its single wholly original component is the separation of church and state. The doctrine of separation has become controversial of late: Numerous ministers and politicians insist that the United States is in truth a "Christian nation" with Christian institutions that has been overtaken by secular humanism; they call for bringing the United States back to its (...) original unity with Christianity. They argue, accordingly, that although toleration of other faiths might be practiced, the explicitly Christian character of the nation and its political institutions should be reasserted in law and policy rather than denied by secularists. Pat Robertson, for example, has maintained that separation of church and state is a "lie of the left.". (shrink)

In DA I.1, Aristotle asks whether nous (understanding or reason) is chōristē (separable) and presents a separability condition: the soul is separable if it has some activity proper to it that is not shared with the body. I argue that Aristotle is speaking here of separability in being, not separability in account or taxonomical separation. In the case of the soul, this sort of separability would allow the soul to exist apart from the body. Met. Λ.3, GA II.3, and DA (...) III.4 suggest that Aristotle introduces the separability condition because understanding meets it. Reason is independent of the body in a way that no other power of the soul is. Nous alone is divine and separable. DA III.5 then situates this claim: there is an aspect of understanding that can only be active in connection with the body, but understanding is what it is and continues to be active apart from the body. This raises further questions about the life and ontological status of the sort of separated human nous Aristotle envisages. While figuring out its precise contours is difficult, Aristotle is, in fact, committed to the possibility of human intellectual activity continuing apart from the body. (shrink)

A model of reality is called separable if the state of a composite system is equal to the union of the states of its parts, located in different regions of space. Spekkens has argued that it is trivial to reproduce the predictions of quantum mechanics using a separable ontological model, provided one allows for arbitrary violations of ‘dynamical locality’. However, since dynamical locality is strictly weaker than local causality, this leaves open the question of whether an ontological model for quantum (...) mechanics can be both separable and dynamically local. We answer this question in the affirmative, using an ontological model based on previous work by Deutsch and Hayden. Although the original formulation of the model avoids Bell’s theorem by denying that measurements result in single, definite outcomes, we show that the model can alternatively be cast in the framework of ontological models, where Bell’s theorem does apply. We find that the resulting model violates local causality, but satisfies both separability and dynamical locality, making it a candidate for the ‘most local’ ontological model of quantum mechanics. (shrink)

We prove that PTCN cannot be a model of U12. This implies that there exists a first order sentence of bounded arithmetic which is provable in U12 but does not hold in PTCN.

In early 2013, the Indian government introduced new rules governing the conduct of clinical trials involving human participants. Among other provisions, the law requires that sponsors of research compensate participants who are injured during the course of their research participation. This article examines the effects of India's compensation law and the efforts that policymakers in India have made to tailor the law since its passage. I use the legal concept of acoustic separation as a framework to explain and justify the (...) approach that India has taken in refining its regulation of research related injuries. I conclude that India's example may provide useful lessons for research sponsors and lawmakers in other regulatory states seeking to promote a well-regulated biomedical research industry. (shrink)

Linear temporal logic with Since and Until modalities is expressively equivalent, over the class of complete linear orders, to a fragment of first-order logic known as FOMLO. It turns out that LTL, under some basic assumptions, is expressively complete if and only if it has the property, called separation, that every formula is equivalent to a Boolean combination of formulas that each refer only to the past, present or future. Herein we present simple algorithms and their implementations to perform separation (...) of the LTL with Since and Until, over discrete and complete linear orders, and translation from FOMLO formulas into equivalent temporal logic formulas. We additionally show that the separation of a certain fragment of LTL results in at most a double exponential size growth. (shrink)

behaviour from the rival manufacturer. We consider the case where franchise fees can be used to extract retailers' surplus. We show that vertical separation is in the collective, as well as individual, interest of manufacturers, and hence facilitates some collusion in the simple setting..

