Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, (...) the axiom of choice, Zorn’s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process. (shrink)

: The Centers for Disease Control and Prevention (CDC) has recommended that HIV testing be routinely offered to certain patients in hospitals with a high prevalence of HIV infection and on all pregnant women. The CDC does not, however, offer implementation level guidelines for obtaining informed consent. We provide a moral justification for requiring informed consent for HIV testing and propose guidelines for securing such consent. In particular we argue that genuine informed consent can be secured without elaborate counseling, such (...) as that currently used at Counseling and Testing Sites, provided that sufficient written notice is given to the patients before testing and that they are specifically asked for permission. (shrink)

This paper explores how gender can operate as a disguise for class in an examination of the self-sacrifice of the Maiden in Euripides' Children of Herakles. In Part I, I discuss the role of human sacrifice in terms of its radical potential to transform society and the role of class struggle in Athens. In Part II, I argue that the representation of women was intimately connected with the social and political life of the polis. In a discussion of iconography, the (...) theater industry and audience I argue that female characters became one of the means by which different groups promoted partisan interests based on class and social status. In Part III, I show how the Maiden solicits the competing interests of the theater audience. After discussing the centrality (as a heroine from an aristocratic family) and marginality (as a woman and associated with other marginal social groups) of the Maiden's character, I draw upon the funeral oration as a comparative model with which to understand the quite different role of self-sacrifice in tragedy. In addition to representing and mystifying the interests of elite, lower class and marginal groups, the play glorifies a subordinate character whose contradictory social status (both subordinate and elite) embodies the social position of other “marginal” members of Athenian society. The play stages a model for taking political action to transform the social system and for commemorating the tragic costs of such undertakings. (shrink)

One of the most potent arguments against physician‐assisted death hinges on the worry that people with disabilities will be subtly coerced to accept death prematurely. The argument is flawed. There is nothing new in PAD: the risk of coercion is already present in current policies about end of life care. And to hold that any such risk is too much is tacitly to endorse vitalism and to deny that people with disabilities are capable of choosing authentically.

_Real Essentialism_ presents a comprehensive defence of neo-Aristotelian essentialism. Do objects have essences? Must they be the kinds of things they are in spite of the changes they undergo? Can we know what things are really like – can we define and classify reality? Many, if not most, philosophers doubt this, influenced by centuries of empiricism, and by the anti-essentialism of Wittgenstein, Quine, Popper, and other thinkers. _Real Essentialism_ reinvigorates the tradition of realist, essentialist metaphysics, defending the reality and knowability (...) of essence, the possibility of objective, immutable definition, and its relevance to contemporary scientific and metaphysical issues such as whether essence transcends physics and chemistry, the essence of life, the nature of biological species, and the nature of the person. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Machine learning algorithms may radically improve our ability to diagnose and treat disease. For moral, legal, and scientific reasons, it is essential that doctors and patients be able to understand and explain the predictions of these models. Scalable, customisable, and ethical solutions can be achieved by working together with relevant stakeholders, including patients, data scientists, and policy makers.

"Nivison brings out the exciting variety within Confucian thought, as he interprets and elucidates key thinkers from over two thousand years, from Confucius himself, through Mencius and Xunzi, to such later Confucians as Wang Yangming, Dai Zhen, and Zhang Xuecheng."--Cover.

DCPS is a connectionist production system interpreter that uses distributed representations. As a connectionist model it consists of many simple, richly interconnected neuron‐like computing units that cooperate to solve problems in parallel. One motivation for constructing DCPS was to demonstrate that connectionist models are capable of representing and using explicit rules. A second motivation was to show how “coarse coding” or “distributed representations” can be used to construct a working memory that requires far fewer units than the number of different (...) facts that can potentially be stored. The simulation we present is intended as a detailed demonstration of the feasibility of certain ideas and should not be viewed as a full implementation of production systems. Our current model only has a few of the many interesting emergent properties that we eventually hope to demonstrate: It is damage‐resistant, it performs matching and variable binding by massively parallel constraint satisfaction, and the capacity of its working memory is dependent on the similarity of the items being stored. (shrink)

