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)

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.

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)

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

Work on the therapeutic misconception suggests that investigators should ensure that potential research subjects understand the fundamental differences between clinical research and clinical care. Yet, what potential research subjects should understand depends on their circumstances and the study in question. This analysis implies that researchers and review committees should stop attempting to define, measure, and dispel the therapeutic misconception, and instead should focus on what potential subjects should understand to participate in individual studies.

As machine learning has gradually entered into ever more sectors of public and private life, there has been a growing demand for algorithmic explainability. How can we make the predictions of complex statistical models more intelligible to end users? A subdiscipline of computer science known as interpretable machine learning (IML) has emerged to address this urgent question. Numerous influential methods have been proposed, from local linear approximations to rule lists and counterfactuals. In this article, I highlight three conceptual challenges that (...) are largely overlooked by authors in this area. I argue that the vast majority of IML algorithms are plagued by (1) ambiguity with respect to their true target; (2) a disregard for error rates and severe testing; and (3) an emphasis on product over process. Each point is developed at length, drawing on relevant debates in epistemology and philosophy of science. Examples and counterexamples from IML are considered, demonstrating how failure to acknowledge these problems can result in counterintuitive and potentially misleading explanations. Without greater care for the conceptual foundations of IML, future work in this area is doomed to repeat the same mistakes. (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)

Through Narcissus' Glass Darkly presents a genealogy and critique of the ideal of conscience in modern philosophical theology, particularly in the writings of ...

This essay challenges the portrayal of philosophical idealism as sinful ‘confinement in the self’, arguing that this obscures a relationship between Hegel and Bonhoeffer characterised by variation rather than contradiction. I first trace a limited congeniality between their respective critiques of the ‘beautiful soul’ and the ‘privately virtuous’, showing how both thinkers resist moral isolation through the call to confession. Second, I follow their attempts to overcome an oppositional logic between such social exchange and divine agency, rooted in the syntax (...) of Hegel’s phrase ‘God existing as community’. This provides sharper focus to Bonhoeffer’s variations, changing the subject from God to Christ and the attendant act from reciprocal confession to intercessory prayer. Rather than merely defensive revision, I argue that this reveals an agile Christology which can sustain an ethical posture of ‘being for others’ through the withheld confession and broken trust typical of a communion of sinners. (shrink)

De Neys argues against assigning exclusive capacities to automatic versus controlled processes. The dual implicit process model provides a theoretical rationale for the exclusivity of automatic threat processing, and corresponding data provide empirical evidence of such exclusivity. De Neys's dismissal of exclusivity is premature and based on a limited sampling of psychological research.

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)

Demands for standardization and accountability as systemic cures for perceived ills in the education system are paralleled by a public and private sector promotion of technology integration as one pedagogical solution. The general critique of education and of technology in society has developed as two related yet separate threads in critical inquiry and discussion. As electronic forms of media and communication are becoming pervasive in society in general, solutions to long-standing educational dilemmas that mirror problems in society at large need (...) to develop from grounded theories for educational practice that embrace technological forms of information, knowledge, and culture production. This needs to be done to reverse the historical trend of education as an institution first adopting and then adapting technological forms to purposes of replicating status quo culture and social relationships. Despite the claims of many to the contrary, new technology may not make any difference in education. Individual attainment and achievement through technological efficiency may prove meaningless in a world pressed to reconcile problems that move diverse societies closer together rather than farther apart. Hope, meaning, belonging, and what has been termed the pedagogy of possibility are posited as an ethical foundation for advancing the integration of technology into education for an equitable, democratic, and different future. (shrink)

Clarke proposes a conception of philosophy that provides an alternative to the reductions of materialism and the search for normative principles. Philosophy's proper role is to describe similarities and differences among differing levels of language, specifically the familiar level of discourse within an ordinary language shared by all and the specialized discourses of social institutions such as science, law, and the arts. By constructing a logical framework in which these comparisons and contrasts can be made, philosophy performs the indispensable role (...) of promoting the integration of disparate elements of our culture. (shrink)

"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.

