Tim Maudlin argues that we should take facts about distance to be analyzed in terms of facts about path lengths. His reason is that if we take distances to be fundamental, we must stipulate that constraints like the triangle inequality hold, but we get these constraints for free if we take path lengths to be prior. I argue that Maudlin is mistaken. Even if we take path lengths as primitive, the triangle inequality follows only if we (...) stipulate that the fundamental properties and relations obey constraints that are just as puzzling as the triangle inequality. (shrink)

Idempotency requires any phonotactically licit forms to be faithfully realized. Output-drivenness requires any discrepancies between underlying and output forms to be driven exclusively by phonotactics. These formal notions are relevant for phonological theory and play a crucial role in learnability. Tesar and Magri provide tight guarantees for OT output-drivenness and idempotency through conditions on the faithfulness constraints. This paper derives analogous faithfulness conditions for HG idempotency and output-drivenness and develops an intuitive interpretation of the various OT and HG faithfulness conditions (...) thus obtained. The intuition is that faithfulness constraints measure the phonological distance between underlying and output forms. They should thus comply with a crucial axiom of the definition of distance, namely that any side of a triangle is shorter than the sum of the other two sides. This intuition leads to a faithfulness triangle inequality which is shown to be equivalent to the faithfulness conditions for idempotency and output-drivenness. These equivalences hold under various assumptions, crucially including McCarthy’s :75–138, 2003b) generalization that constraints are all categorical. (shrink)

§1. Introduction. Asymptotic cones of metric spaces were first invented by Gromov. They are metric spaces which capture the ‘large-scale structure’ of the underlying metric space. Later, van den Dries and Wilkie gave a more general construction of asymptotic cones using ultrapowers. Certain facts about asymptotic cones, like the completeness of the metric space, now follow rather easily from saturation properties of ultrapowers, and in this survey, we want to present two applications of the van den Dries-Wilkie approach. Using ultrapowers (...) we obtain an explicit description of the asymptotic cone of a semisimple Lie group. From this description, using semi-algebraic groups and non-standard methods, we can give a short proof of the Margulis Conjecture. In a second application, we use set theory to answer a question of Gromov.§2. Definitions. The intuitive idea behind Gromov's concept of an asymptotic cone was to look at a given metric space from an ‘infinite distance’, so that large-scale patterns should become visible. In his original definition this was done by gradually scaling down the metric by factors 1/nfornϵ ℕ. In the approach by van den Dries and Wilkie, this idea was captured by ultrapowers. Their construction is more general in the sense that the asymptotic cone exists for any metric space, whereas in Gromov's original definition, the asymptotic cone existed only for a rather restricted class of spaces. (shrink)

This article examines the recent transformations of the Italian welfare state from a familist welfare model to what I term transnational market familism. In this model, families buy in care labour, commonly provided by migrant workers. There is now a growing literature exploring both the transformations of the Italian welfare model and the experiences of migrant workers providing care in Italy. However, what has been overlooked in the current literature is the ethical aspect of this model of welfare provision, which (...) is part of the transnational political economy of care. The article analyses the ethical implications of the migrant-in-the-family model, which transforms the care relationship between the caregiver and care receiver into a complex relationship between the family member organising care, the migrant caregiver and the dependent care receiver. The context of such welfare provision is transnational. Examining this care triangle, I draw on care ethics and individualization perspective for an analysis of how social policies safeguard, or overlook, human interaction and care relationships in the context of global hierarchies. The article draws on ethnographic data gathered in Naples, Italy, during 2004–2005, including interviews with Neapolitan employers and elderly care-receivers, interviews with migrant workers, as well as participant observations. (shrink)

Since Tversky argued that similarity judgments violate the three metric axioms, asymmetrical similarity judgments have been particularly challenging for standard, geometric models of similarity, such as multidimensional scaling. According to Tversky, asymmetrical similarity judgments are driven by differences in salience or extent of knowledge. However, the notion of salience has been difficult to operationalize, especially for perceptual stimuli for which there are no apparent differences in extent of knowledge. To investigate similarity judgments between perceptual stimuli, across three experiments, we collected (...) data where individuals would rate the similarity of a pair of temporally separated color patches. We identified several violations of symmetry in the empirical results, which the conventional multidimensional scaling model cannot readily capture. Pothos et al. proposed a quantum geometric model of similarity to account for Tversky's findings. In the present work, we extended this model to a more general framework that can be fit to similarity judgments. We fitted several variants of quantum and multidimensional scaling models to the behavioral data and concluded in favor of the quantum approach. Without further modifications of the model, the best-fit quantum model additionally predicted violations of the triangle inequality that we observed in the same data. Overall, by offering a different form of geometric representation, the quantum geometric framework of similarity provides a viable alternative to multidimensional scaling for modeling similarity judgments, while still allowing a convenient, spatial illustration of similarity. (shrink)

