Kurt Gödel

Gödel c. 1926

Born|

Kurt Friedrich Gödel

(1906-04-28)April 28, 1906

Brünn, Austria-Hungary

Died| January 14, 1978(1978-01-14) (aged 71)

Princeton, New Jersey, U.S.

Cause of death| Starvation due to a persecutory delusion
Citizenship|

* Austria
* Czechoslovakia
* Germany
* United States

Education| University of Vienna (Dr. Phil., 1930)
Known for|

* Gödel's incompleteness theorems
* Gödel's completeness theorem
* Gödel's constructible universe
* Gödel metric (closed timelike curve)
* Gödel logic
* Gödel–Dummett logic
* Gödel's β function
* Gödel's Loophole
* Gödel numbering
* Gödel operation
* Gödel's speed-up theorem
* Gödel's ontological proof
* Gödel–Gentzen translation
* Gödel–McKinsey–Tarski translation
* Von Neumann–Bernays–Gödel set theory
* ω-consistent theory
* The consistency of the continuum hypothesis with ZFC
* Axiom of constructibility
* Compactness theorem
* Condensation lemma
* Diagonal lemma
* Dialectica interpretation
* Ordinal definable set
* Slingshot argument

Spouse(s)|

Adele Nimbursky (m. 1938)

Awards|

* Albert Einstein Award (1951)
* ForMemRS (1968)[1]
* National Medal of Science (1974)

Scientific career
Fields| Mathematics, mathematical logic, physics
Institutions| Institute for Advanced Study
Thesis| Über die Vollständigkeit des Logikkalküls (1929)
Doctoral advisor| Hans Hahn

* * *

Philosophy career
Era| 20th-century philosophy
Region| Western philosophy
School| Analytic philosophy

Main interests

* Philosophy of logic
* Philosophy of mathematics
* Philosophy of religion
* General relativity

Signature

Kurt Friedrich Gödel (/ˈɡɜːrdəl/ GUR-dəl;[2] de; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel profoundly influenced scientific and philosophical thinking in the 20th century (at a time when Bertrand Russell,[3] Alfred North Whitehead,[3] and David Hilbert were using logic and set theory to investigate the foundations of mathematics), building on earlier work by Frege, Richard Dedekind, and Georg Cantor.

Gödel's discoveries in the foundations of mathematics led to the proof of his completeness theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two years later, in 1931. The incompleteness theorems address limitations of formal axiomatic systems. In particular, they imply that a formal axiomatic system satisfying certain technical conditions cannot decide the truth value of all statements about the natural numbers, and cannot prove that it is itself consistent.[4][5] To prove this, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

Gödel also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted Zermelo–Fraenkel set theory, assuming that its axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.

Born into a wealthy German-speaking family in Brno, Gödel emigrated to the United States in 1939 to escape the rise of Nazi Germany. Later in life, he suffered from mental illness; believing that his food was being poisoned, he refused to eat and starved to death.

## Contents

* 1 Early life and education
* 1.1 Childhood
* 1.2 Studies in Vienna
* 2 Career
* 2.1 Incompleteness theorems
* 2.2 Mid-1930s: further work and U.S. visits
* 2.3 Princeton, Einstein, U.S. citizenship
* 3 Awards and honours
* 4 Personal life and death
* 4.1 Religious views
* 5 Legacy
* 6 Bibliography
* 6.1 German
* 6.2 English
* 6.3 English Translation
* 7 See also
* 8 Notes
* 9 References
* 10 Sources
* 11 Further reading
* 12 External links

## Early life and education

### Childhood

Gödel was born on April 28, 1906, in Brünn, Austria-Hungary (now Brno, Czech Republic), into the German-speaking family of Rudolf Gödel,[6] the managing director and part owner of a major textile firm,[lower-alpha 1] and Marianne Gödel (née Handschuh).[11] His father was Catholic and his mother was Protestant, and the children were raised as Protestants. Many of Kurt Gödel's ancestors were active in Brünn's cultural life. For example, his grandfather Joseph Gödel was a famous singer in his time and for some years a member of the Brünner Männergesangverein (Men's Choral Union of Brünn).[12]