The distinction between the essence of an object and its properties has been obscured in contemporary discussion of essentialism. Locke held that the properties of an object are exclusively those features that ‘flow’ from its essence. Here he follows the Aristotelian theory, leaving aside Locke’s own scepticism about the knowability of essence. I defend the need to distinguish sharply between essence and properties, arguing that essence must be given by form and that properties flow from form. I give a precise (...) definition of what the term of art ‘flow’ amounts to, and apply the distinction to various kinds of taxonomic issues. (shrink)

We examine two different descriptions of the behavioral functions of the hippocampal system. One emphasizes spatially organized behaviors, especially those using cognitive maps. The other emphasizes memory, particularly working memory, a short-term memory that requires iexible stimulus-response associations and is highly susceptible to interference. The predictive value of the spatial and memory descriptions were evaluated by testing rats with damage to the hippocampal system in a series of experiments, independently manipulating the spatial and memory characteristics of a behavioral task. No (...) dissociations were found when the spatial characteristics of the stimuli to be remembered were changed; lesions produced a similar deficit in both spatial and nonspatial test procedures, indicating that the hippocampus was similarly involved regardless of the spatial nature of the task. In contrast, a marked dissociation was found when the memory requirements were altered. Rats with lesions were able to perform accurately in tasks that could be solved exclusively on the basis of reference memory. They performed at chance levels and showed no signs of recovery even with extensive postoperative training in tasks that required working memory. In one experiment all the characteristics of the reference memory and working memory procedures were identical except the type of memory required. Consequently, the behavioral dissociation cannot be explained by differences in attention, motivation, response inhibition, or the type of stimuli to be remembered. As a result of these experiments we propose that the hippocampus is selectively involved in behaviors that require working memory, irrespective of the type of material that is to be processed by that memory. (shrink)

Since the introduction and widespread adoption of chemical herbicides, “weed management” has become almost synonymous with “herbicide management.” Over-reliance on herbicides and herbicide-resistant crops has given rise to herbicide resistant weeds. Integrated weed management (IWM) identifies three strategies for weed management— biological-cultural, chemical-technological, mechanical-physical—and recommends combining all three to mitigate herbicide resistance. However, adoption of IWM has stalled, and research to understand the adoption of IWM practices has focused on single stakeholder groups, especially farmers. In contrast, decisions about weed management (...) often occur within a social ecosystem where multiple stakeholder groups co-create knowledge and practices. To more holistically investigate perceptions and decision-making related to herbicide resistant weed management, we conducted 23 in-depth interviews in combination with Q methodology with farmers and public-/private-sector agricultural professionals in the state of Georgia (U.S.). Our investigation focused on the management of an increasingly herbicide resistant weed, Palmer amaranth, which enabled broader conversations about agricultural systems, farmer livelihoods, and sustainability. Factor and thematic analyses allowed us to identify and characterize two distinct typologies: one primarily valued agronomic efficiency and relied upon chemical-technological management practices, while the other valued diversifying weed management strategies as the pathway to agronomic and economic success. Typologies diverged substantially in attitudes toward the three weed management strategies, the role of technology, and systems management generally. These two viewpoints have implications for how we understand underlying stakeholder motivations and choices around weed management strategies, both of which are crucial in promoting and supporting farmer use of diverse, ecologically-sound, weed management strategies. (shrink)

The Dead Donor Rule holds that removing organs from a living human being without their consent is wrongful killing. The rule still prevails in most countries, and I assume it without argument in order to pose the question: is it possible to have a metaphysically correct, clinically relevant analysis of human death that makes organ donation possible? I argue that the two dominant criteria of death, brain death and circulatory death, are both empirically and metaphysically inadequate as definitions of human (...) death, and therefore of no epistemic value in themselves. I first set out a neo-Aristotelian theory of death as separation of soul (understood as organising principle) and body, which is then fleshed out as loss of organismic integrity. The brain and circulatory criteria are shown to have severe weaknesses as physiological manifestations of loss of integrity. Given the mismatch between what death is metaphysically speaking, and the dominant criteria accepted by clinicians and philosophers, it turns out that only actual bodily decomposition is a sure sign of death. In this I differ from Alan Shewmon, whose important work I discuss in detail. (shrink)

