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What Is Mathematics?: An Elementary Approach to Ideas and Methods

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

Multilevel Synthesis: From the Group to the Individual (The Springer Series on Demographic Methods and Population Analysis #18)

This book presents a historical panorama of the evolution of demographic thought from its eighteenth-century origins up to the present day. The book uses this to demonstrate how the multilevel approach can resolve some of the contradictions that have become apparent and achieve a synthesis of the different approaches employed. This is both a textbook and an assessment of the multilevel analysis that broadens the scope of demography with its approach.

The Reform of the International System of Units: Philosophical, Historical and Sociological Issues (History and Philosophy of Technoscience)

Systems of units still fail to attract the philosophical attention they deserve, but this could change with the current reform of the International System of Units (SI). Most of the SI base units will henceforth be based on certain laws of nature and a choice of fundamental constants whose values will be frozen. The theoretical, experimental and institutional work required to implement the reform highlights the entanglement of scientific, technological and social features in scientific enterprise, while it also invites a philosophical inquiry that promises to overcome the tensions that have long obstructed science studies.

The Reform of the International System of Units: Philosophical, Historical and Sociological Issues (History and Philosophy of Technoscience)

Systems of units still fail to attract the philosophical attention they deserve, but this could change with the current reform of the International System of Units (SI). Most of the SI base units will henceforth be based on certain laws of nature and a choice of fundamental constants whose values will be frozen. The theoretical, experimental and institutional work required to implement the reform highlights the entanglement of scientific, technological and social features in scientific enterprise, while it also invites a philosophical inquiry that promises to overcome the tensions that have long obstructed science studies.

Hobbesian Applied Ethics and Public Policy (Routledge Research in Applied Ethics)

Most philosophers and political scientists readily admit that Thomas Hobbes is a significant figure in the history of political thought. His theory was, arguably, one of the first to provide a justification for political legitimacy from the perspective of each individual subject. Many excellent books and articles have examined the justification and structure of Hobbes’ commonwealth, ethical system, and interpretation of Christianity. What is troubling is that the Hobbesian project has been largely missing in the applied ethics and public policy literature. We often find applications of Kantian deontology, Bentham’s or Mill’s utilitarianism, Rawls’s contractualism, the ethics of care, and various iterations of virtue ethics. Hobbesian accounts are routinely ignored and often derided. This is unfortunate because Hobbes’s project offers a unique perspective. To ignore it, when such a perspective would be fruitful to apply to another set of theoretical questions, is a problem in need of a remedy. This volume seeks to eliminate (or, at the very least, partially fill) this gap in the literature. Not only will this volume appeal to those that are generally familiar with Hobbesian scholarship, it will also appeal to a variety of readers that are largely unfamiliar with Hobbes.

Hobbesian Applied Ethics and Public Policy (Routledge Research in Applied Ethics)

Most philosophers and political scientists readily admit that Thomas Hobbes is a significant figure in the history of political thought. His theory was, arguably, one of the first to provide a justification for political legitimacy from the perspective of each individual subject. Many excellent books and articles have examined the justification and structure of Hobbes’ commonwealth, ethical system, and interpretation of Christianity. What is troubling is that the Hobbesian project has been largely missing in the applied ethics and public policy literature. We often find applications of Kantian deontology, Bentham’s or Mill’s utilitarianism, Rawls’s contractualism, the ethics of care, and various iterations of virtue ethics. Hobbesian accounts are routinely ignored and often derided. This is unfortunate because Hobbes’s project offers a unique perspective. To ignore it, when such a perspective would be fruitful to apply to another set of theoretical questions, is a problem in need of a remedy. This volume seeks to eliminate (or, at the very least, partially fill) this gap in the literature. Not only will this volume appeal to those that are generally familiar with Hobbesian scholarship, it will also appeal to a variety of readers that are largely unfamiliar with Hobbes.