One diagnosis of Bell's theorem is that its premise of Outcome Independence is unreasonably strong, as it postulates one common screener system that purports to explain all the correlations involved. This poses a challenge of constructing a model for quantum correlations that is local, non-conspiratorial, and has many separate screener systems rather than one common screener system. In particular, the assumptions of such models should not entail Bell's inequalities. We prove that the models described do not exist, and hence, (...) the diagnosis above is incorrect. (shrink)

This paper addresses arguments that “separability” is an assumption of Bell’s theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as “holism”) will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately.In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (...) (b) the definition of Bell’s locality condition does not rely on separability in any way; (c) the proof of Bell’s theorem does not use separability as an assumption. If, inspired by considerations of non-separability, the assumptions of Bell’s theorem are weakened, what remains no longer embodies the locality principle. Teller’s argument for “relational holism” and Howard’s arguments concerning separability are criticised in the light of these results. Howard’s claim that Einstein grounded his arguments on the incompleteness of QM with a separability assumption is also challenged. Instead, Einstein is better interpreted as referring merely to the existence of localised events. Finally, it is argued that Bell rejected the idea that separability is an assumption of his theorem. (shrink)

As the prevalence of self-harm among adolescents in Chinese escalates, finding out the potential risk factors associated with self-harm behaviors has aroused much attention. This study aims to explore the association between parent-child separation and series of self-harm subtypes among Chinese adolescents. We survey a total of 4,928 middle school students aged from 12 to 18 years at school. Parent-child separation was investigated from four dimensions—occurrence of parental separation, separation status, age at first separation and duration of separation. Self-harm series (...) are deemed as five subtypes—highly lethal self-harm, less lethal self-harm with visible tissue damage, self-harm without visible tissue damage, self-harmful behaviors with latent damage and psychological self-harm. Multivariate logistic regression is used to explore the associations between parent-child separation and different subtypes of self-harm among adolescents. Paternal separation is associated with each type of self-harm whilst maternal separation is not correlated with highly lethal self-harm. Except for highly lethal self-harm, the other four subtypes of self-harm demonstrate a relation with both length of paternal separation and maternal separation with aOR ranging from 1.02 to 1.06. Individuals who suffer parental separation prior to the age of three were at a higher risk for four types of less-lethal self-harm. The association of parent-child separation with self-harm deserves our attention, and future research is needed to identify the underlying mechanisms. (shrink)

Legal positivism's ``separation thesis'' is usually taken in one of two ways: as an analytic claim about the nature of law – roughly, as some version of the Social Thesis; or as a substantive claim about the moral value of law – roughly, as some version of the Value Thesis. In this paper I argue that we should recognize a third kind of positivist separation thesis, one which complements, but is distinct from, positivism's analytic and moral claims. The Neutrality Thesis (...) says that the correct analytic claim about the nature of law does not by itself entail any substantive claims about the moral value of law. I give careful formulations of these three separation theses, explain the relationships between them, and sketch the role that each plays in the positivist approach to law. (shrink)

L’étude de l’impact émotionnel des séparations entre les mères migrantes, leurs enfants confiés au pays d’origine et ceux nés en pays d’accueil permet d’apporter un éclairage sur une problématique non négligeable au sein d’institutions médico-sociales. Cet article vise à analyser certains effets de ces séparations à partir de l’analyse de cinq entretiens avec des mères migrantes et au travers d’une méthode d’analyse qualitative. Les paramètres mis en avant sont ceux qui influent sur les modalités de choix de confiage des enfants (...) au moment du départ du pays d’origine, les conséquences dépressogènes pour les mères des séparations à long terme et leurs effets sur les interrelations entre frères et sœurs. L’absence de lien proximal avec les enfants confiés conduit les mères à faire appel à des stratégies de transmission de valeurs culturelles éducatives pour maintenir les liens dans la fratrie. (shrink)