Gödel automatically became a citizen of Czechoslovakia at age 12 when the Austro-Hungarian Empire collapsed following its defeat in the First World War. According to his classmate Klepetař, like many residents of the predominantly German Sudetenländer, "Gödel considered himself always Austrian and an exile in Czechoslovakia".[13] In February 1929, he was granted release from his Czechoslovak citizenship and then, in April, granted Austrian citizenship.[14] When Germany annexed Austria in 1938, Gödel automatically became a German citizen at age 32. In 1948, after World War II, at age 42, he became a U.S. citizen.[15]

In his family, the young Gödel was nicknamed Herr Warum ("Mr. Why") because of his insatiable curiosity. According to his brother Rudolf, at the age of six or seven, Kurt suffered from rheumatic fever; he completely recovered, but remained convinced for the rest of his life that his heart had been permanently damaged. Beginning at age four, Gödel had "frequent episodes of poor health", which continued all his life.[16]

Gödel attended the Evangelische Volksschule, a Lutheran school in Brünn, from 1912 to 1916, and was enrolled in the Deutsches Staats-Realgymnasium from 1916 to 1924, excelling with honors in all subjects, particularly mathematics, languages, and religion. Although he had first excelled in languages, he became more interested in history and mathematics. His interest in mathematics increased when in 1920 his older brother Rudolf left for Vienna, where he attended medical school at the University of Vienna. During his teens, Gödel studied Gabelsberger shorthand,[17] criticism of Isaac Newton, and the writings of Immanuel Kant.[18]

### Studies in Vienna

Plaque to Gödel at 43-45 Josefstädter Straße (de), Vienna, where he discovered his incompleteness theorems

At age 18, Gödel joined his brother at the University of Vienna. He had already mastered university-level mathematics.[19] Although initially intending to study theoretical physics, he also attended courses on mathematics and philosophy.[20] During this time, he adopted ideas of mathematical realism. He read Kant's Metaphysische Anfangsgründe der Naturwissenschaft, and participated in the Vienna Circle with Moritz Schlick, Hans Hahn, and Rudolf Carnap. Gödel then studied number theory, but when he took part in a seminar run by Moritz Schlick that studied Bertrand Russell's book Introduction to Mathematical Philosophy, he became interested in mathematical logic. According to Gödel, mathematical logic was "a science prior to all others, which contains the ideas and principles underlying all sciences."[21]

Attending a lecture by David Hilbert in Bologna on completeness and consistency in mathematical systems may have set Gödel's life course. In 1928, Hilbert and Wilhelm Ackermann published Grundzüge der theoretischen Logik (Principles of Mathematical Logic), an introduction to first-order logic in which the problem of completeness was posed: "Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system?"[22]

Gödel chose this topic for his doctoral work.[22] In 1929, aged 23, he completed his doctoral dissertation under Hans Hahn's supervision. In it, he established his eponymous completeness theorem regarding first-order logic.[22] He was awarded his doctorate in 1930,[22] and his thesis (accompanied by additional work) was published by the Vienna Academy of Science.

In 1929 Gödel met Adele Gödel (es ) (née Porkert), a divorcee living with her parents across the street from him.[23] The two married (in a civil ceremony) a decade later, in September 1938.[24] A trained ballet dancer, Adele was working as a masseuse at the time they met.[23] At one point she worked as a dancer at a downtown nightclub called the Nachtfalter ("nocturnal moth").[23] Gödel's parents opposed their relationship because of her background and age (six years older than him).[25] It appears to have been a happy marriage.[26] Adele was an important support to Gödel, whose psychological problems affected their daily lives.[27] The two had no children.

## Career

Gödel as a student in 1925

### Incompleteness theorems

> Kurt Gödel's achievement in modern logic is singular and monumental—indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement.

