First English translation of revolutionary paper that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

Previously published: Princeton University Press, 1940.

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 This third volume of his collected works consists of previously unpublished material, both essays and lectures.

P. Bernays has pointed out that, in order to prove the consistency of classical number theory, it is necessary to extend Hilbert's finitary standpoint by admitting certain abstract concepts in addition to the combinatorial concepts referring to symbols. The abstract concepts that so far have been used for this purpose are those of the constructive theory of ordinals and those of intuitionistic logic. It is shown that the concept of a computable function of finite simple type over the integers can (...) be used instead, where no other procedures of constructing such functions are necessary except simple recursion by an integral variable and substitution of functions in each other (starting with trivial functions). (shrink)

Badania nad podstawami matematyki przyniosły w ostatnich dziesięcioleciach wyniki, które wydają mi się ciekawe nie tylko dla nich samych, lecz także z uwagi na wnioski, jakie płyną z nich w odniesieniu do tradycyjnych problemów filozoficznych dotyczących natury matematyki. Same wyniki są dość szeroko znane, mimo to jednak sądzę, że warto raz jeszcze przedstawić je w zarysie, zwłaszcza w obliczu faktu, że dzięki pracy szeregu matematyków zyskały one znacznie doskonalszą formę, niż miały pierwotnie. Największy postęp, mający decydujące znaczenie dla tych wyników, (...) stał się możliwy dzięki precyzyjnemu zdefiniowaniu pojęcia skończonej procedury. Definicję taką można uzyskać na różne sposoby, które w efekcie dają dokładnie to samo pojęcie. Najbardziej zadowalający sposób polega moim zdaniem na sprowadzeniu pojęcia skończonej procedury do pojęcia maszyny o skończonej liczbie części, co uczynił brytyjski matematyk Turing. Co do filozoficznych konsekwencji wspomnianych wyników, nie sądzę, by kiedykolwiek należycie je przedyskutowano, czy choćby zwrócono na nie uwagę. (shrink)

Over a period of 22 years (1934-1955), the mathematician Kurt Gödel wrote down a series of philosophical reflections, the so-called Philosophical Remarks (Max Phil). They have been handed down in 15 notebooks written in Gabelsberg shorthand. The first notebook contains general philosophical reflections. Notebooks two and three consist of Gödel's individual ethics. The notebooks that follow clearly show that Gödel had designed a philosophy of science in which he placed his discussions of physics, psychology, biology, mathematics, language, theology, and history (...) within the context of a particular metaphysics. For the first time, the Kurt Gödel Research Center of the Berlin-Brandenburg Academy of Sciences is preparing a complete, historical-critical edition of Gödel's philosophical notebooks. A volume will published each year as a part of this edition. Volume 1, which Gödel entitled "Philosophy I Max 0," covers Gödel´s own philosophical reflections as well as those of other authors that were important to him. These were placed by Gödel at the beginning of his overall philosophical project. The introduction of the editor Eva-Maria Engelen provides an overview of this particular body of work. (shrink)

The initial volume of a comprehensive edition of Gödel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936. The volume begins with an informative overview of Gödel's life and work and features facing English translations for all German originals, extensive explanatory and historical notes, and a complete biography. Volume 2 will contain the remainder of Gödel's published work, and subsequent volumes will include unpublished manuscripts, lectures, correspondence and extracts from (...) the notebooks. (shrink)

Kurt Godel was the most outstanding logician of the 20th century. This second volume of Godel's works collects the remainder of his published work, covering the period 1938-1974. Each article or closely related group of articles is preceded by an introductory note that elucidates it and places it in its historical context.

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)