Tetens’s Writings on Method, Language, and Anthropology (Bloomsbury Studies in Modern German Philosophy)

Containing all of the key writings leading up to the publication of his Philosophical Essays in 1777, this volume presents complete works by Johann Nicolaus Tetens (1736-1807) in English for the very first time. These important essays focus on method in metaphysics and mathematics, the analysis of language, and various anthropological questions that occupied thinkers of the period. Key features of the volume include: · Accurate, readable translations · Detailed scholarly notes · A substantial introduction situating Tetens's works in historical context · A German-English glossaryThis collection marks a significant contribution to scholarship on Kant and 18th-century German philosophy.

Elite Schooling and Social Inequality: Privilege and Power in Ireland's Top Private Schools

This book is the first significant sociological study of Ireland’s elite private schools. It takes the reader behind the gates of these secretive institutions, and offers a compelling analysis of their role in the reproduction of social inequality in Ireland. From the selection process to past pupils’ union events, from the dorms to the rugby pitch, the book unravels how these schools gradually reinforce exclusionary practices and socialize their students to power and privilege. It tackles the myths of meritocracy and classlessness in Ireland, while also providing keys to understanding the social practices and legitimacy of elites. By bringing out the voices of past pupils, parents and school staff and incorporating vivid ethnographic descriptions, the book provides a rare snapshot into a privileged world largely hidden from view. It offers a unique contribution to research on elite education as well as to the broader fields of sociology of education and inequality. As such, it will appeal to researchers, practitioners and the general public alike, in Ireland and beyond.

Sceptics of Islam: Revisionist Religion, Agnosticism and Disbelief in the Modern Arab World (Library of Modern Middle East Studies #20180226)

Arab debates about the critical relationship between religion and modernity began in the early nineteenth century. Such debates are now integral to the struggle for power between a variety of political groups and their opponents, and are vital to understanding the modern Middle East. This unique volume introduces the writings of the Muslim and Arab Christian revisionist 'free-thinkers' who have tried to redefine the relationship. It challenges the deeply entrenched idea that the contemporary Islamic world has been impermeable to a critique of religious ideas and practices. Authors from the nineteenth century to the present are included. Some are avowed believers, even if they adopt positions many might regard as heretical; others are openly agnostic and atheistic. Despite their differences, all have been united in disputing the fundamentalist idea that life should conform to a system of values and law based on the Quran. They have also rejected the religious 'liberalism' that has been the chief opposition to traditionalism. The book's originality lies in its evaluation of the social and cultural impact of these radical thinkers.

Trans Feminist Epistemologies in the US Second Wave (Breaking Feminist Waves)

Why do “second wave” and “trans feminism” rarely get considered together? Challenging the idea that trans feminism is antagonistic to, or arrived after, second wave feminism, Emily Cousens re-orients trans epistemologies as crucial sites of second wave feminist theorising. By revisiting the contributions of trans individuals writing in underground print publications, as well as the more well-known arguments of Andrea Dworkin, this book demonstrates that valuable yet overlooked trans feminist philosophies of sex and gender were present throughout the US second wave. It argues that not only were these trans feminist epistemologies an important component of second wave feminism's knowledge production, but that this period has an unacknowledged trans feminist legacy.

Static Analysis: 8th International Symposium, SAS 2001, Paris, France, July 16-18, 2001. Proceedings (Lecture Notes in Computer Science #2126)

Static Analysis: 10th International Symposium, SAS 2003, San Diego, CA, USA, June 11-13, 2003. Proceedings (Lecture Notes in Computer Science #2694)

The refereed proceedings of the 10th International Symposium on Static Analysis, SAS 2003, held in San Diego, CA, USA in June 2003 as part of FCRC 2003. The 25 revised full papers presented together with two invited contributions were carefully reviewed and selected from 82 submissions. The papers are organized in topical sections on static analysis of object-oriented languages, static analysis of concurrent languages, static analysis of functional languages, static analysis of procedural languages, static data analysis, static linear relation analysis, static analysis based program transformation, and static heap analysis.

