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)
In spite of his status as a highly original thinker whose views were, in many ways, ahead of his time and anticipate those of more famous successors, the work of Johann Gottfried von Herder has not received the attention it deserves in mainstream philosophical discourse. In Herder's Hermeneutics, Kristin Gjesdal successfully addresses this deficit by exploring the enlightenment origins of the hermeneutic tradition through a careful and compelling reconstruction of Herder's theory of interpretation. Breaking with the widespread view of Herder (...) as a contra-Enlightenment thinker, Gjesdal conceives of Herder's hermeneutics as contributing to the enlightenment of the Enlightenment project through an immanent critique of... (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. 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. 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)
I attribute an 'intensional reading' of the second incompleteness theorem to its author, Kurt G del. My argument builds partially on an analysis of intensional and extensional conceptions of meta-mathematics and partially on the context in which G del drew two familiar inferences from his theorem. Those inferences, and in particular the way that they appear in G del's writing, are so dubious on the extensional conception that one must doubt that G del could have understood his theorem extensionally. (...) However, on the intensional conception, the inferences are straightforward. For that reason I conclude that G del had an intensional understanding of his theorem. Since this conclusion is in tension with the generally accepted view of G del's understanding of mathematical truth, I explain how to reconcile that view with the intensional reading of the theorem that I attribute to G del. The result is a more detailed account of G del's conception of meta-mathematics than is currently available. (shrink)
This paper considers the place of reasons in the metaphysics of epistemic normativity and defends a middle ground between two popular extremes in the literature. Against members of the ‘reasons first’ movement, we argue that reasons are not the sole fundamental constituents of epistemic normativity. We suggest instead that the virtue-theoretic property of competence is the key building block. To support this approach, we note that reasons must be possessed to play a role in the analysis of central epistemically normative (...) properties, and argue that the relation of possession must be analyzed in terms of competence. But while we diverge with reasons-firsters on this score, we also distance ourselves from those who deny reasons any important role in epistemology. For we maintain that possessed reasons do help to ground deontic facts in the epistemic domain (e.g., facts about what one epistemically ought to believe, may believe, or is justified in believing). Indeed, we present an argument that the possession of sufficient epistemic reasons is necessary and sufficient for propositional justification, and that proper basing on such reasons yields doxastic justification. But since possession and proper basing are themselves grounded in competence, reasons are not the end of the explanatory road: competence enables them to do their work, putting them—and us—in the middle. (shrink)
Contained in the face is a vast body of social information, both fixed and flexible. Across multiple lines of converging evidence it has become increasingly clear that face processing is subject to one of the most potent and best understood of social cognitive phenomena: social categorization. This article reviews this research at the juncture of social psychology and face perception showing the interplay between social categorization and face processing. It lays out evidence indicating that social categories are extracted easily from (...) faces, suggesting that the effects of social categories can occur quickly and unintentionally. Recent evidence that social categories can affect perception of both invariant and variant facial characteristics is discussed. Finally, the article summarizes recent evidence indicating that the motivational consequences of social categories can affect which faces are remembered and how faces are processed. (shrink)
Modern 3D seismic surveys are often of such good quality and 3D interpretation packages so user-friendly that seismic interpretation is no longer exclusively carried out by geophysicists. This ease-of-use has also been extended to more quantitative workflows, such as 3D prestack inversion, putting it in the hands of the “nonexpert” — be it geologist, engineer, or new-hire geophysicist. Indeed, given good quality input seismic data, almost any interpreter who can generate good well ties and define an accurate background model of (...) P-impedance, S-impedance, and density can generate a quality prestack inversion. Two of the authors are new geophysicists who fell into the prestack inversion “pit.” Fortunately, they were able to recognize that something was wrong. We applied prestack inversion to gathers that were carefully reprocessed by a major service company. The problem, however, was not with the processing, but with our lack of understanding of the input legacy data that formed part of a larger “megamerge” survey. Not all of the surveys that were merged had the same offset range. In the migration step, gaps in long offsets of the older surveys were not muted. Migration noise from newer surveys was allowed to fill this space. We share our initial workflow and suspicious results. We also clarify the meaning of “fold” and “offset” for prestack-migrated gathers. In addition to presenting some QC tools useful in analyzing megamerge surveys, we show how, by limiting the offsets used in our prestack inversion, we obtain less aggressive but still useful results. (shrink)