In morally grounding a public justification requirement, public reason liberals frequently invoke the idea that persons should be construed as “free and equal.” But this tells us little with regard to what it is about us that makes us free or how a claim about our status as persons can ultimately ground a requirement of public justification. In light of this worry, I argue that a public justification requirement can be grounded in a Nozick-inspired argument from the separateness of persons (...) (one that is consistent with the idea that individuals are free and equal). As I claim, one particular feature of the fact of our separateness – the possession of a basic psychology consisting of beliefs, intentions, sentiments, and a variety of desire-like psychological states – does the most work in grounding both a principle of liberty (PL) and a requirement of public justification (RPJ). Together, PL and RPJ provide the basic framework for a theory of public reason liberalism. (shrink)

Hume invokes the separability of perceptions to derive some of his most contentious pronouncements. To assess the cogency of the arguments, the notion must first be clarified. The clarification reveals that sic different separability claims must be distinguished. Of these, I consider the three that are rarely discussed. They turn out to be unacceptable. Locke espouses none of them.This Article does not have an abstract.

Evidence for a dichotomy between the planning of an action and its on-line control in humans is reviewed. This evidence suggests that planning and control each serve a specialized purpose utilizing distinct visual representations. Evidence from behavioral studies suggests that planning is influenced by a large array of visual and cognitive information, whereas control is influenced solely by the spatial characteristics of the target, including such things as its size, shape, orientation, and so forth. Evidence from brain imaging and neuropsychology (...) suggests that planning and control are subserved by separate visual centers in the posterior parietal lobes, each constituting part of a larger network for planning and control. Planning appears to rely on phylogenetically newer regions in the inferior parietal lobe, along with the frontal lobes and basal ganglia, whereas control appears to rely on older regions in the superior parietal lobe, along with the cerebellum. Key Words: action; apraxia; control; illusions; optic ataxia; PET; planning; reaching;. (shrink)

Separate and Dominate is Delphy's manifesto, lambasting liberal hypocrisy and calling for a fluid understanding of political identity that does not place different political struggles in a false opposition. She dismantles the absurd claim that Afghanistan was invaded to save women, and that homosexuals and immigrants alike should reserve their self-expression for private settings. She calls for a true universalism that sacrifices no one at the expense of others. In the aftermath of the Charlie Hebdo massacre, her arguments appear (...) more prescient and pressing than ever.--Provided by publisher. (shrink)

À partir de cas cliniques, l’auteure analyse des situations de séparation précoce et met en évidence les conditions pour que cette séparation ne soit pas traumatique.

Standard derivations of the Bell inequalities assume a common-commoncause-system that is a common screener-off for all correlations and some additional assumptions concerning locality and no-conspiracy. In a recent paper Graßhoff et al., "The British Journal for the Philosophy of Science", 56, 663–680 ) Bell inequalities have been derived via separate common causes assuming perfect correlations between the events. In the paper it will be shown that the assumptions of this separate-common-cause-type derivation of the Bell inequalities in the case (...) of perfect correlations can be reduced to the assumptions of a common-common-cause-system-type derivation. However, in the case of non-perfect correlations a non-reducible separate-common-cause-type derivation of some Bell-like inequalities can be given. The violation of these Bell-like inequalities proves Szabo's ) conjecture concerning the non-existence of a local, non-conspiratorial, separate-common-cause-model for a δ-neighborhood of perfect EPR correlations. (shrink)

All separable states satisfy all Bell-type inequalities, which involve as their assumption only existence of local realistic (local hidden variable) models of the correlations of spatially separated systems, observed by two or more observers making independent decisions on what to measure (free will). The recent observation by Loubenets, that some separable states do not satisfy the original Bell inequality (1964) has no consequences whatsoever for the studies of the relation of separability with local realism. The original Bell inequality was derived (...) using an additional assumption that the local results for a certain pair of local settings reveal perfect Einstein–Podolsky–Rosen (EPR) correlations. Therefore violation of this inequality by some quantum predictions implies that either (i) the predictions do not allow a local realistic model, or (ii) the predictions do not have the required EPR correlations, or finally both (i) and (ii). (shrink)

A characterization of the subdirectly irreducible separable dynamic algebras is presented. The notions develo- ped for this study were also suitable to describe the previously found class of simple separable dynamic algebras.