The Metaphysics of Good and Evil is the first, full-length contemporary defence, from the perspective of analytic philosophy, of the Scholastic theory of good and evil - the theory of Aristotle, Augustine, Aquinas, and most medieval and Thomistic philosophers. Goodness is analysed as obedience to nature. Evil is analysed as the privation of goodness. Goodness, surprisingly, is found in the non-living world, but in the living world it takes on a special character. The book analyses various kinds of goodness, showing (...) how they fit into the Scholastic theory. The privation theory of evil is given its most comprehensive contemporary defence, including an account of truthmakers for truths of privation and an analysis of how causation by privation should be understood. In the end, all evil is deviance - a departure from the goodness prescribed by a thing's essential nature. Key Features: Offers a comprehensive defence of a venerable metaphysical theory, conducted using the concepts and methods of analytic philosophy. Revives a much neglected approach to the question of good and evil in their most general nature. Shows how Aristotelian-Thomistic theory has more than historical relevance to a fundamental philosophical issue, but can be applied in a way that is both defensible and yet accessible to the modern philosopher. Provides what, for the Scholastic philosopher, is arguably the only solid metaphysical foundation for a separate treatment of the origins of morality. (shrink)

This paper tests the following hypothesis: that the prime matter of classical Aristotelian-Scholastic metaphysics is numerically identical to energy. Is P=E? After outlining the classical Aristotelian concept of prime matter, I provide the master argument for it based on the phenomenon of substantial change. I then outline what we know about energy as a scientific concept, including its role and application in some key fields. Next, I consider the arguments in favour of prime matter being identical to energy, followed by (...) the arguments against. The method used is that of ontological profile comparison: does the profile of prime matter match, in key features, that of energy? An affirmative answer, that P=E, would be a momentous discovery: it would show that one of the most neglected and derided ideas of pre-modern metaphysics – a contributor to its downfall in the wake of the Scientific Revolution – was right all along. From a negative answer we would still learn much about the interaction of science and metaphysics. It turns out, however, given what we currently know, that the answer is not quite as simple as one might hope. (shrink)

Applied Ethics focuses the central concepts of traditional morality from the companion book Moral Theory - rights, justice, the good, virtue, and the fundamental value of human life - on a number of pressing contemporary problems, including abortion, euthanasia, animals, capital punishment, and war.

Corruptionism is the view that following physical death, the human being ceases to exist but their soul persists in the afterlife. Survivalism holds that both the human being and their soul persist in the afterlife, as distinct entities, with the soul constituting the human. Each position has its defenders, most of whom appeal both to metaphysical considerations and to the authority of St Thomas Aquinas. Corruptionists claim that survivalism violates a basic principle of any plausible mereology, while survivalists tend to (...) reject the principle, though without as much detail as one would like. In this paper I examine both the key exegetical issues and the mereological question, arguing that Aquinas cannot be shown to have supported the principle in question, and that the principle should be rejected on independent grounds. If correct, some key planks in support of survivalism are established, with others to await further examination. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealisedexplanation gamein which players collaborate to find the best explanation(s) for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal patterns of (...) variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a (conditionally) optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

_Moral Theory_ sets out the basic system used to solve moral problems, the system that consequentialists deride as 'traditional morality'. The central concepts, principles and distinctions of traditional morality are explained and defended: rights; justice; the good; virtue; the intention/foresight distinction; the acts/omissions distinction; and, centrally, the fundamental value of human life.

The vigorous legal and ethical debates over conscientious objection have taken place largely within the domain of health care. Is this because conscience in medicine is of a special kind, or are th...