Nous publions sous ce titre la traduction française de l'essai philosophique de Kurt Gödel intitulé: «Is Mathematics Syntax of Language?» Inédit jusqu'à présent, l'original paraîtra dans le 3e volume des Collected Works de Gödel, dont la publication est imminente. Nous savons par Hao Wang que, le 15 mai 1953, Paul Arthur Schilpp avait invité Gödel à apporter sa contribution au volume consacré à Carnap dans The Library of Living Philosophers. Le manuscrit de Gödel «Carnap and the Ontology of Mathematics», devait (...) être remis au plus tard le 2 avril 1954. Dés le 2 juillet 1953, Gödel donnait son accord à Schilpp pour la rédaction d'un article intitulé «Some Observations on the Nominalistic View of the Nature of Mathematics.» Cependant, le volume consacré à Carnap paraîtra en 1963 sans qu'y figure la contribution de Gödel. En effet — toujours selon Wang — Gödel avait informé Schilpp, le 2 février 1959, qu'il renonçait à l'envoi de l'article, dont il avait composé, surtout en 1954–1955, plusieur s versions sous le titre «Is Mathematics Syntax of Language?» Pour expliquer cet abandon, Wang avance les raisons suivantes: En premier lieu, Gödel était bien convaincu d'avoir réfuté la thése syntaxique, mais il n'était pas satisfait de son argumentation en faveur du platonisme. Deuxiémement, les critiques de Gödel s'adressent aux théses soutenues par Carnap en 1934 plutôt qu'à celles que ce dernier défendra vingt ans aprés, et qui paraissent moins hostiles au platonisme de son interlocuteur. II pouvait paraître douteux, en troisieme lieu, que Carnap ait eu le temps de rédiger, en 1959, la réponse qu'il aurait du faire, conformément aux régies de la collection, à Gödel. Or, en 1943 déjà, Gödel avait voulu retirer sa contribution au volume consacré à Russell dans la même serie, parce que ce dernier n'avait pu répondre à l'article de Gödel dont la rédaction lui avait été communiquée trop tardivement. (shrink)

Der Mathematiker Kurt Gödel hat über einen Zeitraum von 22 Jahren philosophische Bemerkungen niedergeschrieben. Sie sind in 15 Notizbüchern in der Kurzschrift Gabelsberger überliefert. Das erste Heft enthält allgemeine philosophische Überlegungen, die Hefte zwei und drei bestehen aus Gödels Individualethik. Die dann folgenden zeigen, 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. Mit Notizbuch ›Maximen III‹ beginnt ein neuer Abschnitt in Gödels Philosophischen Notizbüchern. Das Verhältnis verschiedener Disziplinen zueinander wird ebenso beleuchtet wie ihre jeweilige Bedeutung sowohl für den denkenden und arbeitenden Wissenschaftler als auch für das Wissenssystem. Zu nennen sind hier insbesondere Psychologie, Mathematik und Theologie. Daneben finden sich Überlegungen zur Heuristik und zu wissenschaftlichen Methoden. Auch die Rolle grundlegender oder einfacher Begriffe für das Denken wird erkennbar. (shrink)

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 Heft enthält allgemeine philosophische Überlegungen, die Hefte zwei und drei bestehen aus Gödels Individualethik. Die dann folgenden zeigen, 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. In Band 4 (...) ist fast die Hälfte der Bemerkungen Grundlagenfragen der Mathematik und Logik sowie Fragen der Philosophie der Mathematik gewidmet. 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. In Band 4 setzt Gödel sich mit Grundlagenfragen der Mathematik und Logik sowie der Philosophie der Mathematik auseinander. Zudem stehen das Verhältnis verschiedener wissenschaftlicher Disziplinen zueinander und deren spezifische Fragestellungen im Zentrum seiner Überlegungen. Zu nennen sind hier insbesondere Philosophie, Psychologie, aber auch Theologie. (shrink)

Over a period of 22 years (1934-1955), the mathematician Kurt Gödel wrote down a series of philosophical reflections, the so-called Philosophical Remarks (Max Phil). They have been handed down in 15 notebooks written in Gabelsberg shorthand. The first notebook contains general philosophical reflections. Notebooks two and three consist of Gödel's individual ethics. The notebooks that follow clearly show that Gödel had designed a philosophy of science in which he placed his discussions of physics, psychology, biology, mathematics, language, theology, and history (...) within the context of a particular metaphysics. For the first time, the Kurt Gödel Research Center of the Berlin-Brandenburg Academy of Sciences is preparing a complete, historical-critical edition of Gödel's philosophical notebooks. A volume will published each year as a part of this edition. Volume 1, which Gödel entitled "Philosophy I Max 0," covers Gödel´s own philosophical reflections as well as those of other authors that were important to him. These were placed by Gödel at the beginning of his overall philosophical project. The introduction of the editor Eva-Maria Engelen provides an overview of this particular body of work. (shrink)

Volume 2 contains both notebooks of "Time Management (Max) I and II" and thereby Gödel’s applied individual ethics, which he received among others through his teacher Heinrich Gomperz. Gödel thus incorporates the ethical ideal of self-perfection into his opus. The volume is prefaced by an introduction to relevant considerations from the ethics of the Stoics as well as ancient dietetics, which provide the philosophical background to understand Gödel’s approach. In addition, editor Eva-Maria Engelen presents how this fits into the context (...) of Gödel’s Philosophical Notebooks. (shrink)