In a new study, Ben-Haim et al. use subliminal stimuli to separate conscious and unconscious perception in macaques. A programme of this type, using a range of cognitive tasks, is a promising way to look for conscious perception in more controversial cases.

The difference between the unity of the individual and the separateness of persons requires that there be a shift in the moral weight that we accord to changes in utility when we move from making intrapersonal tradeoffs to making interpersonal tradeoffs. We examine which forms of egalitarianism can, and which cannot, account for this shift. We argue that a form of egalitarianism which is concerned only with the extent of outcome inequality cannot account for this shift. We also argue that (...) a view which is concerned with both outcome inequality and with the unfairness of inequality in individuals‘ expected utilities can account for this shift. Finally, we limn an alternative view, on.. (shrink)

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR+ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.

We investigate separation properties for neighbourhood spaces in some details within a framework of constructive mathematics, and define corresponding separation properties for quasi-apartness spaces. We also deal with separation properties for spaces with inequality.

Let ≤r and ≤sbe two binary relations on 2ℕ which are meant as reducibilities. Let both relations be closed under finite variation and consider the uniform distribution on 2ℕ, which is obtained by choosing elements of 2ℕ by independent tosses of a fair coin.Then we might ask for the probability that the lower ≤r-cone of a randomly chosen set X, that is, the class of all sets A with A ≤rX, differs from the lower ≤s-cone of X. By c osure (...) under finite variation, the Kolmogorov 0-1 aw yields immediately that this probability is either 0 or 1; in case it is 1, the relations are said to be separable by random oracles.Again by closure under finite variation, for every given set A, the probability that a randomly chosen set X is in the upper ≤r-cone of A is either 0 or 1; let Almostr be the class of sets for which the upper ≤r-cone has measure 1. In the following, results about separations by random oracles and about Almost classes are obtained in the context of generalized reducibilities, that is, for binary relations on 2ℕ which can be defined by a countable set of total continuous functionals on 2ℕ in the same way as the usual resource-bounded reducibilities are defined by an enumeration of appropriate oracle Turing machines. The concept of generalized reducibility comprises a natura resource-bounded reducibilities, but is more general; in particular, it does not involve any kind of specific machine model or even effectivity. The results on generalized reducibilities yield corollaries about specific resource-bounded reducibilities, including several results which have been shown previously in the setting of time or space bounded Turing machine computations. (shrink)

The purpose of this paper is to draw out and make explicit the assumptions made in the treatment of technology within business ethics. Drawing on the work of Freeman (1994, 2000) on the assumed separation between business and ethics, we propose a similar separation exists in the current analysis of technology and ethics. After first identifying and describing the separation thesis assumed in the analysis of technology, we will explore how this assumption manifests itself in the current literature. A different (...) stream of analysis, that of science and technology studies (STS), provides a starting point in understanding the interconnectedness of technology and society. As we will demonstrate, business ethicists are uniquely positioned to analyze the relationship between business, technology, and society. The implications of a more complex and rich definition of lsquotechnologyrsquo ripple through the analysis of business ethics. Finally, we propose a pragmatic approach to understanding technology and explore the implications of such an approach to technology. This new approach captures the broader understanding of technology advocated by those in STS and allows business ethicists to analyze a broader array of dilemmas and decisions. (shrink)

My goal in this essay will be to show, contra Parfit, that the separateness of human persons—although metaphysically shallow—has a moral significance that should not be overlooked. Parfit holds that his reductionist view of personal identity lends support to consequentialism; I reject this claim because it rests on the assumption that the separateness of human persons has an arbitrariness that renders it morally insignificant. This assumption is flawed because this separateness is grounded in our 'person practices', which reflect some of (...) the morally relevant aspects of our nature: if we imagine a species of person whose members are not naturally separate from each other, it is reasonable to suppose that the morality of this different species of person would be drastically different from human morality. Thus, if consequentialists aim to offer a human moral theory, they overlook the separateness of human persons with peril. (shrink)