The thesis of 3D/4D equivalence states that every three-dimensional description of the world is translatable without remainder into a four-dimensional description, and vice versa. In representing an object in 3D or in 4D terms we are giving alternative descriptions of one and the same thing, and debates over whether the ontology of the physical world is "really" 3D or 4D are pointless. The twins paradox is shown to rest, in relativistic 4D geometry, on a reversed law of triangle (...) class='Hi'>inequality. But considering the twins as 3D beings who age through time, the paradox implies that time passes at different rates in different reference frames, and therefore that the concept of a single global or Absolute time is unsustainable. (shrink)

While claiming that diagrams can only be admitted as a method of strict proof if the underlying axioms are precisely known and explicitly spelled out, Hilbert praised Minkowski’s Geometry of Numbers and his diagram-based reasoning as a specimen of an arithmetical theory operating “rigorously” with geometrical concepts and signs. In this connection, in the first phase of his foundational views on the axiomatic method, Hilbert also held that diagrams are to be thought of as “drawn formulas”, and formulas as “written (...) diagrams”, thus suggesting that the former encapsulate propositional information which can be extracted and translated into formulas. In the case of Minkowski diagrams, local geometrical axioms were actually being produced, starting with the diagrams, by a process that was both constrained and fostered by the requirement, brought about by the axiomatic method itself, that geometry ought to be made independent of analysis. This paper aims at making a twofold point. On the one hand, it shows that Minkowski’s diagrammatic methods in number theory prompted Hilbert’s axiomatic investigations into the notion of a straight line as the shortest distance between two points, which start from his earlier work focused on the role of the triangle inequality property in the foundations of geometry, and lead up to his formulation of the 1900 Fourth Problem. On the other hand, it purports to make clear how Hilbert’s assessment of Minkowski’s diagram-based reasoning in number theory both raises and illuminates conceptual compatibility concerns that were crucial to his philosophy of mathematics. (shrink)

Mining time series data is of great significance in various areas. To efficiently find representative patterns in these data, this article focuses on the definition of a valid dissimilarity measure and the acceleration of partitioning clustering, a common group of techniques used to discover typical shapes of time series. Dissimilarity measure is a crucial component in clustering. It is required, by some particular applications, to be invariant to specific transformations. The rationale for using the angle between two time series to (...) define a dissimilarity is analyzed. Moreover, our proposed measure satisfies the triangle inequality with specific restrictions. This property can be employed to accelerate clustering. An integrated algorithm is proposed. The experiments show that angle-based dissimilarity captures the essence of time series patterns that are invariant to amplitude scaling. In addition, the accelerated algorithm outperforms the standard one as redundancies are pruned. Our approach has been applied to discover typical patterns of information diffusion in an online social network. Analyses revealed the formation mechanisms of different patterns. (shrink)

To justify certain steps of the computation developed in his Sand-Reckoner, Archimedes cites the following inequalities relative to the sides of right triangles: if of two right-angled triangles, the sides about the right angle are equal , while the other sides are unequal, the greater angle of those toward [sc. next to] the unequal sides has to the lesser a greater ratio than the greater line of those subtending the right angle to the lesser, but a lesser than the greater (...) line of those about the right angle to the lesser. That is, with reference to the two right triangles ABG, DEZ , where AG equals DZ and the angle at B is greater than that at E, ZE:GB < angle B:angle E < DE:AB. (shrink)

