Kurt Gödel was an Austrian-American logician, mathematician, and philosopher who profoundly impacted 20th-century scientific and philosophical thought. He is most celebrated for his two incompleteness theorems, which demonstrated that within any consistent axiomatic system powerful enough to describe natural number arithmetic, there exist true statements that cannot be proven from the axioms. To establish these theorems, Gödel pioneered a technique known as Gödel numbering, which encodes formal expressions as natural numbers. His work also clarified connections between various logical systems and showed that the continuum hypothesis is not disprovable from the accepted axioms of set theory.
Die Maximen Philosophie von Kurt Gödel, niedergeschrieben zwischen 1934 und 1955, umfasst philosophische Überlegungen und angewandte Individualethik. Band 2 der historisch-kritischen Edition behandelt Gödels Ethik und deren Verbindung zur Stoa sowie antiker Diätetik. Eine Einführung bietet Kontext zu seinen Gedanken.
Der Mathematiker Kurt Gödel hat über einen Zeitraum von 22 Jahren (1934-1955) philosophische Bemerkungen, die so genannten Maximen Philosophie (Max Phil), niedergeschrieben. Sie sind in 15 Notizbüchern in der Kurzschrift Gabelsberger überliefert. Das erste Notizheft enthält allgemeine philosophische Überlegungen, die Hefte zwei und drei bestehen aus Gödels Individualethik. Die dann folgenden Notizbücher machen deutlich, dass Gödel eine Wissenschaftsphilosophie entworfen hat, in der er seine Erörterungen zu Physik, Psychologie, Biologie, Mathematik, Sprache, Theologie und Geschichte in den Kontext einer Metaphysik stellt. Erstmals wird nun an der Kurt-Gödel-Forschungsstelle der Berlin-Brandenburgischen Akademie der Wissenschaften eine vollständige, historisch-kritische Edition von Gödels philosophischen Notizbüchern vorbereitet. Im Rahmen dieser Edition erscheint jährlich ein Band. Band 1, von Gödel mit ›Philosophie I Max 0‹ betitelt, umfasst philosophische Überlegungen Gödels sowie anderer für ihn bedeutender Autoren, die er an den Anfang seines philosophischen Gesamtprojektes gestellt hat. Die Einleitung der Herausgeberin Eva-Maria Engelen bietet einen Überblick über das Korpus.
Kurt Gödel was the greatest logician of this century. This third volume of his collected works consists of previously unpublished material, both essays and lectures.
In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
Kurt Gödel (1906-1978) was the most outstanding logician of the twentieth century. This second volume of a comprehensive edition of Gödel's works collects the remainder of his published work, covering the period 1938-1974. (Volume I included all of his publications from 1929-1936). Each article or closely related group of articles is preceded by an introductory note that elucidates it and places it in historical context. The aim is to make the full body of Gödel's work as accessible and useful to as wide an audience as possible, without in any way sacrificing the requirements of historical and scientific accuracy.
Kurt Gödel (1906 - 1978) was a preeminent logician of the twentieth century, renowned for his pivotal contributions to the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. His work also encompassed constructivity, the decision problem, and the foundations of computability theory, alongside a distinctive philosophical perspective on mathematics. Less recognized is his exploration of unique cosmological models that suggest the theoretical possibility of time travel into the past. The Collected Works serves as a significant compilation of Gödel's intellectual legacy. The first two volumes present his published works in full, both in original form and translation, while the third volume includes a selection of unpublished articles and lecture texts from Gödel's Nachlass. The final two volumes feature Gödel's correspondence on logical, philosophical, and scientific topics, with Volume IV covering A to G and Volume V covering H to Z, along with a complete inventory of his Nachlass. Each volume includes introductory notes with extensive commentary, English translations of German texts, and a comprehensive bibliography. This edition aims to be accessible to a broad audience, making it an essential resource for professionals and students in various fields, as well as anyone interested in the insights of one of the twentieth century's great minds.