Lesdits « radicalisés » ne sont pas exceptionnels. Ce sont principalement des adolescents dont la complexité des trajectoires individuelles et familiales peut entraver la nécessaire séparation d’avec l’enfance pour se construire un devenir adulte. La clinique nous fait découvrir la multiplicité des stratégies possibles de l’adolescent prisonnier de ce dilemme. L’article analyse le cas d’une jeune fille aux prises d’un héritage familial traumatique et de sa propre régression archaïque, qui tente une séparation physique avec le vœu inconscient de parvenir à (...) se séparer enfin psychiquement. Mais les séparations physiques, même radicales, ne favorisent, au contraire, que séparation sans séparation. (shrink)

Gabbay's separation theorem about linear temporal logic with past has proved to be one of the most useful theoretical results in temporal logic. In this paper, we establish an analogous statement a...

One of the distinctive ideas of contemporary liberal political philosophy is that the separateness of persons is somehow normatively momentous. A proper respect for separateness is supposed to lead us not only to reject aggregative theories such as utilitarianism, but to embrace some particular positive theory about the sorts of obligations and claims we have amongst each other. Typically, philosophers have focused on the way in which the separateness of persons is important to matters of distribution. Given the intuitively unjust (...) distributions often sanctioned by utilitarianism, such a focus makes sense. Much of the contribution of my dissertation, however, is to argue that separateness is relevant not just as a fact about persons as beneficiaries, but perhaps even more fundamentally, as agents. ;Chapter one explores the connection between respect for the separateness of persons and liberal theory, with reference to the cases of John Rawls and Robert Nozick. Chapter two defends the reasonableness of respect for separateness against the metaphysical critique of Derek Parfit. Chapters three and four spell out the main idea of respect for separateness as agents. Chapter five examines applies this analysis to free markets, and argues that while separateness provides some grounds for criticizing markets, it also provides some interesting, non-efficiency based grounds for praising them. (shrink)

Revenues from television spot-advertising can be viewed as a kind of indirect financing of editorial content. This applies still further to endeavours to incorporate advertising messages into programming. In order to identify problems associated with doing away with the separation principle, it is meaningful to adopt a perspective that brings together theories and findings which are genuinely embedded in economics and communication science. Such a perspective shows that appealing to the self-regulating forces of the market is nonsensical in a sector (...) where market failure is the rule as opposed to the exception. And when it comes to media competence of television viewers, audience research and research on media effects indicates that expectations with respect to the advertising effectiveness of product placement are unlikely to be met. (shrink)

Discusses the sense of separability in Aristotle and how they apply to the separability of mind or nous.

The question of the status and the mode of functioning of technologies which participate in our cognitive activity (action, perception, reasoning) is inseparable from the question of the bodily inscription of these faculties. One can adopt the principle that a tool is fully appropriate when it functions as a component of the organs of our lived body. However, these technical entities can be differentiated along a scale according to the role played by their separability. The possibility of picking up and (...) putting down a hammer, a pair of spectacles, an agenda is part of the meaning of these tools. When they are “in hand”, they become transparent for the subject and serve in the constitution of his lived experience. Put down, they can be transmitted, modified, received. According to the frequency of the transition picking up/putting down, the tool can be picked up while anticipating that it can just as quickly put down again (the mouse of a computer, cutlery at table, an agenda, …). At the other extreme, another sort of tool functions rather as a prosthetic device that is taken up with the prospect of remaining attached to the body for a long time (an artificial leg, spectacles, clothes, …). This differentiation of technologies along a continuum which depends on forms of use seems to us sufficient to distinguish extension and embodiment. (shrink)

