INTRODUCTION: REASON AND THE PASSIONS i. Philosophy? This same philosophy is a good horse in the stable, but an arrant jade on a journey. ...

The Greek philosopher Aristotle, writing over two thousand years before Wall Street, called people who engaged in activities which did not contribute to society "parasites." In his latest work, renowned scholar Robert C. Solomon asserts that though capitalism may require capital, but it does not require, much less should it be defined by the parasites it inevitably attracts. Capitalism has succeeded not with brute strength or because it has made people rich, but because it has produced responsible citizens and--however (...) unevenly--prosperous communities. It cannot tolerate a conception of business that focuses solely on income and vulgarity while ignoring traditional virtues of responsibility, community, and integrity. Many feel that there is too much lip-service and not enough understanding of the importance of cooperation and integrity in corporate life. This book rejects the myths and metaphors of war-like competition that cloud business thinking and develops an "Aristotelean" theory of business. The author's approach emphasizes several core concepts: the corporation as community, the search for excellence, the importance of integrity and sound judgment, as well as a more cooperative and humane vision of business. Solomon stresses the virtues of honesty, trust, fairness, and compassion in the competitive business world, and confronts the problem of "moral mazes" and what he posits as its solution--moral courage. (shrink)

Abstract:Should the responsibilities of business managers be understood independently of the social circumstances and “market forces” that surround them, or (in accord with empiricism and the social sciences) are agents and their choices shaped by their circumstances, free only insofar as they act in accordance with antecedently established dispositions, their “character”? Virtue ethics, of which I consider myself a proponent, shares with empiricism this emphasis on character as well as an affinity with the social sciences. But recent criticisms of both (...) empiricist and virtue ethical accounts of character deny even this apparent compromise between agency and environment. Here is an account of character that emphasizes dynamic interaction both in the formation and in the interplay between personal agency and responsibility on the one hand and social pressures and the environment on the other. (shrink)

Is business ethics a contradiction in terms? Absolutely not, says Robert Solomon. In fact, he maintains that sound ethics is a necessary precondition of any long-term business enterprise, and that excellence in business must exist on the foundation of values that most of us hold dear. Drawing on twenty years of experience consulting with major corporations on ethics, Solomon clarifies the difficult ethical choices all people in business are faced with from time to time. He takes an "Aristotelian" (...) approach to ethical questions, reminding readers that a corporation--like an individual--is embedded in a community, and that corporate values such as fairness and honesty are meaningless until transformed into action. Values--coupled with action--become virtues, and virtues make possible any good business corporate relationship. Without a base of shared values, trust and mutual benefits, today's national and international business world will fall apart. In keeping with his conviction that virtue and profit must thrive together, Solomon both examines the ways in which deficient values actually destroy businesses, and debunks the pervasive myths that encourage unethical business practices. Complete with a working catalog of virtues designed to illustrate the importance of integrity in any business situation, this compelling handbook contains a goldmine of wisdom for either the small business manager or the corporate executive struggling with ethical issues. (shrink)

The Joy of Philosophy is a return to some of the perennial questions of philosophy--questions about the meaning of life; about death and tragedy; about the respective roles of rationality and passion in the good life; about love, compassion, and revenge; about honesty, deception, and betrayal; and about who we are and how we think about who we are. Recapturing the heart-felt confusion and excitement that originally brings us all to philosophy, internationally renowned teacher and lecturer Robert C. Solomon (...) offers both a critique of contemporary philosophy and an invitation to engage in philosophy in a different way. He attempts to save philosophy from itself and its self-imposed diet of thin arguments and logical analysis to recover the richness and complexity of life in thought. Solomon defends the passionate life in contrast to the life of thoughtful contemplation idealized by so many philosophers, attempting to recapture the kind of philosophy that Nietzsche celebrated as a "joyful wisdom.". (shrink)

A subtle and distinguished work by a philosopher renowned for his groundbreaking analysis of human emotions, About Love.

