Machine generated contents note: Part I. General: 1. The Gödel editorial project: a synopsis Solomon Feferman; 2. Future tasks for Gödel scholars John W. Dawson, Jr., and Cheryl A. Dawson; Part II. Proof Theory: 3. Kurt Gödel and the metamathematical tradition Jeremy Avigad; 4. Only two letters: the correspondence between Herbrand and Gödel Wilfried Sieg; 5. Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counter-example interpretation W. W. Tait; 6. Gödel on intuition and on Hilbert's finitism W. (...) W. Tait; 7. The Gödel hierarchy and reverse mathematics Stephen G. Simpson ; 8. On the outside looking in: a caution about conservativeness John P. Burgess; Part III. Set Theory: 9. Gödel and set theory Akihiro Kanamori; 10. Generalizations of Gödel's universe of constructible sets Sy-David Friedman; 11. On the question of absolute undecidability Peter Koellner; Part IV. Philosophy of Mathematics: 12. What did Gödel believe and when did he believe it? Martin Davis; 13. On Gödel's way in: the influence of Rudolf Carnap Warren Goldfarb; 14. Gödel and Carnap Steve Awodey and A. W. Carus; 15. On the philosophical development of Kurt Gödel Mark van Atten and Juliette Kennedy; 16. Platonism and mathematical intuition in Kurt Gödel's thought Charles Parsons; 17. Gödel's conceptual realism Donald A. Martin. (shrink)

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

Kurt Gödel was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of (...) unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full, and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. L All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German, and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century. (shrink)

Kurt Gödel was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of (...) unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full, and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German, and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century. (shrink)

This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.

Kurt Godel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for (...) Einstein's equations, permitting "time-travel" into the past. This second volume of a comprehensive edition of Godel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks. Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century. (shrink)

Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught a (...) seminar at Princeton in 1934. Seen in the historical context, Gödel was an important catalyst for the emergence of computability theory in the mid 1930s. (shrink)

This chapter describes Kurt Gödel's paper on the incompleteness theorems. Gödel's incompleteness results are two of the most fundamental and important contributions to logic and the foundations of mathematics. It had been assumed that first-order number theory is complete in the sense that any sentence in the language of number theory would be either provable from the axioms or refutable. Gödel's first incompleteness theorem showed that this assumption was false: it states that there are sentences of number theory that (...) are neither provable nor refutable. The first theorem is general in the sense that it applies to any axiomatic theory, which is ω-consistent, has an effective proof procedure, and is strong enough to represent basic arithmetic. Their importance lies in their generality: although proved specifically for extensions of system, the method Gödel used is applicable in a wide variety of circumstances. Gödel's results had a profound influence on the further development of the foundations of mathematics. It pointed the way to a reconceptualization of the view of axiomatic foundations. (shrink)

Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency (...) of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond. (shrink)

Ogni tentativo di ripensare le nostre categorie politiche deve muovere dalla consapevolezza che della distinzione classica fra zoé e bios, tra vita naturale ed esistenza politica, non ne sappiamo piú nulla. Nel diritto romano arcaico homo sacer era un uomo che chiunque poteva uccidere senza commettere omicidio e che non doveva però essere messo a morte nelle forme prescritte dal rito. È la vita uccidibile e insacrificabile dell' 'uomo sacro' a fornire qui la chiave per una rilettura critica della nostra (...) tradizione politica. Quando la vita diventa la posta in gioco della politica e questa si trasforma in biopolitica, tutte le categorie fondamentali della nostra riflessione, dai diritti dell'uomo alla democrazia alla cittadinanza, entrano in un processo di svuotamento e di dislocazione il cui risultato sta oggi davanti ai nostri occhi. Seguendo il filo del rapporto costitutivo fra nuda vita e potere sovrano, da Aristotele ad Auschwitz, dall'Habeas corpus alle Dichiarazioni dei diritti, il libro di Agamben cerca di decifrare gli enigmi - prima di tutti il fascismo e il nazismo - che il nostro secolo ha proposto alla ragione storica. Fino a vedere, nel campo di concentramento, il paradigma biopolitico nascosto della modernità in cui città e casa sono diventate indiscernibili e la possibilità di distinguere tra il nostro corpo biologico e il nostro corpo politico ci è stata tolta una volta per tutte. (shrink)

This volume represents the beginning of a new stage of research in interpreting Kurt Gödel’s philosophy in relation to his scientific work. It is more than a collection of essays on Gödel. It is in fact the product of a long enduring international collaboration on Kurt Gödel’s Philosophical Notebooks (Max Phil). New and significant material has been made accessible to a group of experts, on which they rely for their articles. In addition to this, Gödel’s Nachlass is presented (...) anew by the current state of research and the corpus of Gödel’s Philosophical Notebooks (Max Phil) is described in its entirety for the first time in its details. The volume is sub-divided into three parts. The fist part is dedicated to descriptions of the Gödel Nachlass that is to be found in The Shelby White and Leon Levy Archives Center des Institute for Advanced Study in Princeton. This part starts with an updated overview on Kurt Gödel’s Nachlass by the current state of research and is followed by a detailed description of Gödel’s Philosophical Notebooks (Max Phil). The second part is dedicated by several Gödel scholars to the close reading of single remarks in the Max Phil. And the third part of this volume unites a variety of papers by experts in Gödel studies, logic, and Leibniz as well as by some enthusiasts for Gödel. These papers are nearly all written for this volume. (shrink)

