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.

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.

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.

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.

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.