The question whether two things can be in the same place at the same time is an ambiguous one. At least three distinct questions could be meant: Can two things simpliciter be in the same place at the same time? Can two things of the same kind be in the same place at the same time? Can two substances of the same kind be in the same place at the same time? The answers to these questions vary. In what follows, (...) all three will be discussed in the light both of recent and of classic earlier examinations of the matter. The following theses will be defended. (shrink)

Caretaker-infant attachment is a complex but well-recognized adaptation in humans. An early instance of (or precursor to) attachment behavior is the dyadic interaction between adults and infants of 6 to 24 weeks, commonly called "babytalk." Detailed analysis of 1 minute of spontaneous babytalk with an 8-week infant shows that the poetic texture of the mother’s speech—specifically its use of metrics, phonetics, and foregrounding—helps to shape and direct the baby’s attention, as it also coordinates the partners’ emotional communication. We hypothesize that (...) the ability to respond to poetic features of language is present as early as the first few weeks of life and that this ability attunes cognitive and affective capacities in ways that provide a foundation for the skills at work in later aesthetic production and response. By linking developmental social processes with formal cognitive aspects of art, we challenge predominant views in evolutionary psychology that literary art is a superfluous byproduct of adaptive evolutionary mechanisms or primarily an ornament created by sexual selection. (shrink)

The old scholastic principle of the "convertibility" of being and goodness strikes nearly all moderns as either barely comprehensible or plain false. "Convertible" is a term of art meaning "interchangeable" in respect of predication, where the predicates can be exchanged salva veritate albeit not salva sensu: their referents are, as the maxim goes, really the same albeit conceptually different. The principle seems, at first blush, absurd. Did the scholastics literally mean that every being is good? Is that supposed to include (...) a cancer, a malaria parasite, an earthquake that kills millions? If every being is good, then no being is bad—but how can that be? To the contemporary philosophical mind, such bafflement is understandable. It derives from the systematic dismantling of the great scholastic edifice that took place over half a millennium. With the loss of the basic concepts out of which that edifice was built, the space created by those concepts faded out of existence as well. The convertibility principle, like virtually all the other scholastic principles (not all, since some do survive and thrive in analytic philosophy), could not persist in a post-scholastic space wholly alien to it. (shrink)

Things change. If anything counts as a datum of metaphysics, that does. Change occurs in many ways: it can be accidental or substantial; essential or non-essential; intrinsic or extrinsic; subjective or objective. Changes can be physical, spatial, quantitative, qualitative, natural, artefactual, conceptual, linguistic. Events are arguably best defined as changes in an object or objects. All change is from something and into something, and hence is at least a two-term relation, involving a term from which and a term to which.

mix of the concrete and the abstract (if we include universals, laws, propositions and the like), but whichever of these is the case, the world is not purely abstract, as a formal structure is. One might claim, however, that the world is a structure1 in the sense that it instantiates a structure and is nothing else. In other words, all there is to the..

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Many scholars have argued that the Protestant Reformation generally departed from virtue ethics, and this claim is often accepted by Protestant ethicists. This essay argues against such discontinuity by demonstrating John Calvin’s reception of ethical concepts from Augustine and Aristotle. Calvin drew on Augustine’s concept of eudaimonia and many aspects of Aristotle’s Nicomachean Ethics , including concepts of choice, habit, virtue as a mean, and the specific virtues of justice and prudence. Calvin also evaluated the problem of pagan virtue in (...) light of traditional Augustinian texts discussed in the medieval period. He interpreted the Decalogue as teaching virtue, including the cardinal virtues of justice and temperance. Calvin was not the harbinger of an entirely new ethical paradigm, but rather a participant in the mainstream of Christian thinkers who maintained a dual interest in Aristotelian and Augustinian eudaimonist virtue ethics. (shrink)