— John von Neumann[28]

In 1930 Gödel attended the Second Conference on the Epistemology of the Exact Sciences, held in Königsberg on September 5–7. There, he presented his completeness theorem of first-order logic, and, at the end of the talk, mentioned that this result does not generalise to higher-order logic, thus hinting at his incompleteness theorems.[29]

Gödel published his incompleteness theorems in Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme (called in English "On Formally Undecidable Propositions of Principia Mathematica and Related Systems"). In that article, he proved for any computable axiomatic system powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that:

1. If a (logical or axiomatic formal) system is omega-consistent, it cannot be syntactically complete.
2. The consistency of axioms cannot be proved within their own system.[30]

These theorems ended a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's program, to find a non-relatively consistent axiomatization sufficient for number theory (that was to serve as the foundation for other fields of mathematics).[31]

Gödel constructed a formula that claims it is itself unprovable in a given formal system. If it were provable, it would be false. Thus there will always be at least one true but unprovable statement. That is, for any computably enumerable set of axioms for arithmetic (that is, a set that can in principle be printed out by an idealized computer with unlimited resources), there is a formula that is true of arithmetic, but not provable in that system. To make this precise, Gödel had to produce a method to encode (as natural numbers) statements, proofs, and the concept of provability; he did this by a process known as Gödel numbering.[32]

In his two-page paper Zum intuitionistischen Aussagenkalkül (1932), Gödel refuted the finite-valuedness of intuitionistic logic. In the proof, he implicitly used what has later become known as Gödel–Dummett intermediate logic (or Gödel fuzzy logic).[33]

### Mid-1930s: further work and U.S. visits

Gödel earned his habilitation at Vienna in 1932, and in 1933 became a Privatdozent (unpaid lecturer) there. In 1933, Adolf Hitler came to power in Germany, and over the following years the Nazis rose in influence in Austria and among Vienna's mathematicians. In June 1936, Moritz Schlick, whose seminar had aroused Gödel's interest in logic, was murdered by one of his former students, Johann Nelböck. This triggered "a severe nervous crisis" in Gödel.[34] He developed paranoid symptoms, including a fear of being poisoned, and spent several months in a sanitarium for nervous diseases.[35]

In 1933, Gödel first traveled to the U.S., where he met Albert Einstein, who became a good friend.[36] He delivered an address to the annual meeting of the American Mathematical Society. During this year, Gödel also developed the ideas of computability and recursive functions to the point where he was able to present a lecture on general recursive functions and the concept of truth. This work was developed in number theory, using Gödel numbering.

In 1934, Gödel gave a series of lectures at the Institute for Advanced Study (IAS) in Princeton, New Jersey, titled On undecidable propositions of formal mathematical systems. Stephen Kleene, who had just completed his PhD at Princeton, took notes on these lectures that were later published.

Gödel visited the IAS again in the autumn of 1935. The traveling and hard work had exhausted him and the next year he took a break to recover from a depressive episode. He returned to teaching in 1937. During this time, he worked on the proof of consistency of the axiom of choice and of the continuum hypothesis; he went on to show that these hypotheses cannot be disproved from the common system of axioms of set theory.

After marrying Adele Nimbursky in 1938, he visited the U.S. again, spending the autumn of 1938 at the IAS and publishing Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory,[37] a classic of modern mathematics. In it, he introduced the constructible universe, a model of set theory in which the only sets that exist are those that can be constructed from simpler sets. Gödel showed that both the axiom of choice (AC) and the generalized continuum hypothesis (GCH) are true in the constructible universe, and therefore must be consistent with the Zermelo–Fraenkel axioms for set theory (ZF). This result has considerable consequences for working mathematicians, as it means they can assume the axiom of choice when proving the Hahn–Banach theorem. Paul Cohen later constructed a model of ZF in which AC and GCH are false; together these proofs mean that AC and GCH are independent of the ZF axioms for set theory.

Gödel spent the spring of 1939 at the University of Notre Dame.[38]

### Princeton, Einstein, U.S. citizenship

After the Anschluss on March 12, 1938, Austria became a part of Nazi Germany. Germany abolished the title Privatdozent, so Gödel had to apply for a different position under the new order. His former association with Jewish members of the Vienna Circle, especially Hahn, weighed against him. The University of Vienna turned his application down.

His predicament worsened when the German army found him fit for conscription. World War II started in September 1939. Before the year was up, Gödel and his wife left Vienna for Princeton. To avoid the difficulty of an Atlantic crossing, the Gödels took the Trans-Siberian Railway to the Pacific, sailed from Japan to San Francisco (which they reached on March 4, 1940), then traveled to Princeton by train.[39] During this trip, Gödel was supposed to be carrying a secret letter to Einstein from Viennese physicist Hans Thirring to alert President Franklin D. Roosevelt of the possibility that Hitler was making an atom bomb. Gödel never conveyed that letter to Einstein, although they did meet, because he was not convinced Hitler could achieve this feat.[40] In any case, Leo Szilard had already conveyed the message to Einstein, and Einstein had already warned Roosevelt.