To justify certain steps of the computation developed in his Sand-Reckoner, Archimedes cites the following inequalities relative to the sides of right triangles: if of two right-angled triangles, the sides about the right angle are equal, while the other sides are unequal, the greater angle of those toward [sc. next to] the unequal sides has to the lesser a greater ratio than the greater line of those subtending the right angle to the lesser, but a lesser than the greater line (...) of those about the right angle to the lesser. That is, with reference to the two right triangles ABG, DEZ, where AG equals DZ and the angle at B is greater than that at E, ZE:GB < angle B:angle E < DE:AB. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:61. HUME'S GEOMETRIC "OBJECTS" Arithmetic and algebra allow of precision and certainty. The science of geometry is not likewise a perfect and infallible science. At any rate, this is Hume's teaching in the Treatise. When two numbers are so combin ' d, as that the one has always an unite answering to every unite of the other, we pronounce them equal; and 'tis for want of such a standard (...) of equality in extension, that geometry can scarce be esteem'd a perfect and infallible science. 1 The ideas of, say, equality and right line shade into· inequality and curve. It must not be supposed, however, that the vagueness of these ideas renders all judgments uncertain and fallible. 'Tie evident, that the eye, or rather the mind is often able at one view to determine the proportions of bodies....Such judgments are not only common, but in many cases certain and infallible. (T47) Nevertheless, geometry is a fallible science because its essential ideas are vague. Vagueness, due to lack of boundaries between ideas, is in the ideas themselves. For this reason, 'tis impossible to produce any definition of them, which will fix the precise boundaries betwixt them. (T49) (Yet, some forty pages earlier Hume argued at length that the mind cannot form any notion of quantity or quality without forming a precise notion of the degrees of each [T18]) As far as the Treatise goes, geometry is the science of measurement and as such it must allow for error. Even if precise geometric standards could be had, they would not make the propositions of geometry certain. Thus, we might precisely define a right line by a rule of order of indivisible points. But geometry, construed as the science of measurement, would not be perfected. Nor, if it were (the standard), is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserv ' d. The original standard of a right line is in reality nothing but a certain general appearance. (T52) 62. In the Enquiries, Hume continues to hold that notions essential to geometry, for example, equality, right line, and so on, are sensibles. But they are no longer generic appearances. They are determinate. The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate... even when no definition is employed, the object itself may be presented to the senses, and by that means be steadily and clearly apprehended. 2 In addition, geometry is no longer merely the science of measurement. The truths of Euclid, Hume holds, would remain truths even if there were no figures in nature. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. (EHU25) Professor Zabeeh, in his commentary on Hume, holds that Hume did not mean to imply that Euclid could dispense with the observation of figures. However, whenever possible Hume should be taken at his word: observation of figures is not a truth condition for propositions of geometry. A distinction must be drawn between discovery conditions and what Hume calls the "truth or evidence" of a geometric proposition. We may suppose that observation of figures is a discovery condition. But it is hardly a truth condition. The certainty, as opposed to the discovery, of geometric propositions does not depend on the existence in nature of any figure. I am mainly concerned, however, with Professor Zabeeh' s account of how, according to Hume, geometric propositions retain their certainty and evidence in the face of recalcitrant experience. Noting that Hume does not "fully explain," he gives the real reason for Hume's belief in the apodeictic certainty of mathematical truths. He appears to assume we never allow such truths to be controverted by empirical evidence. That is to say, if perchance we find, by measurement, that the sum of the angles of a Euclidean triangle 63. does not equal 180 degrees, either we say that we measured wrongly or we say that the triangle we have been measuring is not Euclidean.4 This formulation of Hume's reason avoids... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:61. HUME'S GEOMETRIC "OBJECTS" Arithmetic and algebra allow of precision and certainty. The science of geometry is not likewise a perfect and infallible science. At any rate, this is Hume's teaching in the Treatise. When two numbers are so combin ' d, as that the one has always an unite answering to every unite of the other, we pronounce them equal; and 'tis for want of such a standard (...) of equality in extension, that geometry can scarce be esteem'd a perfect and infallible science. 1 The ideas of, say, equality and right line shade into· inequality and curve. It must not be supposed, however, that the vagueness of these ideas renders all judgments uncertain and fallible. 'Tie evident, that the eye, or rather the mind is often able at one view to determine the proportions of bodies....Such judgments are not only common, but in many cases certain and infallible. (T47) Nevertheless, geometry is a fallible science because its essential ideas are vague. Vagueness, due to lack of boundaries between ideas, is in the ideas themselves. For this reason, 'tis impossible to produce any definition of them, which will fix the precise boundaries betwixt them. (T49) (Yet, some forty pages earlier Hume argued at length that the mind cannot form any notion of quantity or quality without forming a precise notion of the degrees of each [T18]) As far as the Treatise goes, geometry is the science of measurement and as such it must allow for error. Even if precise geometric standards could be had, they would not make the propositions of geometry certain. Thus, we might precisely define a right line by a rule of order of indivisible points. But geometry, construed as the science of measurement, would not be perfected. Nor, if it were (the standard), is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserv ' d. The original standard of a right line is in reality nothing but a certain general appearance. (T52) 62. In the Enquiries, Hume continues to hold that notions essential to geometry, for example, equality, right line, and so on, are sensibles. But they are no longer generic appearances. They are determinate. The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate... even when no definition is employed, the object itself may be presented to the senses, and by that means be steadily and clearly apprehended. 2 In addition, geometry is no longer merely the science of measurement. The truths of Euclid, Hume holds, would remain truths even if there were no figures in nature. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. (EHU25) Professor Zabeeh, in his commentary on Hume, holds that Hume did not mean to imply that Euclid could dispense with the observation of figures. However, whenever possible Hume should be taken at his word: observation of figures is not a truth condition for propositions of geometry. A distinction must be drawn between discovery conditions and what Hume calls the "truth or evidence" of a geometric proposition. We may suppose that observation of figures is a discovery condition. But it is hardly a truth condition. The certainty, as opposed to the discovery, of geometric propositions does not depend on the existence in nature of any figure. I am mainly concerned, however, with Professor Zabeeh' s account of how, according to Hume, geometric propositions retain their certainty and evidence in the face of recalcitrant experience. Noting that Hume does not "fully explain," he gives the real reason for Hume's belief in the apodeictic certainty of mathematical truths. He appears to assume we never allow such truths to be controverted by empirical evidence. That is to say, if perchance we find, by measurement, that the sum of the angles of a Euclidean triangle 63. does not equal 180 degrees, either we say that we measured wrongly or we say that the triangle we have been measuring is not Euclidean.4 This formulation of Hume's reason avoids... (shrink)

