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Philosophy in the twentieth century has been dominated by the urge for analysis, a methodology that is supposed to be comparable in clarity and correctness to scientific thought. In this brilliant and devastating attack on such exaggerated claims, Stanley Rosen demonstrates how analysis alone lacks the power to approach the deepest and most important philosophical questions. He thus provides us with a new and deeper understanding of the nature and limits of analytic thinking.
The tension between what we wish for and what we can get, between values and opportunities, exists even at the purely individual level. A hermit on a mountain may value warm clothing and yet be hard-pressed to make it from the leaves, bark, or skins he can find. But when many people are competing with each other for satisfaction of their wants, learning how to exploit what is available becomes more difficult. In this volume, Nobel Laureate Kenneth J. Arrow analyzes why - and how - human beings organize their common lives to overcome the basic economic problem: the allocation of scarce resources. The price system is one means of organizing society to mediate competition, and Arrow analyzes its successes and failures. Alternative modes of achieving efficient allocation of resources are explored: government, the internal organization of the firm, and the 'invisible institutions' of ethical and moral principles. Professor Arrow shows how these systems create channels to make decisions, and discusses the costs of information acquisition and retrieval. He investigates the factors determining which potential decision variables are recognized as such. Finally, he argues that organizations must achieve some balance between the power of the decision makers and their obligation to those who carry out their decisions - between authority and responsibility.
Details methods for computing valid limits of detection. Clearly explains analytical detection limit theory, thereby mitigating incorrect detection limit concepts, methodologies and results Extensive use of computer simulations that are freely available to readers Curated short-list of important references for limits of detection Videos, screencasts, and animations are provided at an associated website, to enhance understanding Illustrated, with many detailed examples and cogent explanations
Intended as an undergraduate text on real analysis, this book includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a novel approach to the subject matter, which has not previously appeared in book form. The author defines the term limit once only, and all of the subsequent limiting processes are seen to be special cases of this one definition. Accordingly, the subject matter attains a unity and coherence that is not to be found in the traditional approach. Students will be able to fully appreciate and understand the common source of the topics they are studying while also realising that they are "variations on a theme", rather than essentially different topics, and therefore, will gain a better understanding of the subject.
Tim Button explores the relationship between minds, words, and world. He argues that the two main strands of scepticism are deeply related and can be overcome, but that there is a limit to how much we can show. We must position ourselves somewhere between internal realism and external realism, and we cannot hope to say exactly where.
“The Limits to Growth” (Meadows, 1972) generated unprecedented controversy with its predictions of the eventual collapse of the world's economies. First hailed as a great advance in science, “The Limits to Growth” was subsequently rejected and demonized. However, with many national economies now at risk and global peak oil apparently a reality, the methods, scenarios, and predictions of “The Limits to Growth” are in great need of reappraisal. In The Limits to Growth Revisited, Ugo Bardi examines both the science and the polemics surrounding this work, and in particular the reactions of economists that marginalized its methods and conclusions for more than 30 years. “The Limits to Growth” was a milestone in attempts to model the future of our society, and it is vital today for both scientists and policy makers to understand its scientific basis, current relevance, and the social and political mechanisms that led to its rejection. Bardi also addresses the all-important question of whether the methods and approaches of “The Limits to Growth” can contribute to an understanding of what happened to the global economy in the Great Recession and where we are headed from there.
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.
Reflecting upon some problems of the moral life, Gilbert Meilaender considers their difficulties within a vision that accentuates not only the limits, but also the promise, of the Christian story. Created by God as finite beings, we make particular attachments. Redeemed by God for a community transcending nature and history, our love always carries us beyond the special bonds of time and place. We live, therefore, with a sense of permanent tension. If this tension heightens our sense of the perplexities of life, it should not free us from the obligation to probe, clarify, and (where we can) resolve some of those difficulties. The author holds that theological ethics must clarify the direction for growth and development within the Christian life. He undertakes such analysis, emphasizing throughout the limits of the human condition, the importance of our nature as embodied persons, and the danger and pretension in some of our attempts to take control of and master human life. This Christian vision is developed in chapters that explore a range of moral problems, such as abortion, artificial reproduction, euthanasia, care for defective infants, provision of artificial nutrition and hydration, and marital and political community. These are throughout, however, theological explorations. Taken together they illumine not only particular problems of the moral life but a vision of life--classically Christian in its conception, humane in its care for particular bonds of attachment, and modest in its recognition of moral limits on our ability to seek the good. Meilaender has developed a broad recognition both among scholars and students of ethics and among interested general readers. He has the capacity to throw fresh angles of vision on complex problems so as to help both the sophisticated and the uninitiated reader to think more penetratingly about moral questions.
This book features challenging problems of classical analysis that invite the reader to explore a host of strategies and tools used for solving problems of modern topics in real analysis. This volume offers an unusual collection of problems — many of them original — specializing in three topics of mathematical analysis: limits, series, and fractional part integrals. The work is divided into three parts, each containing a chapter dealing with a particular problem type as well as a very short section of hints to select problems. The first chapter collects problems on limits of special sequences and Riemann integrals; the second chapter focuses on the calculation of fractional part integrals with a special section called ‘Quickies’ which contains problems that have had unexpected succinct solutions. The final chapter offers the reader an assortment of problems with a flavor towards the computational aspects of infinite series and special products, many of which are new to the literature. Each chapter contains a section of difficult problems which are motivated by other problems in the book. These ‘Open Problems’ may be considered research projects for students who are studying advanced calculus, and which are intended to stimulate creativity and the discovery of new and original methods for proving known results and establishing new ones. This stimulating collection of problems is intended for undergraduate students with a strong background in analysis; graduate students in mathematics, physics, and engineering; researchers; and anyone who works on topics at the crossroad between pure and applied mathematics. Moreover, the level of problems is appropriate for students involved in the Putnam competition and other high level mathematical contests.