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)

Dietrich Bonhoeffer’s account of a transnational “confessing” church, developed with allusion to W.E.B. Du Bois, offers critical potential for addressing the problem of the global color line. To make this case, I first trace the ways in which Du Bois’s and Bonhoeffer’s German–American exchange studies contribute to their critical standpoints. Bonhoeffer’s “Protestantism without Reformation” is then examined to show that its view of American denominations is not mere German paternalism but a critique of how atomized churches can mask racial segregation, (...) even as it takes seriously America’s founding as a “nation of refugees.” Finally, Bonhoeffer’s references to intercultural encounter, particularly with respect to the Jewish diaspora in his later Ethics, provide for the extension of his ecclesiology beyond Germany and the “West.” Specifically, Du Bois’s own creedal language and pan-Africanism require that a truly global confession of the “form of Christ” must attend to unrecognized histories from the “Black Atlantic.”. (shrink)

An inadequate grasp of the role of imagination has vitiated understanding of human cognition in western thinking. Extending a project initiated with George Lakoff in _Metaphors we Live By_ (1980), Mark Johnson's book _The Body in the Mind_ (1987) offers the claim that all thinking originates in bodily experience. A range of schemata formed during our early experience manipulating a physical world of surfaces, distances, and forces, lays the foundation of later, more abstract modes of thought. In presenting his argument, (...) Johnson lays special stress on the qualities and dynamics of the image schemata, the (generally unnoticed) metaphoricity of the transformations underlying abstract thought, and the new significance that should be attributed to the imagination, which is the general term Johnson wishes to claim for the mental processes he expounds. In this paper I draw attention to the importance of Johnson's insights for understanding literary response. In particular, I will show how a typical procedure of literary texts involves bringing to awareness image schemata of the kind that Johnson describes. At the same time, several problems in Johnson's account which limit its usefulness will also be examined: an undue reliance upon the spatial properties of schemata; a conflation of dead with live or poetic metaphors; and a neglect of other bodily influences on thought, especially kinaesthetic and affective aspects. These problems, for example, limit the usefulness of Johnson's attempt to build on Kant's theory of imagination. In comparison with Coleridge, who also attempted to build on Kant, Johnson is unable to overcome the formalism of Kant's theory. Coleridge's account of imagination, I will suggest, provides a better foundation for examining the bodily basis of meaning, while remaining compatible with Johnson's intentions and his more valuable insights. (shrink)

Although biologists and philosophers of science generally agree that genes cannot determine the forms of biological and psychological traits, students, journalists, politicians, and other members of the general public nonetheless continue to embrace genetic determinism. This article identifies some of the concerns typically raised by individuals when they first encounter the systems perspective that biologists and philosophers of science now favor over genetic determinism, and uses arguments informed by that perspective to address those concerns. No definitive statements can yet be (...) made about why genetic determinism has proven so resilient in the face of empirical evidence pointing up its deficiencies, but conveying the essential interdependence of 'nature' and 'nurture' to the general public will likely require deployment of the arguments that systems theorists ordinarily use to reject genetic determinism. In addition, the elaboration of new metaphors that focus attention on the dynamic nature of trait construction will likely prove valuable, because re-conceptualizing notions like 'genes' and 'nature' will probably be one of the most effective ways to help students and the general public abandon the genetic determinism that biologists now recognize as indefensible. (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)

In 1982, without waiting for the findings of the National Hospice Study, Congress passed legislation enabling certified hospices to receive Medicare reimbursement. What emerged is a reimbursement program that differs substantially from the movement that spawned it. Hospices now face many dilemmas, among them shifting the burden of care to the family, determining who controls the course of patient care, and breaking even financially.

In response to recent corporate ethical and financial disasters there has been increased pressure on business schools to improve their teaching of corporate ethics. Accreditation bodies, such as the Association to Advance Collegiate Schools of Business (AACSB), now require member institutions to develop the ethical awareness of business students, either through a dedicated subject or an integrated coverage of ethics across the curriculum. This paper describes an institutional approach to the incorporation of a comprehensive multi-disciplinary ethics framework into the business (...) curriculum. We discuss important implications for the assessment of ethics within institutional assurance practices, and address critical issues related to the support of academics whenrequired to incorporate new ethics material within their subject which may be outside their field of expertise. As an example, the successful application of the framework within the marketing discipline is presented and discussed. (shrink)

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..

From Kierkegaard’s famous polemic against Hegel’s system, and Marx’s rejection of the “mysticism” of reason, to Heidegger’s claim that Hegel completes the tradition of western metaphysics, and contemporary critics’ identification of Hegel as the authoritative spokesman — the “Master” — for the principles of unity and identity, a standard view has governed interpretations and evaluations of Hegel’s philosophy. Though familiarity with the positions just cited reveals considerable disparity, one does not need an especially discerning eye to recognize the common features (...) of the figures drawn. Hegel is, in all of them, the philosopher of the Absolute, the proponent of metaphysics without equal in the modern world. (shrink)

Although Mealey's account provides several interesting hypotheses, her integration across disparate samples renders the value of her explanation for psychopathy ambiguous. Recent evidence on Psychopathy Checklist-identified samples (Hare, 1991) suggests primary emotional and cognitive deficits inconsistent with her model. Whereas high-anxious psychopaths display interpersonal deficits consistent with Mealey's hypotheses, low-anxious psychopaths' deficits appear more sensitive to situational parameters than predicted.