Insect vision is nothing if not active. The regular head movements, called saccades, enable the fly Drosophila to keep a straight path in flight despite inequalities in the thrust of the wings. Using their own motion, bees in flight measure the ranges of nearby objects. A long history of research shows that bees discriminate visually in ways that depend on their activity or task, so we must distinguish between vision during flying, fixating or hovering and landing.Bees return again and again (...) for a reward of sugar solution and use their eyes to find their way. In an apparatus that makes them discriminate between two simulataneously visible but regularly interchanged targets, seen at a distance of 27 cm, bees are able to distinguish a remarkable number of simple patterns, but they fail in certain critical cases. The results can be explained with the hypothesis that bees have several broadly tuned overlapping filters with large fields that respond to the predominant orientation in a region of the image, and others for radial and circular patterns. Together with colour, these filters are independent of range. Bees prefer to use landmarks where they can, then global pattern at the largest scale, and lastly the detail around the goal. The way that discrimination of one visual feature is independent of other variables can be explained by models analogous to the colour triangle in colour discrimination. (shrink)

Contrary to Bell’s theorem it is demonstrated that with the use of classical probability theory the quantum correlation can be approximated. Hence, one may not conclude from experiment that all local hidden variable theories are ruled out by a violation of inequality result.

Moving deftly among literary and visual arts, as well as the modern critical canon, Christopher Prendergast's book explores the meaning and value of representation as both a philosophical challenge (What does it mean to create an image that "stands for" something absent?) and a political issue (Who has the right to represent whom?). _The Triangle of Representation_ raises a range of theoretical, historical, and aesthetic questions, and offers subtle readings of such cultural critics as Raymond Williams, Paul de Man, (...) Edward Said, Walter Benjamin, and Hélène Cixous, in addition to penetrating investigations of visual artists like Gros, Ingres, and Matisse and significant insights into Proust and the onus of translating him. Above all, Prendergast's work is a striking display of how a firm grounding in theory is essential for the exploration of art and literature. (shrink)

This work empirically tests the concept of the ‘whistleblowing triangle,’ which is modeled on the three factors encapsulated by the fraud triangle, in the Indonesian context. Anchored in the proposition of an original research framework on the whistleblowing triangle and derived hypotheses, this work aims to expand the body of knowledge on this topic by providing empirical evidence. The sample used is taken from audit firms affiliated with both the big 4 and non-big 4 companies operating in (...) Indonesia. The results of analysis using the PLS-PM method found a significant relationship between the components of the whistleblowing triangle and the intention of blowing the whistle. We found that financial incentives are the most significant predictor of auditors’ intention to blow the whistle in Indonesia. Other components, such as opportunity and rationalization, also play an important role in supporting auditors’ intention to blow the whistle. Our findings also suggest that related pressures are the top priority for audit firms in Indonesia to consider in increasing whistleblowing intention. We expand the previous literature on whistleblowing which has been derived from the components of the fraud triangle :28–56, 2016; Smaili and Arroyo in J Bus Ethics, https://doi.org/10.1007/s10551-017-3663-7, 2017) by adding empirical evidence. (shrink)