Static Analysis: 17th International Symposium, SAS 2010, Perpignan, France, September 14-16, 2010, Proceedings (Lecture Notes in Computer Science #6337)

Sloterdijk (Key Contemporary Thinkers)

This is the first English-language introduction to Peter Sloterdijk, the distinguished German philosopher and controversial public intellectual. Sloterdijk, in the tradition of Nietzsche and Heine, is an iconoclast who uses humour and biting critique to challenge many of modernity's sacred thinkers, from Kant to Heidegger, in the process radically reinterpreting the canon of Western philosophy. In this unique textbook, leading Sloterdijk expert Jean-Pierre Couture explains in accessible language Sloterdijk's exceptional contribution, breaking his thought down into five key approaches: psychopolitics, anthropotechnics, spherology, controversy, and therapeutics. Sloterdijk's frequent public controversies, with supporters of Habermas and the Frankfurt school in particular, are assessed and their significance for current philosophical debates explained. This fascinating book will be an essential companion for those interested in the hybrid aesthetics of thought situated at the crossroads of art and philosophy. Its up-to-date analyses of Sloterdijk's recently translated corpus will make it essential reading for all students and scholars of modern European thought.

Sloterdijk (Key Contemporary Thinkers)

This is the first English-language introduction to Peter Sloterdijk, the distinguished German philosopher and controversial public intellectual. Sloterdijk, in the tradition of Nietzsche and Heine, is an iconoclast who uses humour and biting critique to challenge many of modernity's sacred thinkers, from Kant to Heidegger, in the process radically reinterpreting the canon of Western philosophy. In this unique textbook, leading Sloterdijk expert Jean-Pierre Couture explains in accessible language Sloterdijk's exceptional contribution, breaking his thought down into five key approaches: psychopolitics, anthropotechnics, spherology, controversy, and therapeutics. Sloterdijk's frequent public controversies, with supporters of Habermas and the Frankfurt school in particular, are assessed and their significance for current philosophical debates explained. This fascinating book will be an essential companion for those interested in the hybrid aesthetics of thought situated at the crossroads of art and philosophy. Its up-to-date analyses of Sloterdijk's recently translated corpus will make it essential reading for all students and scholars of modern European thought.

The Philosophy of Science: Science and Objectivity

This comprehensive textbook provides a clear nontechnical introduction to the philosophy of science. Through asking whether science can provide us with objective knowledge of the world, the book provides a thorough and accessible guide to the key thinkers and debates that define the field. George Couvalis surveys traditional themes around theory and observation, induction, probability, falsification and rationality as well as more recent challenges to objectivity including relativistic, feminist and sociological readings. This provides a helpful framework in which to locate the key intellectual contributions to these debates, ranging from those of Mill and Hume, through Popper and Kuhn to Laudan, Bloor and Garfinkel among others.

The Philosophy of Science: Science and Objectivity (PDF)

This comprehensive textbook provides a clear nontechnical introduction to the philosophy of science. Through asking whether science can provide us with objective knowledge of the world, the book provides a thorough and accessible guide to the key thinkers and debates that define the field. George Couvalis surveys traditional themes around theory and observation, induction, probability, falsification and rationality as well as more recent challenges to objectivity including relativistic, feminist and sociological readings. This provides a helpful framework in which to locate the key intellectual contributions to these debates, ranging from those of Mill and Hume, through Popper and Kuhn to Laudan, Bloor and Garfinkel among others.

Advances in Experimental Philosophy of Aesthetics (Advances in Experimental Philosophy)

Experimental philosophy has blossomed into a variety of philosophical fields including ethics, epistemology, metaphysics and philosophy of language. But there has been very little experimental philosophical research in the domain of philosophical aesthetics. Advances to Experimental Philosophy of Aesthetics introduces this burgeoning research field, presenting it both in its unity and diversity, and determining the nature and methods of an experimental philosophy of aesthetics. Addressing a wide variety of empirical claims that are of interest to philosophers and psychologists, a team of authors from different disciplines tackle traditional and new problems in aesthetics, including the nature of aesthetic properties and norms, the possibility of aesthetic testimony, the role of emotions and moral judgment in art appreciation, the link between art and language, and the role of intuitions in philosophical aesthetics.Interacting with other disciplines such as moral psychology and linguistics, it demonstrates how philosophical aesthetics can integrate empirical methods and discover new ways of approaching core problems. Advances to Experimental Philosophy of Aesthetics is an important contribution to understanding aesthetics in the 21st century.

