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This long-anticipated work shares the aims of its celebrated companion: namely, to provide an introduction for students and a reference for researchers to the techniques, results, and terminology of multiplicative number theory. This volume builds on the earlier one (which served as an introduction to basic, classical results) and focuses on sieve methods. This area has witnessed a number of major advances in recent years, e.g. gaps between primes, large values of Dirichlet polynomials and zero density estimates, all of which feature here. Despite the fact that the book can serve as an entry to contemporary mathematics, it remains largely self-contained, with appendices containing background or material more advanced than undergraduate mathematics. Again, exercises, of which there is a profusion, illustrate the theory or indicate ways in which it can be developed. Each chapter ends with a thorough set of references, which will be essential for all analytic number theorists.
A practical and interdisciplinary guide to creating liveable, circular economy cities. Practical strategies enhance the book's theoretical exploration of circular economies, providing a solution-oriented perspective on creating more resilient, environmentally sustainable and liveable cities. The chapter authors offer interdisciplinary perspectives on the transformative potential of circular economies when incorporating ecological and social aspects with innovative technologies. The topics covered range from sustainable agriculture and water management to renewable energy and environmental justice. Case studies of cities from around the world promote effective best practices in circular economy implementations across diverse cities, including Tokyo, Singapore, New York, Vancouver, Sydney, the Hague, Barcelona, and Stockholm. This book introduces and discusses the 5R framework - Reduce, Reuse, Recycle, Restore, Recover - as a guiding principle, elaborating its applications across various urban sectors. This book is indispensable for advanced students, researchers, city planners, and policymakers working in urban planning and sustainable development.
Moral philosophy can and ought to be a source of moral wisdom. Wisdom is a special kind of understanding, in particular, an ethical understanding of what it is to be a success as a human being, a healthy and fully formed specimen. Such understanding involves both a delicate grasp of the grammar of moral concepts and an appreciation of their import for a human life, including the philosopher’s. Virtue ethics is an important department of moral philosophy, especially for the philosophical goal of becoming wise. It consists in a careful investigation of the concepts of moral virtues (generosity, justice, the sense of duty, and so forth), both in their conceptual contours and in their importance for a human life.
The sense of duty is a virtue of caring, not directly about the good, or even about justice, but about doing one’s duty. Insofar as doing what one takes to be one’s duty is in fact to do what is good, the sense of duty functions as a backup for the more direct virtues of caring – generosity, compassion, and truthfulness, as well as justice. Being a virtue of caring, the sense of duty can be expressed in emotions: a feeling of satisfaction in having done one’s duties or feelings of guilt or shame at having neglected them. The sense of duty can vary, emotionally, according to how one conceives the authoritative source of duty, on a spectrum from reverence, through respect, to resentful acceptance. Example of the extremes beyond the spectrum are some Hebrew psalmists’ delight in the law of God and the contempt of the utter moral cynic.
‘Truth’ refers to reality – what is, was, will be, and should be – and its aspects, in the context of representations thereof. A true something is the real thing, and a true proposition, belief, hypothesis, exemplar, and so forth is a successful representation of truth in the first sense. The virtue of truthfulness is the judicious love of truth in both senses. From love of reality and correct representations of it, the truthful person tends to tell others the truth as she sees it, but is not fanatical about telling it, because virtues like justice, compassion, and gentleness, which themselves are a kind of truth, can enjoin the withholding or even distortion of truths. Truths can be horrible, and it can take courage and humility to admit them.
To be compassionate is to care about others specifically in opposition to their suffering or deficiency. While the distress of compassion is paradigmatic of the virtue, a wide range of emotion types – gratitude, anger, fear, joy, and so forth – can express it. Aristotle offers an analysis of the emotion of compassion as entailing propositions (1) that the other is suffering, (2) that the other doesn’t deserve the suffering, and (3) that oneself is vulnerable to the kind of suffering one sees in the other. In dialogue with Martha Nussbaum’s exposition and adaptation of Aristotle’s analysis of the emotion of compassion, this chapter compares Aristotelian compassion with the compassion that is commended in the New Testament. Differences between the two turn on differences in the concept of suffering, in the presence of a concept of forgiveness, and in the locus of commonality.
The virtues whose function is to regulate impulses, emotions, thoughts, and habits in the interest of larger purposes, including ethical ones, are courage, patience, perseverance, and self-control. They have a different grammar from the virtues of caring. Because they are not concerns, they are not defined by the motives or reasons for action or emotion that such concerns supply. Instead, they are differentiated by the kind of impulses that they manage. The situations they address are not outward, like the ones to which the virtues of caring respond, but are states of the self. Thus, self-control is the paradigm. They contribute to our integrity, our self-possession, and our freedom as authors of our character. They don’t in themselves have moral worth, are often used for non-moral purposes, and may even be used for evil. But in the context of good character they function in support of the virtues of caring.
Temperance is a condition of a person’s physical appetites (for food, drink, and sexual contact) in which those appetites themselves conform to a rational standard. Temperance is possible for human beings because of the sophistication with which we can conceptualize the objects of our appetites and because an appetite’s object is internal to the appetite’s identity. A salmon steak construed as poisoned appeals to our appetite (and thus affects the pleasure of satisfying it) differently than one construed as healthful. Temperance differs from self-control, which doesn’t involve a conformity of the appetites themselves, but imposes rational control on unmodified appetites. The rational standard for temperance is the human good, which is the object of the virtues of caring. Thus, the temperate person’s physical appetites are such that, without being controlled, they fit the person to participate in an order of peace.
In acts that are properly acts of justice (rather than, say, compassion or generosity), what is good for people is sought under the mediating description what is due them. The virtue of justice is the generalized concern that people get what is due them. Objective justice is the property of states of affairs, actions, institutions, and personal relationships in which people tend to get what is due them. So the virtue of justice is the concern that such objects have that property. When is some good or evil due a person? It is due on at least eight kinds of basis: desert, status, need, current possession, agreement, legality, parity, and freedom. We appeal to these conditions in justifying justice claims. The person who has the virtue of justice is one who is consistently and intelligently concerned that states of affairs, actions, institutions, and personal relationships be objectively just.
Forgivingness is virtue, a specification of generosity, a disposition to give offenders, especially against oneself, more of good and less of evil than they deserve. It is an interconnected set of sensitivities to features of situations marked by wrongdoing. The forgiving person is responsive to these features in ways that tend to mitigate, eliminate, or forestall anger in the interest of wishing the wrongdoer well and/or of enjoying a positive and harmonious relationship with him or her. The chief considerations favoring forgiveness are (1) the offender’s repentance, (2) excuses for the offender, (3) the offender’s suffering, (4) moral commonality with the offender, and (5) relationship to the offender.
Generosity and gratitude are prime examples of gracious traits – traits of concern for the other for the other’s sake. They are virtues of direct caring. They are complementary dispositions, readying their possessors to occupy reciprocal roles in gracious transactions. Their grammar contrasts with that of virtues of requirement such as justice and the sense of duty. Gratitude and justice both involve debt and obligation, but in different senses of ‘debt’ and ‘obligation.’ Certain cases of genuine gratitude in which the subject doesn’t believe the reason for his gratitude confirm the superiority of the view of emotions as concern-based construals over judgment theories. The concepts of gratitude and generosity specify, in their grammar, reasons that are internal to (definitive of) gratitude or generosity, but they can also be incited by reasons that don’t belong to their grammar, as long as such external reasons can trigger internal ones.