A standard interpretation of Plato’s metaphysics holds that sensible particulars are images of Forms. Such particulars are fairly independent, like Aristotelian substances. I argue that this is incorrect: Platonic particulars are not Form images but aggregates of Form images, which are property-instances. Timaeus 49e-50a focuses on “this-suches” and even goes so far as to claim that they compose other things. I argue that Form images are this-suches, which are tropes. I also examine the geometrical account, showing that the geometrical constituents (...) of the elements are also Form images. Thus everything in the sensible world is composed of tropes. (shrink)

This work empirically tests the concept of the ‘whistleblowing triangle,’ which is modeled on the three factors encapsulated by the fraud triangle (pressure or financial incentives, opportunity and rationalization), in the Indonesian context. Anchored in the proposition of an original research framework on the whistleblowing triangle and derived hypotheses, this work aims to expand the body of knowledge on this topic by providing empirical evidence. The sample used is taken from audit firms affiliated with both the big (...) 4 and non-big 4 companies operating in Indonesia. The results of analysis using the PLS-PM method found a significant relationship between the components of the whistleblowing triangle and the intention of blowing the whistle. We found that financial incentives are the most significant predictor of auditors’ intention to blow the whistle in Indonesia. Other components, such as opportunity and rationalization, also play an important role in supporting auditors’ intention to blow the whistle. Our findings also suggest that related pressures are the top priority for audit firms in Indonesia to consider in increasing whistleblowing intention. We expand the previous literature on whistleblowing which has been derived from the components of the fraud triangle (Brown et al. in Account Public Interest 16(1):28–56, 2016; Smaili and Arroyo in J Bus Ethics, 10.1007/s10551-017-3663-7, 2017) by adding empirical evidence. (shrink)

In this paper we examine the role the Dutch gymnasium continues to play in the institutional maintenance of educational inequality. To that end we examine the relational and spatial features of state-sponsored elite education in the Dutch system: the unique identity the gymnasium seeks to cultivate; its value to its consumers; its geographic significance; and its market position amidst a growing array of other selective forms of schooling. We argue that there is a strong correlation between a higher social (...) class background and the concern to transmit one’s cultural habitus. We further speculate on the moral implications of state-sponsored elite education, both as it concerns the specific role of the gymnasium in the reproduction of social inequality as well as the curious tendency among its supporters to rationalise the necessity of its existence. (shrink)

It has been acknowledged that education includes ‘a love of what one teaches and a love of those whom one teaches’ (Hogan 2010: 81), but two traditions of writing in philosophy of education—concerning love for student and love for subject—have rarely been brought together. This paper considers the extent to which the ‘triangular’ relationship of teacher, student and subject matter runs the risk of the rivalry, jealousy and strife that are characteristic of ‘tragic’ love triangles, or entails undesirable consequences such (...) as transference from one intended object of love to another. It argues that this faultline in the literature of educational love corresponds to education's ‘divided heart’. The implication of this exploration of education's triangular relationship is that we cannot ignore the ‘dark of love’, nor can we address it simply by asserting that educational love must be of a more honourable sort than romantic love. These tensions can be reconciled through the loving recourse of ‘ceasing to strive’ and the possibility of sublimating the two originary loves into a higher ‘love of truth’. (shrink)

The infant mortality rate in Liberia is 50 times higher than it is in Sweden, whilst a child born in Japan has a life expectancy at birth of more than double that of one born in Zambia. 1 And within countries, we see differences which are nearly as great. For example, if you were in the USA and travelled the short journey from the poorer parts of Washington to Montgomery County Maryland, you would find that ‘for each mile travelled life (...) expectancy rises about a year and a half. There is a twenty-year gap between poor blacks at one end of the journey and rich whites at the other’. (Marmot, 2004, p.2). There are two types of questions which it is important to ask about inequalities in health such as these. The first are social scientific questions about the extent of inequalities in health and the factors which are causally responsible for these inequalities. Examples of social scientific questions to ask might be: how do infant mortality rates in the UK differ according to social class? What is the difference in life expectancy between Japanese who emigrate to the US and those who remain in Japan? Why do civil servants in higher ranked jobs tend to live longer than civil servants in lower ranked jobs? The second type are normative questions about the reasons we have to care about inequalities in health. Important normative questions to answer are: which inequalities in health should we care about (all inequalities or merely some of them)? When is an inequality in health unjust? How should we weigh our concern for equality in health against other factors such as maximising the.. (shrink)