Advances in Experimental Philosophy of Aesthetics (Advances in Experimental Philosophy)

Experimental philosophy has blossomed into a variety of philosophical fields including ethics, epistemology, metaphysics and philosophy of language. But there has been very little experimental philosophical research in the domain of philosophical aesthetics. Advances to Experimental Philosophy of Aesthetics introduces this burgeoning research field, presenting it both in its unity and diversity, and determining the nature and methods of an experimental philosophy of aesthetics. Addressing a wide variety of empirical claims that are of interest to philosophers and psychologists, a team of authors from different disciplines tackle traditional and new problems in aesthetics, including the nature of aesthetic properties and norms, the possibility of aesthetic testimony, the role of emotions and moral judgment in art appreciation, the link between art and language, and the role of intuitions in philosophical aesthetics.Interacting with other disciplines such as moral psychology and linguistics, it demonstrates how philosophical aesthetics can integrate empirical methods and discover new ways of approaching core problems. Advances to Experimental Philosophy of Aesthetics is an important contribution to understanding aesthetics in the 21st century.

Agency in Action: The Practical Rational Agency Machine (Studies in Cognitive Systems #11)

This series will include monographs and collections of studies devoted to the investigation and exploration of knowledge, information, and data-processing systems of all kinds, no matter whether human, (other) animal, or machine. Its scope is intended to span the full range of interests from classical problems in the philosophy of mind and philosophical psychology through issues in cognitive psychology and sociobiology (concerning the mental capabilities of other species) to ideas related to artificial intelligence and to computer science. While primary emphasis will be placed upon theoretical, conceptual, and epistemological aspects of these problems and domains, empirical, experimental, and methodological studies will also appear from time to time. Sam Coval and Peter Campbell provide a painstaking and distinctive analysis of the nature of action and agency. They introduce a conception of acts which encompasses the purposes that motivate them, the beliefs on the basis of which they are undertaken, and the effects that they bring about. They compare and contrast their account with ones advanced by Davidson, Brand, Searle, Danto, and other, while elaborating its consequences for understanding the nature of alibis, mistakes, accidents, inadvertence, and the like. The valuable diagrams and the discussion of the software program they have developed, which implements their theory, amply displays the potential of combining philosophy and AI with law and other disciplines focused upon agency. J.H.F.

Scepticism and the First Person (Routledge Library Editions: Epistemology)

Originally published in 1966. This book considers the perceived asymmetries between the self and others, or between self and things. An in-depth analysis of scepticism, dualism, belief, knowledge and semantics. A topic which is central to both epistemology but also the whole of contemporary philosophy.

Scepticism and the First Person (Routledge Library Editions: Epistemology)

Originally published in 1966. This book considers the perceived asymmetries between the self and others, or between self and things. An in-depth analysis of scepticism, dualism, belief, knowledge and semantics. A topic which is central to both epistemology but also the whole of contemporary philosophy.

Hobbes, Realism and the Tradition of International Law

Charles Covell considers the poltical thought of Thomas Hobbes in relation to the tradition of international law, and with the intention to challenge the reading of Hobbes as the exponent of the realist standpoint in international thought and practice. The relation of Hobbes to international law is explained through attention to the place that he occupies among the modern secular natural law thinkers, such as Grotius, Pufendorf, Wolff and Vattel, who founded the modern system of the law of nations.

Kant and the Law of Peace: A Study in the Philosophy of International Law and International Relations

Kant and the Law of Peace is a critical examination of the jurisprudential aspects of Kant's international thought, with reference to the argument of his treatise Perpetual Peace (1795). Kant's international thought is situated in the wider context of his moral and political philosophy. Particular attention is given to explaining how Kant saw law as providing the basis for peace among men and states in the international sphere, and how, in his exposition of the elements of the law of peace, he broke with the secular natural law tradition of Grotius, Hobbes, Wolff and Vattel.

The Law of Nations in Political Thought: A Critical Survey from Vitoria to Hegel

Charles Covell examines the law of nations encountered in the work of major political thinkers from Vitoria to Hegel. He explains how these thinkers contributed to the current theories of natural law and just war and how they played a key role in the elaboration of the principles which are central to the modern system of the law of nations.