In Princeton, Gödel accepted a position at the Institute for Advanced Study (IAS), which he had visited during 1933–34.[41]

Einstein was also living in Princeton during this time. Gödel and Einstein developed a strong friendship, and were known to take long walks together to and from the IAS. The nature of their conversations was a mystery to the other Institute members. Economist Oskar Morgenstern recounts that toward the end of Einstein's life, Einstein confided that his "own work no longer meant much, that he came to the Institute merely ... to have the privilege of walking home with Gödel".[42]

Gödel and his wife spent the summer of 1942 in Blue Hill, Maine, at the Blue Hill Inn at the top of the bay. Gödel had a very productive summer of work. Using Heft 15 [volume 15] of Gödel's still-unpublished Arbeitshefte [working notebooks], John W. Dawson Jr. conjectures that Gödel discovered a proof for the independence of the axiom of choice from finite type theory, a weakened form of set theory, while in Blue Hill in 1942. Gödel's close friend Hao Wang supports this conjecture, noting that Gödel's Blue Hill notebooks contain his most extensive treatment of the problem.[43]

On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that could allow the U.S. to become a dictatorship; this has since been dubbed Gödel's Loophole. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. The judge turned out to be Phillip Forman, who knew Einstein and had administered the oath at Einstein's own citizenship hearing. Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery to Forman. Forman understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion.[44][45]

Gödel became a permanent member of the Institute for Advanced Study at Princeton in 1946. He became a full professor at the Institute in 1953 and an emeritus professor in 1976.[46]

During his time at the institute, Gödel's interests turned to philosophy and physics. In 1949, he demonstrated the existence of solutions involving closed timelike curves, to Einstein's field equations in general relativity.[47] He is said to have given this elaboration to Einstein as a present for his 70th birthday.[48] His "rotating universes" would allow time travel to the past and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric (an exact solution of the Einstein field equation).

Gödel studied and admired the work of Gottfried Leibniz, but came to believe that a hostile conspiracy had caused some of Leibniz's work to be suppressed.[49] To a lesser extent he studied Kant and Edmund Husserl. In the early 1970s, Gödel circulated among his friends an elaboration of Leibniz's version of Anselm of Canterbury's ontological argument for God's existence. This is now known as Gödel's ontological proof.

## Awards and honours

Gödel was awarded (with Julian Schwinger) the first Albert Einstein Award in 1951 and the National Medal of Science in 1974.[50] Gödel was elected a resident member of the American Philosophical Society in 1961 and a Foreign Member of the Royal Society (ForMemRS) in 1968.[51][1] He was a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts.[52]

## Personal life and death

Gravestone of Kurt and Adele Gödel in the Princeton, N.J., cemetery

Gödel married Adele Nimbursky in Vienna in 1938. They emigrated to the United States a year later.

In his later life, Gödel suffered periods of mental instability and illness. Some scholars have suggested Asperger syndrome and obsessive-compulsive disorder as diagnoses.[53] After his close friend Moritz Schlick was murdered,[54] Gödel developed an obsessive fear of being poisoned, and ate only food prepared by his wife, Adele. Adele was hospitalized beginning in late 1977, and in her absence Gödel refused to eat;[55] he weighed 29 kilograms (65 lb) when he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978.[56] He was buried in Princeton Cemetery. Adele died in 1981, donating Gödel's papers to the Institute for Advanced Study upon her death.[57]

### Religious views

Gödel believed that God was personal,[58] and called his philosophy "rationalistic, idealistic, optimistic, and theological".[59] He formulated a draft of formal proof of God's existence known as Gödel's ontological proof.