We investigate the connection between $\triangle^1_3$-stability for random and Cohen forcing notions and the measurability and categoricity of the $\triangle^1_3$-sets. We show that Shelah's model for $\triangle^1_3$-measurability and categoricity satisfies $\triangle^1_3$-random-stability while it does not satisfy $\triangle^1_3$-Cohen-stability. This gives an example of measure-category asymmetry. We also present a result concerning finite support iterations of Suslin forcing.

"C'est un palimpseste : une succession de textes tirés des oeuvres complètes des auteurs à peu près complets. Le choix effectué par la lecture se trouve incarné dans l'ordre de l'écriture. Et cet ordre est porteur d'un message, il véhicule une thèse, il articule une idée dont le sens ne devient transparent que par le tout. Désormais les fragments extraits des texte ne représentent que le maillons d'une unique chaîne connexe de paroles, segmentss d'un entier : le texte du Palimpseste. (...) Derrière ce choix un axiome est caché, une assertion qui stimule et justifie la composition et, en dernière instance, garantit l'existence et légitime la subsistance autonome du texte. C'est ce que, par un terme emprunté à la théorie des ensembles de Georg Cantor, on pourra appeler "axiome du choix" ou encore, en une formulation quelque peu différente mais peut-être plus adéquate pour le traitement des textes, "axiome de sélection". L'axiome du choix permet donc l'assemblage d'un texte uniquement constitué de citations. Il permet aussi de citer des textes inexistants : ce sont alors des textes écrits exprès et pour l'unique raison d'être cités.... Le parler, comme l'a fait remarquer à plusieurs reprises Platon, est une praxis et l'axiome du choix confère au sujet le privilège d'exercer la fonction de choix : de sélectionner, de découper et d'assembler en un polymère verbal des fragments hétérogènes appartenant initialement à des textes préexistants. Le choix qui a présidé et guidé la navigation dans la métagalaxie des textes préexistants relève de cette liberté : sélectionner des "Propos" concernant le "Triangle", euclidien ou non, et de les assembler en un unique lieu et dans le présent indivisible d'une unique écriture étalée sur la surface du papier.". (shrink)

In this book Larry Temkin examines the concepts of equality and inequality, and addresses one particular question in depth: how can we judge between different sorts of inequality? When is one inequality worse than another? Temkin shows that there are many different factors underlying and influencing our egalitarian judgments and that the notion of inequality is surprisingly complex. He looks at inequality as applied to individuals and to groups, and at the standard measures of (...) class='Hi'>inequality employed by economists and others, and considers whether inequality matters more in a poor society than a rich one. The arguments of non-egalitarians are also examined. Temkin's book presents a new way of thinking about equality and inequality which challenges the assumptions of philosophers, welfare economists, and others concerned with these notions on a practical as well as a theoretical level. (shrink)

Temkin presents a new way of thinking about equality and inequality that challenges the assumptions of philosophers, welfare economists, and others, and has significant implications on both a practical and theoretical level.

Integrated assessment models of climate and the economy provide estimates of the social cost of carbon and inform climate policy. We create a variant of the Regional Integrated model of Climate and the Economy (RICE)—a regionally disaggregated version of the Dynamic Integrated model of Climate and the Economy (DICE)—in which we introduce a more fine-grained representation of economic inequalities within the model’s regions. This allows us to model the common observation that climate change impacts are not evenly distributed within regions (...) and that poorer people are more vulnerable than the rest of the population. Our results suggest that this is important to the social cost of carbon—as significant, potentially, for the optimal carbon price as the debate between Stern and Nordhaus on discounting. (shrink)

We build models where all $\underset{\sim}{\triangle}^1_3$-sets of reals are measurable and (or) have the property of Baire and (or) are Ramsey. We will show that there is no implication between any of these properties for $\underset{\sim}{\triangle}^1_3$-sets of reals.