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }$$\end{document} be a set of outcomes, and let I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{I }$$\end{document} be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} on XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }^\mathcal{I }$$\end{document} admits an additive representation. That is: there exists a linearly ordered abelian group R\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document} and a ‘utility function’ u:X⟶R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u:\mathcal{X }{{\longrightarrow }}\mathcal{R }$$\end{document} such that, for any x,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document} which differ in only finitely many coordinates, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∑i∈Iu-u≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i\in \mathcal{I }} \left[u-u\right]\ge 0$$\end{document}. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document}, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∗∑i∈Iu≥∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u\ge {}^*\!\sum _{i\in \mathcal{I }}u$$\end{document}. Here, ∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u$$\end{document} represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\mathcal{R }$$\end{document}, which is an ultrapower extension of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document}. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. (shrink)

This chapter sets out the theorems, and presents some examples that show in a rough way how the theorems work. It explains separability precisely, and states the theorems. The chapter starts the work of interpreting the theorems, and also explains the significance of their conclusions from a formal, mathematical point of view. It then discusses a significant assumption that is used in the proofs of the theorems. The published proofs of both the separability theorems depend on an assumption that may (...) be objectionable in some contexts. These theorems are about an ordering defined on a field of alternatives. If an ordering can be represented by an additively separable utility function, the theorem shows it can be represented by a whole family of additively separable functions. Each member of the family is an increasing linear transform of the others, and the family includes every increasing linear transform of each of its members. (shrink)

Professor Weil’s thesis seems largely correct with respect to the United States, whose law on religious establishment I regularly teach. Funding is central to American debates over religious establishment. The fight over religious establishments in Virginia, which inspired both James Madison’s “Memorial and Remonstrance against Religious Assessments” and Thomas Jefferson’s “An Act for Establishing Religious Freedom,” was over whether persons could be forced to pay taxes to support religious instruction. Financial concerns were at the root of church-state debates in the (...) nineteenth century, when Protestants repeatedly rebuffed Catholics who wanted funding for Catholic private schools. Many state constitutions still have what are known as mini-Blaine Amendments that forbid public funding for religious institutions. Whether proponents of a strong separation between church and state in the United States are fighting the same battles as proponents of a strong separation of church and state in France is nevertheless problematic. The French revolutionaries had to subordinate a reactionary church. The American revolutionaries merely had to negotiate peace treaties among the different sects that supported the Declaration of Independence. Separation of church and state in the United States is best conceptualized as a division of labor among liberal institutions rather than a means for purging anti-liberal religion from the liberal public sphere. (shrink)

In the early nineties of the previous century, leaf languages were introduced as a means for the uniform characterization of many complexity classes, mainly in the range between P and PSPACE . It was shown that the separability of two complexity classes can be reduced to a combinatorial property of the corresponding defining leaf languages. In the present paper, it is shown that every separation obtained in this way holds for every generic oracle in the sense of Blum and Impagliazzo. (...) We obtain several consequences of this result, regarding, e. g., universal oracles, simultaneous separations and type-2 complexity. (shrink)

La séparation parentale apparaît comme un événement fréquent, mais néanmoins majeur dans la vie d’un sujet, surtout à l’adolescence. Comment se conjuguent adolescence et les problématiques psychiques (œdipienne et de perte) et relationnelles qu’elle implique, avec la séparation parentale? L’article discute ici le cas d’Adèle, âgée de 22 ans, pour qui la séparation des parents a eu lieu lorsqu’elle avait 16 ans. Adèle a été rencontrée trois fois dans le contexte d’une recherche. Les éléments cliniques recueillis lors des entretiens mènent (...) sur la voie d’effets négatifs toujours actuels en lien avec la séparation parentale et qui se télescopent avec une sensibilité préalable à la perte. On peut repérer, dans le cas d’Adèle, une instabilité identificatoire, un clivage des figures parentales, une accentuation de l’ambivalence à l’égard du parent de sexe opposé, une errance scolaire et des difficultés relationnelles. Ce cas clinique illustre la nécessité de procéder à un repérage des adolescents en souffrance suite à la séparation parentale et d’offrir un accompagnement aux parents. (shrink)