Gödel believed in an afterlife, saying, "Of course this supposes that there are many relationships which today's science and received wisdom haven't any inkling of. But I am convinced of this [the afterlife], independently of any theology." It is "possible today to perceive, by pure reasoning" that it "is entirely consistent with known facts." "If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife]."[60] He also read widely on other paranormal topics, including telepathy, reincarnation, and ghosts.[61]

In an unmailed answer to a questionnaire, Gödel described his religion as "baptized Lutheran (but not member of any religious congregation). My belief is theistic, not pantheistic, following Leibniz rather than Spinoza."[62] Of religion(s) in general, he said: "Religions are for the most part bad, but not religion itself."[63] According to his wife, Adele, "Gödel, although he did not go to church, was religious and read the Bible in bed every Sunday morning",[64] while of Islam, he said, "I like Islam: it is a consistent [or consequential] idea of religion and open-minded."[65]

## Legacy

Douglas Hofstadter's 1979 book Gödel, Escher, Bach: an Eternal Golden Braid interweaves the work and ideas of Gödel, M. C. Escher, and Johann Sebastian Bach. It partly explores the ramifications of the fact that Gödel's incompleteness theorem can be applied to any Turing-complete computational system, which may include the human brain. In 2005, John W. Dawson Jr. published a biography, Logical Dilemmas: The Life and Work of Kurt Gödel.[66] That year, Rebecca Goldstein published Incompleteness: The Proof and Paradox of Kurt Gödel as part of the Great Discoveries series. Stephen Budiansky's Gödel's biography, Journey to the Edge of Reason: The Life of Kurt Gödel,[67] was a New York Times Critics' Top Book of 2021.[68] Gödel was one of four mathematicians examined in David Malone's 2008 BBC documentary Dangerous Knowledge.[69]

The Kurt Gödel Society, founded in 1987, is an international organization for the promotion of research in logic, philosophy, and the history of mathematics. The University of Vienna hosts the Kurt Gödel Research Center for Mathematical Logic. The Association for Symbolic Logic has held an annual Gödel Lecture since 1990. The Gödel Prize is given annually to an outstanding paper in theoretical computer science. Gödel's philosophical notebooks[70] are being edited at the Kurt Gödel Research Centre at the Berlin-Brandenburg Academy of Sciences and Humanities.[71] Five volumes of Gödel's collected works have been published. The first two include his publications; the third includes unpublished manuscripts from his Nachlass, and the final two include correspondence.

In the 1994 film I.Q., Lou Jacobi portrays Gödel. In the 2023 movie Oppenheimer, Gödel, played by James Urbaniak, briefly appears walking with Einstein in the gardens of Princeton.

## Bibliography

### German

* 1930, "Die Vollständigkeit der Axiome des logischen Funktionenkalküls." Monatshefte für Mathematik und Physik 37: 349–60.
* 1931, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I." Monatshefte für Mathematik und Physik 38: 173–98.
* 1932, "Zum intuitionistischen Aussagenkalkül", Anzeiger Akademie der Wissenschaften Wien 69: 65–66.

### English

* 1940\. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. Princeton University Press.
* 1947\. "What is Cantor's continuum problem?" The American Mathematical Monthly 54: 515–25. Revised version in Paul Benacerraf and Hilary Putnam, eds., 1984 (1964). Philosophy of Mathematics: Selected Readings. Cambridge Univ. Press: 470–85.
* 1950, "Rotating Universes in General Relativity Theory." Proceedings of the International Congress of Mathematicians in Cambridge, Vol. 1, pp. 175–81.