The Phenomenology of Spirit was Hegel's grandest experiement, changing our vision of the world and the very nature of philosophical enterprise. In this book, Solomon captures the bold and exhilarating spirit, presenting the Phenomenology as a thoroughly personal as well as philosophical work. He begins with a historical introduction, which lays the groundwork for a section-by-section analysis of the Phenomenology. Both the initiated as well as readers unacquainted with the intricacies of German idealism will find this to be an (...) accessible and exciting introduction to this great philosopher's monumental work. (shrink)

Extensive case studies, questionnaires, and problem-solving exercises make this an essential guide for business people.

Friedrich Nietzsche is one of the most popular and controversial philosophers of the last 150 years. Narcissistic, idiosyncratic, hyperbolic, irreverent--never has a philosopher been appropriated, deconstructed, and scrutinized by such a disparate array of groups, movements, and schools of thought. Adored by many for his passionate ideas and iconoclastic style, he is also vilified for his lack of rigor, apparent cruelty, and disdain for moral decency. In Living with Nietzsche, Solomon suggests that we read Nietzsche from a very different (...) point of view, as a provocative writer who means to transform the way we view our lives. This means taking Nietzsche personally. Rather than focus on the "true" Nietzsche or trying to determine "what Nietzsche really meant" by his seemingly random and often contradictory pronouncements about "the Big Questions" of philosophy, Solomon reminds us that Nietzsche is not a philosopher of abstract ideas but rather of the dazzling personal insight, the provocative challenge, the incisive personal probe. He does not try to reveal the eternal verities but he does powerfully affect his readers, goading them to see themselves in new and different ways. It is Nietzsche's compelling invitation to self-scrutiny that fascinates us, engages us, and guides us to a "rich inner life." Ultimately, Solomon argues, Nietzsche is an example as well as a promulgator of "passionate inwardness," a life distinguished by its rich passions, exquisite taste, and a sense of personal elegance and excellence. (shrink)

In this accessible and comprehensive work, Robert Solomon and Kathleen Higgins cover the entire history of philosophy--ancient, medieval, and modern, from cultures both East and West--in its broader historical and cultural contexts. Major philosophers and movements are discussed along with less well-known but interesting figures. The authors examine the early Greek, Indic, and Chinese philosophers and the mythological traditions that preceded them, as well as the great religious philosophies, including Christianity, Hinduism, Judaism, and Taoism. Easily understandable to students without (...) specialized knowledge of philosophy, A Short History of Philosophy demonstrates the relevance of philosophy to our times, illuminating the impact of the revolutions wrought by science, industry, colonialism, and sectarian warfare; the two world wars and the Holocaust; and the responses of philosophy in the schools of existentialism, postmodernism, feminism, and multiculturalism. In addition, the authors provide their own twists and interpretations of events, resulting in a broad view of the nature of philosophy as an intellectual discipline and its sometimes odd and dramatic consequences. (shrink)