The Fort Worth basin is one of the most fully developed shale gas fields in North America. Although there are hundreds of drilled wells in the basin, almost none of them reach the Precambrian basement. Imaged by perhaps 100 3D seismic surveys, the focus on the relatively shallow, flat-lying Barnett Shale objective has resulted in little published work on the basement structures underlying the Lower Paleozoic strata. Subtle folds and systems of large joints are present in almost all 3D seismic (...) surveys in the FWB. At the Cambro-Ordovician Ellenburger level, these joints are often diagenetically altered and exhibit collapse features at their intersections. We discovered how the basement structures relate to overlying Paleozoic reservoirs in the Barnett Shale and Ellenburger Group. In support of our investigation, the Marathon Oil Company provided a high-quality, wide-azimuth, 3D seismic data near the southeast fringe of the FWB. In addition to the seismic volume, we integrated the seismic results with gravity, magnetic, well log, and geospatial data to understand the basement and subbasement structures in the southeast FWB. Major tectonic features including the Ouachita frontal thrust belt, Lampasas arch, Llano uplift, and Bend arch surround the southeast FWB. Euler deconvolution and integrated forward gravity modeling helped us extend our interpretation beyond the 3D seismic survey into a regional context. (shrink)
The dominant unspoken philosophical basis of medical care in the United States is a form of Cartesian reductionism that views the body as a machine and medical professionals as technicians whose job is to repair that machine. The purpose of this paper is to advocate for an alternative philosophy of medicine based on the concept of healing relationships between clinicians and patients. This is accomplished first by exploring the ethical and philosophical work of Pellegrino and Thomasma and then by connecting (...) Martin Buber's philosophical work on the nature of relationships to an empirically derived model of the medical healing relationship. The Healing Relationship Model was developed by the authors through qualitative analysis of interviews of physicians and patients. Clinician-patient healing relationships are a special form of what Buber calls I-Thou relationships, characterized by dialog and mutuality, but a mutuality limited by the inherent asymmetry of the clinician-patient relationship. The Healing Relationship Model identifies three processes necessary for such relationships to develop and be sustained: Valuing, Appreciating Power and Abiding. We explore in detail how these processes, as well as other components of the model resonate with Buber's concepts of I-Thou and I-It relationships. The resulting combined conceptual model illuminates the wholeness underlying the dual roles of clinicians as healers and providers of technical biomedicine. On the basis of our analysis, we argue that health care should be focused on healing, with I-Thou relationships at its core. (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 book looks at the ways in which conditionals, an integral part of philosophy and logic, can be of practical use in computer programming. It analyzes the different types of conditionals, including their applications and potential problems. Other topics include defeasible logics, the Ramsey test, and a unified view of consequence relation and belief revision. Its implications will be of interest to researchers in logic, philosophy, and computer science, particularly artificial intelligence.
In this paper, we compare one Nez Perce myth, namely lepuu ’Iceyeeye, or “Two Coyotes,” to some passages from Plato’s dialogues. Our point is to show how “Two Coyotes,” like Plato’s dialogues, serves as an instrument of philosophical reflection by engaging the listener/reader in aporia and paradox that motivate multiple reflections on the One, the Many, the nature and relation of kinds to instances, and thus the process and meaning of naming. If we are correct about the uses of “Two (...) Coyotes,” this might warrant a reevaluation of other first Nations’ myths. (shrink)
This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger . The generalized systemT(V′) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V′) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V′) is provable in a formal system of second order arithmetic with the axiom schema ofΠ 2 1 -comprehension in a similar way, as it is proved in  for the weaker notation systemT(V′).
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