J.P. Moreland—Christian philosopher, theologian, and apologist—issues a call to recapture the drama and power of kingdom living—to cultivate a revolution of Evangelical life, spirituality, thought, and Spirit-led power. Drawing insights from the early church, he unpacks three essential ingredients of this revolution: Recovery of the Christian mind. Renovation of Christian spirituality. Restoration of the power of the Holy Spirit. Western society is in crisis: the result of our culture's embrace of naturalism and postmodernism, and a biblical worldview has been pushed (...) to the margins. Christians have been strongly influenced by these trends, with the result that their personal lives often reflect the surrounding culture more than the way of Christ, and the church's transforming influence on society has waned as a result. Kingdom Triangle is divided into two major sections: The first examines and provides a critique of secular worldviews and shows how they have ushered in the current societal crisis. The second lays out a strategy for the Christian community to regain the potency of kingdom life and influence in the world. Moreland believes that evangelical Christianity can mature and lead the surrounding society out of the meaningless morass it finds itself in with humility and vision. With clear insight, he puts the thoughtful Christian in a position to understand our current cultural struggle and to return to a responsible presentation of "the way of Christ" as not just a way of right living, but also a way of knowledge and meaningful life. (shrink)

In the present article, we consider the question of the primary elements in Plato’s Timaeus, the components of the whole universe reduced, by an extraordinarily elegant construction, to two right triangles. But how does he reconcile such a model with the infinite diversity of the universe? A large part of this study is devoted to Cornford’s explanation in his commentary of the Timaeus and its shortcomings, in order to finally propose a revised one, which we think to be entirely consistent (...) with Plato’s text. This analysis is an essential step for the understanding of the connection between the sensible world and the mathematical principles that underlies Timaeus’ cosmological account. (shrink)

Sufficientarian theories of distributive justice are often considered to be vulnerable to the ‘blindness to inequality and other values objection’. This objection targets their commitment to holding the moral irrelevance of requirements of justice above absolute thresholds of advantage, making them insufficiently sensitive to egalitarian moral concerns that do have relevance for justice. This paper explores how sufficientarians could reply to this objection. Particularly, I claim that, if we accept that the force of the aforementioned objection comes from relational, (...) and not distributive, inequalities, different strategies are open for sufficientarians in order to be sensitive to these concerns. Drawing on recent literature about the relation between distributive and relational egalitarianism, and the possibility of reducing one to the other, strategies of ‘internalizing’ and ‘externalizing’ relational egalitarian concerns to a distributive sufficientarian framework are explored. In turn, I suggest that both strategies fail in their standard versions, but argue that a particular ‘hybrid view’ about justice is an attractive candidate for the sufficientarian theorist. (shrink)

Michael Otsuka sets out to vindicate left-libertarianism, a political philosophy which combines stringent rights of control over one's own mind, body, and life with egalitarian rights of ownership of the world. Otsuka reclaims the ideas of John Locke from the libertarian Right, and shows how his Second Treatise of Government provides the theoretical foundations for a left-libertarianism which is both more libertarian and more egalitarian than the Kantian liberal theories of John Rawls and Thomas Nagel. Otsuka's libertarianism is founded on (...) a right of self-ownership. Here he is at one with 'right-wing' libertarians, such as Robert Nozick, in endorsing the highly anti-paternalistic and anti-moralistic implications of this right. But he parts company with these libertarians in so far as he argues that such a right is compatible with a fully egalitarian principle of equal opportunity for welfare. In embracing this principle, his own version of left-libertarianism is more strongly egalitarian than others which are currently well known. Otsuka argues that an account of legitimate political authority based upon the free consent of each is strengthened by the adoption of such an egalitarian principle. He defends a pluralistic, decentralized ideal of political society as a confederation of voluntary associations. Part I of Libertarianism without Inequality concerns the natural rights of property in oneself and the world. Part II considers the natural rights of punishment and self-defence that form the basis for the government's authority to legislate and punish. Part III explores the nature and limits of the powers of governments which are created by the consensual transfer of the natural rights of the governed. Libertarianism without Inequality is a book which everyone interested in political theory should read. (shrink)