### English Translation

* Kurt Gödel, 1992. On Formally Undecidable Propositions Of Principia Mathematica And Related Systems, tr. B. Meltzer, with a comprehensive introduction by Richard Braithwaite. Dover reprint of the 1962 Basic Books edition.
* Kurt Gödel, 2000.[72] On Formally Undecidable Propositions Of Principia Mathematica And Related Systems, tr. Martin Hirzel
* Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press.
* 1930\. "The completeness of the axioms of the functional calculus of logic," 582–91.
* 1930\. "Some metamathematical results on completeness and consistency," 595–96. Abstract to (1931).
* 1931\. "On formally undecidable propositions of Principia Mathematica and related systems," 596–616.
* 1931a. "On completeness and consistency," 616–17.
* Collected Works: Oxford University Press: New York. Editor-in-chief: Solomon Feferman.
* Gödel, Kurt. Collected Works. New York: Oxford University Press.
* ~~~~ (1986). Publications 1929–1936. I. ISBN 978-0-19-503964-1. https://antilogicalism.com/wp-content/uploads/2021/12/Godel-1.pdf. / Paperback: ISBN 978-0-19-514720-9
* ~~~~ (1990). Publications 1938–1974. II. Oxford University Press. ISBN 978-0-19-503972-6. https://antilogicalism.com/wp-content/uploads/2021/12/Godel-2.pdf. / Paperback: ISBN 978-0-19-514721-6
* ~~~~ (1995). Unpublished Essays and Lectures. III. ISBN 978-0-19-507255-6. https://antilogicalism.com/wp-content/uploads/2021/12/Godel-3.pdf. / Paperback: ISBN 978-0-19-514722-3
* ~~~~ (2003). Correspondence A–G. IV. Clarendon Press. ISBN 978-0-19-850073-5. https://antilogicalism.com/wp-content/uploads/2021/12/Godel-4.pdf.
* ~~~~ (2003). Correspondence H–Z. V. Clarendon Press. ISBN 978-0-19-850075-9. https://antilogicalism.com/wp-content/uploads/2021/12/Godel-5.pdf.

* Kurt Gödel, Philosophische Notizbücher / Philosophical Notebooks: De Gruyter: Berlin/München/Boston. Editor: Eva-Maria Engelen (de).
* Volume 1 (2019): Philosophie I Maximen 0 / Philosophy I Maxims 0. ISBN 978-3-11-058374-8 / Paperback: ISBN 978-3-11-077683-6.
* Volume 2 (2020): Zeiteinteilung (Maximen) I und II / Time Management (Maxims) I and II. ISBN 978-3-11-067409-5 / Paperback: ISBN 978-3-11-221621-7.
* Volume 3 (2021): Maximen III / Maxims III. ISBN 978-3-11-075325-7 / Paperback: ISBN 978-3-11-221622-4.
* Volume 4 (2023): Maximen IV / Maxims IV. ISBN 978-3-11-077294-4 / Paperback: ISBN 978-3-11-162253-8.
* Volume 5 (2024): Maximen V / Maxims V. ISBN 978-3-11-108114-4 / Paperback: ISBN 978-3-11-221623-1.
* Volume 6 (2025): Maximen VI / Maxims VI. ISBN 978-3-11-139031-4.
* Volume 7 (2026): Maximen VII / Maxims VII. ISBN 978-3-11-140466-0.

## See also

* Gödel fuzzy logic
* Gödel machine
* Gödel Prize
* Gödel t-norm
* Gödel's ontological proof
* Gödel's Dialectica interpretation
* Infinite-valued logic
* List of Austrian scientists
* List of pioneers in computer science
* Mathematical Platonism
* Original proof of Gödel's completeness theorem
* Primitive recursive functional
* Gödel–Löb logic
* Strange loop
* Tarski's undefinability theorem
* World Logic Day

## Notes

1. ↑ The factory was involved in wool trade - originally founded by Friedrich Redlich (1828, Brno – 1893/4, Brno) 1850 for worsted yarn imported from England, France and Belgium - had a weaving mill and finishing shop, no spinning mill.[7] [8] [9] [6] [10]

## References

1. ↑ 1.0 1.1 Kreisel, G. (1980). "Kurt Godel. 28 April 1906–14 January 1978". Biographical Memoirs of Fellows of the Royal Society 26 (26): 148–224. doi:10.1098/rsbm.1980.0005.
2. ↑ "Gödel". Merriam-Webster Dictionary. https://www.merriam-webster.com/dictionary/Gödel.