Machine generated contents note: Preface; Introduction; Part I. Global Health, Definitions and Descriptions: 1. What is global health? Solly Benatar and Ross Upshur; 2. The state of global health in a radically unequal world: patterns and prospects Ron Labonte and Ted Schrecker; 3. Addressing the societal determinants of health: the key global health ethics imperative of our times Anne-Emmanuelle Birn; 4. Gender and global health: inequality and differences Lesley Doyal and Sarah Payne; 5. Heath systems and health Martin McKee; Part (...) II. Global Health Ethics, Responsibilities and Justice: Some Central Issues: 6. Is there a need for global health ethics? For and against David Hunter and Angus Dawson; 7. Justice, infectious disease and globalisation Michael Selgelid; 8. International health inequalities and global justice: toward a middle ground Norman Daniels; 9. The human right to health Jonathan Wolff; 10. Responsibility for global health? Allen Buchanan and Matt DeCamp; 11. Global health ethics: the rationale for mutual caring Solly Benatar, Abdallah Daar and Peter Singer; Part III. Analyzing Some Reasons for Poor Health: 12. Trade and health: the ethics of global rights, regulation and redistribution Meri Koivusalo; 13. Debt, structural adjustment and health Jeff Rudin and David Sanders; 14. The international arms trade and global health Salahaddin Mahmudi-Azer; 15. Allocating resources in humanitarian medicine Samia Hurst, Nathalie Mezger and Alex Mauron; 16. International aid and global health Anthony Zwi; 17. Climate change and health: risks and inequities Sharon Friel, Colin Butler and Anthony McMichael; 18. Animals, the environment and global health David Benatar; 19. The global crisis and global health Stephen Gill and Isabella Bakker; Part IV. Shaping the Future: 20. Health impact fund: how to make new medicines accessible to all Thomas Pogge; 21. Biotechnology and global health Hassan Masun, Justin Chakma and Abdallah Daar; 22. Food security and global health Lynn McIntyre and Krista Rondeau; 23. International taxation Gillian Brock; 24. Global health research: changing the agenda Tikki Pang; 25. Justice and research in developing countries Alex John London; 26. Values in global health governance Kearsley Stewart, Gerald T. Keusch and Arthur Kleinman; 27. Poverty, distance and two dimensions of ethics Jonathan Glover; 28. Teaching global health ethics James Dwyer; 29. Towards a new common sense: the need for new paradigms of global health Isabella Bakker and Stephen Gill; Index. (shrink)

Philosophers since Aristotle have explored emotion, and the study of emotion has always been essential to the love of wisdom. In recent years Anglo-American philosophers have rediscovered and placed new emphasis on this very old discipline. The view that emotions are ripe for philosophical analysis has been supported by a considerable number of excellent publications. In this volume, Robert Solomon brings together some of the best Anglo-American philosophers now writing on the philosophy of emotion, with chapters from philosophers who (...) have distinguished themselves in the field of emotion research and have interdisciplinary interests, particularly in the social and biological sciences. The reader will find a lively variety of positions on topics such as the nature of emotion, the category of "emotion," the rationality of emotions, the relationship between an emotion and its expression, the relationship between emotion, motivation, and action, the biological nature versus social construction of emotion, the role of the body in emotion, the extent of freedom and our control of emotions, the relationship between emotion and value, and the very nature and warrant of theories of emotion. In addition, this book acknowledges that it is impossible to study the emotions today without engaging with contemporary psychology and the neurosciences, and moreover engages them with zeal. Thus the essays included here should appeal to a broad spectrum of emotion researchers in the various theoretical, experimental, and clinical branches of psychology, in addition to theorists in philosophy, philosophical psychology, moral psychology, and cognitive science, the social sciences, and literary theory. (shrink)

The Phenomenology of Spirit was Hegel's grandest experiment, changing our vision of the world and the very nature of philosophical enterprise. In this book, Solomon captures the bold and exhilarating spirit, presenting the Phenomenology as a thoroughly personal as well as philosophical work. He begins with a historical introduction, which lays the groundwork for a section-by-section analysis of the Phenomenology. Both the initiated and readers unacquainted with the intricacies of German idealism will find this to be an accessible and (...) exciting introduction to this great philosopher's monumental work. (shrink)

From 1931 until late in his life (at least 1970) Godel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in his incompleteness results) and undecided set-theoretical propositions (in particular CH). As to the nature of these, Godel made a variety of suggestions, but most frequently he emphasized the route of introducing ever higher axioms of in nity. In particular, he speculated (in his 1946 Princeton remarks) that there might be (...) a uniform (though non-decidable) rationale for the choice of the latter. Despite the intense exploration of the \higher in nite" in the last 30-odd years, no single rationale of that character has emerged. Moreover, CH still remains undecided by such axioms, though they have been demonstrated to have many other interesting set-theoretical consequences. (shrink)