Many meta-ethicists have thought that rationality requires us to heed apparent normative reasons, not objective normative reasons. But what are apparent reasons? There are two kinds of standard answers. On de dicto views, R is an apparent reason for S to \ when it appears to S that R is an objective reason to \ . On de re views, R is an apparent reason for S to \ when R’s truth would constitute an objective reason for S to \ (...) , and it appears to S that R. De re views are currently more popular because they avoid overintellectualizing rationality. But they face problems owing to the way in which they do so. Some assume that we can escape these problems by requiring more information to be apparent or by appealing to defeat. But these strategies fail. So, I defend a new view: apparent reasons are apparent facts that agents are competently attracted to treat like objective reasons, where competence is indirectly defined in terms of objective reasons and a competence/performance distinction is honored. Since one can treat X like an F without having the concept of an F, the view does not overintellectualize rationality. But it is also strong enough to dodge the pitfalls of de re views. (shrink)

Foreword by Oliver Sacks Kurt Goldstein (1878-1965) was already an established neuropsychologist when he emigrated from Germany to the United States in the 1930s. This book, his magnum opus and widely regarded as a modern classic in psychology and biology, grew out of his dissatisfaction with traditional natural science techniques for analyzing living beings. It offers a broad introduction to the sources and ranges of application of the "holistic" or "organismic" research program that has since become a standard part (...) of biological thought. Goldstein was especially concerned with the breakdown of organization and the failure of central controls that take place in catastrophic responses to situations such as physical or mental illness. But he was equally attuned to the amazing powers of the organism to readjust to such catastrophic losses, if only by withdrawal to a more limited range that it could manage by a redistribution of its reduced energies, thus reclaiming as much wholeness as new circumstances allowed. Goldstein's theses in The Organism have had an important impact on philosophical and psychological thought throughout the twentieth century, as evidenced in the work of Maurice Merleau-Ponty, Georges Canguilhem, Ernst Cassirer, and Ludwig Binswanger. (shrink)

Reasons fundamentalists maintain that we can analyze all derivative normative properties in terms of normative reasons. These theorists famously encounter the Wrong Kind of Reasons problem, since not all reasons for reactions seem relevant for reasons-based analyses. Some have argued that this problem is a general one for many theorists, and claim that this lightens the burden for reasons fundamentalists. We argue in this paper that the reverse is true: the generality of the problem makes life harder for reasons fundamentalists. (...) We do this in two stages. First, we show that reflection on the generality of the distinction between wrong-kind reasons and right-kind reasons shows that not all right-kind reasons are normative reasons. So, not only do reasons-based analyses require a distinction between right-kind reasons and wrong-kind reasons, they also need a distinction between normative right-kind reasons from nonnormative right-kind reasons. We call this the Right Kind of Reasons Problem. In the second stage of the paper, we argue that reasons fundamentalism places tight constraints on its proper solution: in particular, it forbids one from appealing to anything normative to distinguish normative RKRs from nonnormative RKRs. It hence seems that reasons fundamentalists can only appeal to natural facts to solve the problem, but it is unclear which ones can do the job. So, reflection on the generality of the distinction only multiplies the fundamentalist’s problems. We end by exploring several solutions to these problems, and recommend a form of constitutivism as the best. (shrink)

This article traces Kurt H. Wolff’s involvement with Italy, from his first sojourn in the 1930s as a German Jewish intellectual in exile to the end of his life. Wolff developed profound ties with the country that hosted him, and that he was forced to abandon once racial laws were introduced there on the eve of World War II. Nonetheless, throughout his life he regarded Italy as an elective homeland of sorts. Wolff’s Italian experience is revisited through a detailed (...) examination of the places where he resided, his activities as a student, teacher, and scholar, and the many individuals with whom he associated, many of whom became his lifelong friends and collaborators. The documentary evidence collected here includes unpublished conversations with some of Wolff’s Italian connections and serves for a consideration of how his ties to Italy had an impact on the development of his sociological and esthetic theories. (shrink)

This paper re-examines Kurt Lewin's classic leadership studies, using them as a concrete example to explore his wider legacy to social psychology. Lewin distinguished between advanced “Galileian” science, which was based on analysing particular examples, and backward “Aristotelian” science, which used statistical analyses. Close examination of the way Lewin wrote about the leadership studies reveals that he used the sort of binary, value-laden concepts that he criticised as “Aristotelian”. Such concepts, especially those of “democracy” and “autocracy”, affected the way (...) that he analysed the results and the ways that later social scientists have understood, and misunderstood, the studies. It is argued that Lewin's famous motto—“there is nothing as practical as a good theory”—is too simple to fit the tensions between the leadership studies and his own views of what counts as good theory. (shrink)