3. ↑ 3.0 3.1 For instance, in their "Principia Mathematica " (Stanford Encyclopedia of Philosophy edition).
4. ↑ Smullyan, R. M. (1992). Gödel's Incompleteness Theorems. New York, Oxford: Oxford University Press, ch. V.
5. ↑ Smullyan, R. M. (1992). Gödel's Incompleteness Theorems. New York, Oxford: Oxford University Press, ch. IX.
6. ↑ 6.0 6.1 "Rudolf Gödel". Encyklopedie dějin Brna. 2004. https://encyklopedie.brna.cz/home-mmb/?acc=profil-osobnosti&load=1977.
7. ↑ "Friedrich Redlich". Encyklopedie dějin Brna. 2004. https://encyklopedie.brna.cz/home-mmb/?acc=profil-osobnosti&load=11410.
8. ↑ "Friedrich Ignaz Anton Redlich". Encyklopedie dějin Brna. 2004. https://encyklopedie.brna.cz/home-mmb/?acc=profil-osobnosti&load=9201.
9. ↑ "Friedrich Sigmund Redlich". Encyklopedie dějin Brna. 2004. https://encyklopedie.brna.cz/home-mmb/?acc=profil-osobnosti&load=11454.
10. ↑ "Portrét ulice Václavská – Hybešova". Národní památkový ústav (National Heritage Institute). p. 3 ("Úvod"), 3rd column-2nd para. https://www.npu.cz/uop/brno/publikacni_cinnost/portrety_ulic/Portret_ulic_20210212.pdf.
11. ↑ "Kurt Gödel: Life, Work, and Legacy". Institute for Advanced Study, Princeton, New Jersey. September 11, 2009. https://www.ias.edu/kurt-gödel-life-work-and-legacy.
12. ↑ Procházka 2008, pp. 30–34.
13. ↑ Dawson 1997, p. 15.
14. ↑ Gödel, Kurt (1986). Collected works. Feferman, Solomon. Oxford: Oxford University Press. p. 37. ISBN 0-19-503964-5. OCLC 12371326. https://books.google.com/books?id=5ya4A0w62skC&pg=PA37.
15. ↑ Balaguer, Mark. "Kurt Godel". Encyclopædia Britannica, Inc.. https://school.eb.com/levels/high/article/Kurt-Gödel/37162.
16. ↑ Kim, Alan (January 1, 2015). Zalta, Edward N.. ed. Johann Friedrich Herbart (Winter 2015 ed.). Metaphysics Research Lab, Stanford University. http://plato.stanford.edu/archives/win2015/entries/johann-herbart/.
17. ↑ "Gabelsberger stenography | Gödel Enigma | University of Helsinki". https://www.helsinki.fi/en/researchgroups/godel-enigma/research/gabelsberger-stenography.
18. ↑ Parsons, Charles (2010). "Gödel and philosophical idealism". Philosophia Mathematica. Series III 18 (2): 166–192. doi:10.1093/philmat/nkq001.
19. ↑ Dawson 1997, p. 24.
20. ↑ At the University of Vienna, Gödel attended mathematics and philosophy courses side by side with Hermann Broch, who was in his early forties. See: Sigmund, Karl; Dawson Jr., John W.; Mühlberger, Kurt (2007). Kurt Kurt Gödel: Das Album. Springer-Verlag. p. 27. ISBN 978-3-8348-0173-9. https://books.google.com/books?id=BFgpBAAAQBAJ&pg=PA27.
21. ↑ Gleick, J. (2011) The Information: A History, a Theory, a Flood, London, Fourth Estate, p. 181.
22. ↑ 22.0 22.1 22.2 22.3 "In the Scope of Logic, Methodology and Philosophy of Science". 11th International Congress of Logic, Methodology and Philosophy of Science, Cracow, August 1999. 1. 2002. p. 291.
23. ↑ 23.0 23.1 23.2 Dawson Jr., John W., and Karl Sigmund. “Gödel’s Vienna.” Mathematical Intelligencer, vol. 28, no. 3, Summer 2006, Page 46. EBSCOhost, https://doi.org/10.1007/BF02986884.M
24. ↑ Dawson Jr., John W., and Karl Sigmund. “Gödel’s Vienna.” Mathematical Intelligencer, vol. 28, no. 3, Summer 2006, Page 52. EBSCOhost, https://doi.org/10.1007/BF02986884.M
25. ↑ Wang 1987. Page 80.
26. ↑ Brewer, William D. "Kurt Gödel: The Genius of Metamathematics". Springer Nature. 2022. Page 250
27. ↑ Toates, Frederick. Olga Coschug-Toates. "Obsessive Compulsive Disorder: Practical, Tried-and-tested Strategies to Overcome OCD." Class Publishing Ltd. 2002. Page 221.
28. ↑ Halmos, P.R. (April 1973). "The Legend of von Neumann". The American Mathematical Monthly 80 (4): 382–94. doi:10.1080/00029890.1973.11993293.