Philosophy has as much to do with feelings as it does with thoughts and thinking. Philosophy, accordingly, requires not only emotional sensitivity but an understanding of the emotions, not as curious but marginal psychological phenomena but as the very substance of life. In this, the second book in a series devoted to his work on the emotions, Robert Solomon presents a defense of the emotions and of sentimentality against the background of what he perceives as a long history of (...) abuse in philosophy and social thought and art and literary criticism. The title piece reopens a classic debate about the role of sentimentality in art and literature. In subsequent chapters, Solomon discusses not only such "moral sentiments" as sympathy and compassion but also grief, gratitude, love, horror, and even vengeance. He also defends, with appropriate caution, the "seven deadly sins." The emotions, at least some emotions--are essential to a well-lived life. They are or can be virtues, features of the human condition without which civilized life would be unimaginable. (shrink)

The flowering of creative and speculative philosophy that emerged in modern Europe--particularly in Germany--is a thrilling adventure story as well as an essential chapter in the history of philosophy. In this integrative narrative, Solomon provides an accessible introduction to the major authors and movements of modern European philosophy, including the Enlightenment and Romanticism, Rousseau, German Idealism, Kant, Fichte, Schelling and the Romantics, Hegel, Schopenhauer, Kierkegaard, Feuerbach, Max Brentano, Meinong, Frege, Dilthey, Bergson, Nietzsche, Husserl, Freud, Wittgenstein, Heidegger, hermeneutics, Sartre, Postmodernism, (...) Structuralism, Foucault, and Derrida. (shrink)

Albert Camus and Jean-Paul Sartre were the giants of 20th-century “existentialism”, although neither of them was comfortable with that title. Their famous differences aside, they shared a “phenomenological” sensibility and described personal experience in exquisite and excruciating detail and reflected on the meaning of this experience with both sensitivity and insight. That is the focus of this book: Camus and Sartre, their descriptions of personal experience, and their reflections on the meaning of this experience. They also reflected, worriedly, on the (...) nature of reflection. The thematic problem of the book is the relationship between experience and reflection. The book explores this relationship through novels and plays, Camus’ The Stranger, The Plague, and The Fall, Sartre’s Nausea and No Exit, and Sartre’s great philosophical tome, Being and Nothingness. (shrink)

Is it possible to be spiritual and yet not believe in the supernatural? Can a person be spiritual without belonging to a religious group or organization? In Spirituality for the Skeptic, philosopher Robert Solomon explores what it means to be spiritual in today's pluralistic world. Based on Solomon's own struggles to reconcile philosophy with religion, this book offers a model of a vibrant, fulfilling spirituality that embraces the complexities of human existence and acknowledges the joys and tragedies of (...) life. Solomon has forged an enlightened new path that synthesizes spirituality with emotions, intellect, science, and common sense. His new paradigm, "naturalized" spirituality, establishes as its cornerstone the "thoughtful love of life"--a passionate concern for the here-and-now, and not the by-and-by. Being spiritual doesn't mean being holed up as a recluse, spending hours in meditation and contemplation, Solomon argues. It demands involvement and emotional engagement with others in the struggle to find meaning in our lives. As such, this modern-day spirituality encompasses a passionate enthusiasm for the world, the transformation of self, cosmic trust and rationality, coming to terms with fate, and viewing life as a gift, all of which are explored in depth throughout this book. Spirituality for the Skeptic answers the need for a non-institutional, non-dogmatic spirituality that leads to personal fulfillment and satisfaction. By examining the ideas of great thinkers from Socrates and Nietzsche to Buddha to Kafka, Solomon arrives at a practical vision of spirituality that should appeal to many seekers looking to make sense of the human condition. (shrink)