We live in a liberal, pluralistic, largely secular society where, in theory, there is fundamental protection for freedom of conscience generally and freedom of religion in particular. There is, however, both in statute and common law, increasing pressure on religious believers and conscientious objectors to act in ways that violate their sincere, deeply held beliefs. This is particularly so in health care, where conscientious objection is coming under extreme pressure. I argue that freedom of religion and conscience need to be (...) put on a sounder footing both legislatively and by the courts, particularly in health care. I examine a number of important legal cases in the UK and US, where freedom of religion and conscience have come into conflict with government mandates or equality and anti-discrimination law. In these and other cases we find one of two results: either the conscientious objector loses out against competing rights, or the conscientious objector succeeds, but due to what I consider unsound judicial reasoning. In particular, cases involving cooperation in what the objector considers morally impermissible according to their beliefs have been wrongly understood by some American courts. I argue that a reasonable theory of cooperation incorporated into judicial thinking would enable more acceptable results that gave sufficient protection to conscientious objectors without risking a judicial backlash against objectors who wanted to take their freedoms too far. I also venture into broader, more controversial waters concerning what I call freedom of dissociation – the fundamental right to withdraw from associating with people, groups, and activities. It is no more than the converse of freedom of association, which all free societies recognise as a basic right. How far should freedom of dissociation go? What might society be like if freedom of dissociation were given more protection in law than it currently has? It would certainly give freedom of religion and conscience a substantial foundation, but it could also lead to discriminatory behaviour to which many people would object. I explore some of these issues, before going back to the narrower area of freedom of conscience and religion in health care, making some proposals about how the law could strengthen these basic pillars of a liberal, free society. (shrink)

Proponents of physical intentionality argue that the classic hallmarks of intentionality highlighted by Brentano are also found in purely physical powers. Critics worry that this idea is metaphysically obscure at best, and at worst leads to panpsychism or animism. I examine the debate in detail, finding both confusion and illumination in the physical intentionalist thesis. Analysing a number of the canonical features of intentionality, I show that they all point to one overarching phenomenon of which both the mental and the (...) physical are kinds, namely finality. This is the finality of ‘final causes’, the long-discarded idea of universal action for an end to which recent proponents of physical intentionality are in fact pointing whether or not they realise it. I explain finality in terms of the concept of specific indifference, arguing that in the case of the mental, specific indifference is realised by the process of abstraction, which has no correlate in the case of physical powers. This analysis, I conclude, reveals both the strength and weakness of rational creatures such as us, as well as demystifying the way in which powers work. (shrink)

The first English-language collection devoted to Hegel’s Philosophy of Subjective Spirit.

The narratives studied by schema-based models or story grammars are generally simpler than those found in literary texts, such as short stones or novels. Literary narratives are indeterminate, exhibiting conflicts between schemata and frequent ambiguities in the status of narrative elements. An account of the process of comprehending such complex narratives is beyond the reach of purely cognitive models. It is argued that during comprehension response is controlled by affect, which directs the creation of schemata more adequate to the text. (...) Several properties of affect that make it appropriate for this model of narrative are discussed. A short story by Virginia Woolf is analysed in the light of the proposed model. A study with readers of the story is described, which illustrates the process of schema formation: Shifts in the relative importance of story phrases across the reading and the comments made by readers point to a process of schema creation under the control of affect. It is argued that affect may play a more productive role in cognitive processes than is generally acknowledged. (shrink)

There is a tension between the reasonable desire not to be judgmental of other people’s behaviour or character, and the moral necessity of making negative judgments in some cases. I sketch a way in which we might accommodate both, via an evaluation of the good of reputation and the ethics of judgment of other people’s character and behaviour. I argue that a good reputation is a highly valuable good for its bearer, akin to a property right, and not to be (...) damaged without serious reason deriving from the demands of justice and the common welfare. Rash judgment wrongfully damages reputation and is sometimes a seriously immoral act. Rashness is not merely about lack of evidence, but involves lack of charity and is to be avoided even in some cases where the evidence of bad character or action is epistemically sufficient for judgment. I argue that the desirability of a good name for its holder, whether the reputation is deserved or not, means that in all but a relatively narrow range of cases it is always wrong to think badly of someone, even if they are bad. (shrink)

abstract This paper re‐examines some well‐known and commonly accepted arguments for the non‐individuality of the embryo, due mainly to the work of John Harris. The first concerns the alleged non‐differentiation of the embryoblast from the trophoblast. The second concerns monozygotic twinning and the relevance of the primitive streak. The third concerns the totipotency of the cells of the early embryo. I argue that on a proper analysis of both the empirical facts of embryological development, and the metaphysical importance or otherwise (...) of those facts, all three arguments are found wanting. None of them establishes that the embryo is not an individual human being from the moment of conception. (shrink)