In this article, the author addresses two feminist issues: first, how to conceptualize intersectionality, the mutual reproduction of class, gender, and racial relations of inequality, and second, how to identify barriers to creating equality in work organizations. She develops one answer to both issues, suggesting the idea of “inequality regimes” as an analytic approach to understanding the creation of inequalities in work organizations. Inequality regimes are the interlocked practices and processes that result in continuing inequalities in all (...) work organizations. Work organizations are critical locations for the investigation of the continuous creation of complex inequalities because much societal inequality originates in such organizations. Work organizations are also the target for many attempts to alter patterns of inequality: The study of change efforts and the oppositions they engender are often opportunities to observe frequently invisible aspects of the reproduction of inequalities. The concept of inequality regimes may be useful in analyzing organizational change projects to better understand why these projects so often fail and why they succeed when this occurs. (shrink)

Social and regional inequality remained of secondary importance in the 2017 House of Representatives election, especially in comparison to national security and constitutional reform. Still, the election victory of the coalition between the Liberal Democratic Party (LDP) and Kōmeitō was also due to its ability to shape the debate concerning Japan’s political-economic model of growth and inequality. Abenomics and regional revitalization were the dominating policies, which opposition parties criticized without having a real counter-model. A more detailed analysis shows, (...) however, that Abenomics has not yet fulfilled its promise of shared growth, and that the governing coalition’s discursive control over the political-economic agenda has significantly weakened. This creates opportunities for opposition parties in the future. (shrink)

Some political philosophers have recently argued that providing K–12 students with an adequate education suffices for social justice in education provided that the threshold of educational adequacy is properly understood. Others have argued that adequacy is insufficient for social justice. In this article I side with the latter group. I extend this debate to racial inequality in education by considering the controversial practice of paying students cash for grades to close the racial achievement gap. I then argue that framing (...) the demand for racial justice in education solely in terms of educational adequacy leaves us unable to take issue with the cash for grades policy as a matter of principle. While this does not entail that educational adequacy is unimportant, it adds to the general case for why adequacy does not suffice for social justice. (shrink)

Higher education in general, and more specifically in the South African environment, is under pressure to transform. Although learning is often seen as the main focal point, the education process consists of three equally important pillars that form the triangle of effective education that fits within the intersection of the spheres of the community of inquiry framework. The basic pillars expand to student-centred teaching, blended learning and transformative assessment. This study is a short explanation of how these three pillars (...) form a basic framework for effective theological training. This is a qualitative study, using a philosophical and analytical research design and illuminative evaluation as research method. This is a model for effective higher education in Theology. The triangle of effective education is formed by student-centred teaching, blended learning and transformative assessment. The model fits into the intersection of the spheres identified by the community of inquiry framework of Garrison, Anderson and Archer. (shrink)

Following a discourse analysis approach this study examines triadic encounters of nine medical consultations carried out in an outpatient cancer clinic in Santiago, Chile involving an oncologist, a patient and a patient’s companion. Consultations are fully transcribed and analysed to understand the participatory roles patients’ companions play in the medical exchanges. In addition, the type of linguistic functions associated with each role and the advantages or downsides of companions’ involvement in the encounters are also investigated. The analysis reveals seven prominent (...) roles that companions may engage in during the visits. These are studied in detail. The results show that although companions may not always provide information that is consistent with the patients’ views, they can be of great help. Relieving the patients of many daunting tasks, monitoring their well-being, establishing a partnership and bringing vital information to the clinic are instances where the controlling power that some may exercise in the medical encounter can be outweighed. (shrink)

Résumé Entre la construction d’une monstruosité étatique absolue, censée anéantir toute rébellion par la crainte et la menace (d’un côté) et la monstrification de la part du Pouvoir de tout «autre» rebelle, hérétique, contestataire (de l’autre), l’auteur indique la possibilité d’un troisième concept de la monstruosité. Une monstruosité qui échappe à cette alternative pour affirmer son altérité radicale, monstrueuse non pas par son apparence mais par sa revendication d’autonomie par rapport à toute norme transcendante et finaliste, dans l’immanence absolue de (...) sa condition actuelle et puissante. (shrink)

Callicott’s basic mistake in his much regretted paper ”Animal Liberation: A Triangular Affair” is to think of the anthropocentric, zoocentric, and biocentric perspectives as mutually exclusive alternatives. An environmental ethics requires, instead, a polycentric perspective that accommodates and does justice to all three positions in question. I explain the polycentric perspective in terms of an analogy derived from the pioneering work of Canadian philosopher Rupert C. Lodge and distinguish it from both pragmatism and moral pluralism.