I had the pleasure of renewing my acquaintance with Per Lindström at the meeting of the Seventh Scandinavian Logic Symposium, held in Uppsala in August 1996. There at lunch one day, Per said he had long been curious about the development of some of the ideas in my paper [1960] on the arithmetization of metamathematics. In particular, I had used the construction of a non-standard definition !* of the set of axioms of P (Peano Arithmetic) to show that P + (...) {¬ Con!} is interpretable in P, where ! is a standard definition of the axioms of P and Con! expresses the consistency of P via that presentation. Per pointed out that there is a simple “two-line” proof of this interpretability result which does not require the use of such formulas as !*, and he wondered whether I had been aware of that. In fact, his proof had never occurred to me, and if it had at the time, it is possible I would never have been led to the use of non-natural definitions. Per regarded this as a happy accident, since subsequent work by him and others on interpretability made essential use of such definitions. In our conversation, I enlarged a bit on the background to my work on arithmetization, and when I was invited to contribute to this special issue of Theoria dedicated to Lindström, it seemed a natural choice to use the occasion to fill out the story. One caveat, though: the following is drawn largely from memory, not always reliable, supplemented by consultation of the 1960 paper and the 1957 dissertation from which it was drawn. (shrink)

Robert Solomon, widely recognized as a leading authority of continental philosophy and respected as a philosopher in his own right, here brings together twelve of his published articles focusing on key issues in the writings of major continental philosophers including Hegel, Nietzsche, Kierkegaard, Sartre, and Camus. The essays not only shed light on the thought and interrelations of these writers, but also develop a set of provocative and forcefully argued original theses, and encapsulate some of the central ideas of (...) Solomon's most important books. (shrink)

This volume draws together important selections from the rich history of theories and debates about emotion. Utilizing sources from a variety of subject areas including philosophy, psychology, and biology, the editors provide an illuminating look at the "affective" side of psychology and philosophy from the perspective of the world's great thinkers. Part One features classic readings from Aristotle, Descartes, Spinoza, and Hume. Part Two, entitled "The Meeting of Philosophy and Psychology," samples the theories of thinkers such as Darwin, James, and (...) Freud. The third section presents some of the extensive work on emotion that has been done by European philosophers over the past century, and the final section comprises essays from modern British and American philosophers. (shrink)

In this enduring text, renowned philosopher Robert C. Solomon provides students with a detailed introduction to modern existentialism.

Introduction -- What is ethics? -- Ethics and religion -- The history of ethics -- Ethical questions -- What is the good life? -- Why be good : the problem of justification -- Why be rational : the place of reason in ethics -- Which is right : ethical dilemmas -- Ethical concepts -- Universality -- Prudence and morals -- Happiness and the good -- Egoism and altruism -- Virtue and the virtues -- Facts and values -- Justice and equality (...) -- Rights and duties -- Ethical theories and approaches -- Teleology -- Utilitarianism -- Kant and deontology -- Social contract theory -- Ethical relativism -- Pluralism and history -- Feminist ethics -- Prologue : ethics and religion -- The Hebrew Bible -- The Ten commandments -- The New Testament -- The Qur'an -- Ancient Asia -- India : Hinduism and Buddhism -- Buddhism -- China : Confucianism and Taoism -- China : Taoism -- Plato -- Aristotle -- Epicurus -- Augustine -- Thomas Hobbes -- David Hume -- Immanuel Kant -- Mary Wollstonecraft -- John Stuart Mill -- Friedrich Nietzsche -- John Rawls. (shrink)

Reviews the book, Upheavals of thought: The intelligence of emotions by Martha C. Nussbaum . Drawing from an astounding array of sources, Nussbaum argues against the common understanding of emotions as irrational and animalistic impulses disconnected from our thoughts and reason. Rather, she argues that emotions are highly discriminating responses to what is of value and importance that are, therefore, suffused with intelligence and discernment. Nussbaum explores the structure of a wide range of emotions, in particular, compassion and love, in (...) order to show that there can be no adequate ethical theory without an adequate theory of emotional experience and meaning. 2012 APA, all rights reserved). (shrink)