Back cover: How is God revealed through the life of a human community? Dietrich Bonhoeffer's theological ethics begins from the claim to 'Christ existing as community', which David Robinson presents as one of several critical and politically astute variations on G.W.F. Hegel's philosophy of religion.

Contemporary liberal societies are seeing increasing pressure on individuals to act against their consciences. Most of the pressure is directed at freedom of religion but it also affects ethical beliefs more generally, contrary to the recognition of freedom of religion and conscience as a basic human right. I propose that freedom of dissociation, as a corollary of freedom of association, could be a practical and ethically acceptable solution to the conscience problem. I examine freedom of association and explain how freedom (...) of dissociation follows from it, showing how dissociation protects freedom of religion and conscience. Extreme cases, such as the problem of the Satanist nurse, can be handled within a dissociationist framework, so it is reasonable to think less extreme cases can also be dealt with. The serious objection that dissociationism entails unjust discrimination is answered primarily by appeal to the need for ‘full and fair access’ to goods and services by all groups. I then allay important concerns about what kind of liberal society we should want to live in. Next, I refute the charge that a dissociationist society violates liberalism's ‘higher good’, arguing that liberalism strictly does not have a higher good. I conclude with some reflections on what a dissociationist society might look like. (shrink)

The public forum has been connected to the functioning of democracy, expressive freedom, and the media's role in society. While the public forum's legal contours have been examined, the ethical foundation of the public forum has not. Relying on archival research, this article argues that ideas about the public forum can be traced to the pragmatism of Grenville Clark, who influenced ideas about the public forum through his work on the American Bar Association's Bill of Rights Committee.

Human rights discourse has been likened to a global lingua franca, and in more ways than one, the analogy seems apt. Human rights discourse is a language that is used by all yet belongs uniquely to no particular place. It crosses not only the borders between nation-states, but also the divide between national law and international law: it appears in national constitutions and international treaties alike. But is it possible to conceive of human rights as a global language or lingua (...) franca not just in a figurative or metaphorical sense, but in a literal or linguistic sense as a legal dialect defined by distinctive patterns of word choice and usage? Does there exist a global language of human rights that transcends not only national borders, but also the divide between domestic and international law? Empirical analysis suggests that the answer is yes, but this global language comes in at least two variants or dialects. New techniques for performing automated content analysis enable us to analyze the bulk of all national constitutions over the last two centuries, together with the world’s leading regional and international human rights instruments, for patterns of linguistic similarity and to evaluate how much language, if any, they share in common. Specifically, we employ a technique known as topic modeling that disassembles texts into recurring verbal patterns. The results highlight the existence of two species or dialects of rights talk—the universalist dialect and the positive-rights dialect—both of which are global in reach and rising in popularity. The universalist dialect is generic in content and draws heavily on the type of language found in international and regional human rights instruments. It appears in particularly large doses in the constitutions of transitional states, developing states, and states that have been heavily exposed to the influence of the international community. The positive-rights dialect, by contrast, is characterized by its substantive emphasis on positive rights of a social or economic variety, and by its prevalence in lengthier constitutions and constitutions from outside the common law world, especially those of the Spanish-speaking world. Both dialects of rights talk are truly transnational, in the sense that they appear simultaneously in national, regional, and international legal instruments and transcend the distinction between domestic and international law. Their existence attests to the blurring of the boundary between constitutional law and international law. (shrink)

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...) necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks. (shrink)