Philosophy is an exciting and accessible subject, and this engaging text acquaints students with the core problems of philosophy and the many ways in which they are and have been answered. Introducing Philosophy: A Text with Integrated Readings, Eighth Edition, insists both that philosophy is very much alive today and that it is deeply rooted in the past. Accordingly, it combines substantial original sources from significant works in the history of philosophy and current philosophy with detailed commentary and explanation that (...) help to clarify the readings. The selections range from the oldest known fragments to cutting-edge essays in feminism, multiculturalism, and cognitive science. At the end of each chapter is a summary, a list of review questions, a glossary, and a bibliography with suggestions for further reading. Important philosophical terms are carefully introduced in the text and also summarized at the end of each chapter, and brief biographies of the philosophers are provided at the end of the book. New to the Eighth Edition: Addressing the needs of a new generation of students, Robert C. Solomon has included for the first time more than 300 study and review questions. Appearing throughout the text and at the end of each chapter, these questions require immediate feedback from students. They encourage students to articulate the central ideas of what they have just read, instead of just "passing through" on the way to the next reading . New selections expand and update the chapters on religion, knowledge, mind and body, freedom, ethics, justice, and beauty. The selections include work by Charles Hartshorne, Cory Juhl, Friedrich Nietzsche, Jean-Paul Sartre, Sextus Empiricus, Edmund L. Gettier, David Braddon-Mitchell and Frank Jackson, Colin McGinn, Daniel Dennett, Harry Frankfurt, Gilbert Harman, Emma Goldman, and Arthur C. Danto. A companion website at www.oup.com/us/solomon8e features 300 study and review questions (100 multiple-choice, 100 true-or-false, and 100 fill-in-the-blank), discussion questions, chapter overviews and summaries, topical links, suggestions for further reading, and PowerPoint lecture aids. (shrink)

The social scientist is now applying his knowledge and skills in various fields. But in the American trade-union movement he faces unusual problems. His challenges are essentially those of determining how to serve, and how to implant a belief in the value of his findings and reports. There is no widespread acceptance of the conclusion that he can make a real contribution. He is still not considered necessary or likely to be useful in the routine operation of the union or (...) in the development of its policy and tactics. Progress has been made during the last few years in securing his admission to the staff of unions. But much pioneering work has still to be done to obtain frank acknowledgment of his potential usefulness and free acceptance of his experimental, inquiring and critical approaches. (shrink)

This book brings together several directions of work in model theory between the late 1950s and early 1980s.

In 1958, G¨ odel published in the journal Dialectica an interpretation of intuitionistic number theory in a quantifier-free theory of functionals of finite type; this subsequently came to be known as G¨ odel’s functional or Dialectica interpretation. The article itself was written in German for an issue of that journal in honor of Paul Bernays’ 70th birthday. In 1965, Bernays told G¨.

The belief amongst some Christians that it is God’s plan for everyone to have children, and that barrenness is a punishment from God is apparently derived from the Old Testament. This article attempts a holistic study of the biblical perspectives on childlessness with a view to ascertain whether procreation is a moral responsibility of every individual. The target group includes Nigerian Christian couples suffering from infertility. The article employs the descriptive and exegetical methods. The study revealed that the belief that (...) the OT views barrenness as caused by sin and a punishment from God was erroneous. A critical examination of the relevant texts revealed that infertility is a natural phenomenon, and God gives children as a blessing but not necessarily to every individual. In the New Testament, the attitude towards childlessness is characterised by the concept of ‘alternative family models’, by which some Christians could adopt children whilst others might choose to be celibate, being satisfied with their membership of the community of believers. Paul’s teaching in 1 Corinthians 7 clearly mitigates natural childbearing, and thus negates any attitude of desperation for bearing children. In the Nigerian context, this interpretation necessitates a change of attitude towards infertility. The church has to develop a theological reconstruction with regard to procreation in marriage, in a manner that will assure Christians that a childless marriage is not lacking in any way.Contribution: The article is a contribution in the area of theology of marriage, and thus of high relevance in contemporary Africa, particularly Nigeria, where people, including Christians, still have the traditional belief that it is morally mandatory for everyone to have biological children. (shrink)

We study theorems of ordered groups from the perspective of reverse mathematics. We show that suffices to prove Hölder's Theorem and give equivalences of both (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure).

Interest in the ethics of research on human subjects, stimulated by atrocious human experimentation during WWII and the resultant Nuremberg Code, has been sustained by examples of unethical research in many countries and by proliferation of codes and guidelines. Such interest has intensified in recent years in association with expanding international collaborative research endeavors. The ongoing controversy in international research ethics takes place at two levels. At the practical level it is about the competing concerns of those predominantly interested in (...) doing research to advance knowledge and those who, while supporting the need for research, are more acutely aware of the potential to exploit vulnerable participants, especially in developing countries. At the level of theory the controversy pits ethical universalism against moral relativism.In her recent review of agreements and controversies in international research ethics, Ruth Macklin has concluded that, despite seeming agreement on several issues, many different viewpoints persist. In her view it is unlikely that these will be resolved easily. (shrink)

Interest in the ethics of research on human subjects, stimulated by atrocious human experimentation during WWII and the resultant Nuremberg Code, has been sustained by examples of unethical research in many countries and by proliferation of codes and guidelines. Such interest has intensified in recent years in association with expanding international collaborative research endeavors. The ongoing controversy in international research ethics takes place at two levels. At the practical level it is about the competing concerns of those predominantly interested in (...) doing research to advance knowledge and those who, while supporting the need for research, are more acutely aware of the potential to exploit vulnerable participants, especially in developing countries. At the level of theory the controversy pits ethical universalism against moral relativism.In her recent review of agreements and controversies in international research ethics, Ruth Macklin has concluded that, despite seeming agreement on several issues, many different viewpoints persist. In her view it is unlikely that these will be resolved easily. (shrink)

The background to the development of proof theory since 1960 is contained in the article (MATHEMATICS, FOUNDATIONS OF), Vol. 5, pp. 208- 209. Brie y, Hilbert's program (H.P.), inaugurated in the 1920s, aimed to secure the foundations of mathematics by giving nitary consistency proofs of formal systems such as for number theory, analysis and set theory, in which informal mathematics can be represented directly. These systems are based on classical logic and implicitly or explicitly depend on the assumption of \completed (...) in nite" totalities. Consistency of a system S (containing a modicum of elementary number theory) is su cient to ensure that any nitary meaningful statement about the natural numbers which is provable in S is correct under the intended interpretation. Thus, in Hilbert's view, consistency of S would serve to eliminate the \completed in nite" in favor of the \potential in nite" and thus secure the body of mathematics represented in S. Hilbert established the subject of proof theory as a technical part of mathematical logic by means of which his program was to be carried out its methods will be described below. In 1931, Godel's second incompleteness theorem raised a prima facieobstacle to H.P. for the system Z of elementary number theory (also called Peano Arithmetic, and denoted below by PA) since all previously recognized forms of nitary reasoning could be formalized within it. In any case, Hilbert's program could not possibly succeed for any system such as set theory in which all nitary notions and reasoning could unquestionably be formalized. These obstacles led workers in proof theory to modify H.P. in two kinds of ways. The rst was to seek reductions of various formal systems S to more constructive systems S 0. The second was to shift the aims from foundational ones to more mathematical ones. Examples of 1 the former move are the reductions of PA to intuitionistic arithmetic HA, and Gentzen's consistency proof of PA by nitary reasoning coupled with quanti er-free trans nite induction up to the ordinal , TI( 0), both obtained in the 1930s (cf.. (shrink)

In his 1918 monograph \Das Kontinuum", Hermann Weyl initiated a program for the arithmetical foundations of mathematics. In the years following, this was overshadowed by the foundational schemes of Hilbert's nitary consistency program and Brouwer's intuitionistic redevelopment of mathematics. In fact, not long after his own venture, Weyl became a convert to Brouwerian intuitionism and criticized his old teacher's program. Over the years, though, he became more and more pessimistic about the practical possibilities of reworking mathematics along intuitionistic lines, and (...) pointed to the value of his own early foundational e orts. Weyl 's work in Das Kontinuum has come to be recognized for its importance as the opening chapter in the actual development of predicative mathematics, whose extent has been plumbed both mathematically and logically since the 1960s. (shrink)