29. ↑ Stadler, Friedrich (2015) (in en). The Vienna Circle: Studies in the Origins, Development, and Influence of Logical Empiricism. Springer. ISBN 978-3-319-16561-5. https://books.google.com/books?id=2rAlCQAAQBAJ&q=Erkenntnis+1930+Konigsberg&pg=PA161.
30. ↑ Dawson 1997, pp. 61–63.
31. ↑ Nagel, Ernest (2001). Gödel's Proof. New York University Press. pp. 85–87.
32. ↑ Raatikainen, Panu (2015). Gödel's Incompleteness Theorems. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/goedel-incompleteness/.
33. ↑ Troelstra, A. S. (1988). Constructivism in Mathematics: An Introduction. 1. North-Holland. pp. 64–66.
34. ↑ Casti, John L.; Depauli, Werner (2001). Godel: A Life Of Logic, The Mind, And Mathematics. Cambridge, Mass.: Basic Books. ISBN 978-0-7382-0518-2. . From p. 80, which quotes Rudolf Gödel, Kurt's brother and a medical doctor. The words "a severe nervous crisis", and the judgment that Schlick's murder was its trigger, are Rudolf Gödel's. Rudolf knew Kurt well in those years.
35. ↑ Dawson 1997, pp. 110–12
36. ↑ Hutchinson Encyclopedia (1988), p. 518
37. ↑ Gödel, Kurt (November 9, 1938). "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". Proceedings of the National Academy of Sciences of the United States of America 24 (12): 556–57. doi:10.1073/pnas.24.12.556. ISSN 0027-8424. PMID 16577857. Bibcode: 1938PNAS...24..556G.
38. ↑ Dawson, John W. Jr. "Kurt Gödel at Notre Dame". p. 4. https://math.nd.edu/assets/13975/logicatndweb.pdf. "the Mathematics department at the University of Notre Dame was host ... for a single semester in the spring of 1939 [to] Kurt Gödel"
39. ↑ Dawson Jr, John W (October 2002). "Max Dehn, Kurt Gödel, and the Trans-Siberian Escape Route". Notices of the American Mathematical Society 49 (9): 1068–1075. https://www.ams.org/notices/200209/fea-dawson.pdf.
40. ↑ "The spy who flunked it: Kurt Gödel's forgotten part in the atom-bomb story". Nature 627 (8002): 26–28. March 2024. doi:10.1038/d41586-024-00644-1. PMID 38438543. Bibcode: 2024Natur.627...26S.
41. ↑ "Kurt Gödel". December 9, 2019. https://www.ias.edu/scholars/godel.
42. ↑ Goldstein 2005, p. 33
43. ↑ Suber, Peter (August 27, 1992). "50 Years Later, The Questions Remain: Kurt Gödel in Blue Hill". http://nrs.harvard.edu/urn-3:HUL.InstRepos:4725029.
44. ↑ Dawson 1997, pp. 179–80. The story of Gödel's citizenship hearing has many versions. Dawson's account is the most carefully researched, but was written before the rediscovery of Morgenstern's written account. Most other accounts appear to be based on Dawson, hearsay, or speculation.
45. ↑ Oskar Morgenstern (September 13, 1971). "History of the Naturalization of Kurt Gödel". https://robert.accettura.com/wp-content/uploads/2010/10/Morgenstern_onGoedelcitizenship.pdf.
46. ↑ "Kurt Gödel – Institute for Advanced Study". https://www.ias.edu/people/godel.
47. ↑ Gödel, Kurt (July 1, 1949). "An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation". Rev. Mod. Phys. 21 (447): 447–450. doi:10.1103/RevModPhys.21.447. Bibcode: 1949RvMP...21..447G.
48. ↑ "Das Genie & der Wahnsinn" (in de). Der Tagesspiegel. January 13, 2008. http://www.tagesspiegel.de/magazin/wissen/Albert-Einstein-Kurt-Goedel;art304,2454513.
49. ↑ Dawson, John W. Jr. (2005). Logical Dilemmas: The Life and Work of Kurt Gödel.. A K Peters. p. 166. ISBN 978-1-56881-256-4. https://books.google.com/books?id=gA8SucCU1AYC&q=godel+leibniz&pg=PA166.
50. ↑ "The President's National Medal of Science: Recipient Details | NSF – National Science Foundation". https://www.nsf.gov/od/nms/recip_details.jsp?recip_id=138.
51. ↑ "APS Member History". https://search.amphilsoc.org/memhist/search?creator=Kurt+Gödel&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced.
52. ↑ Gödel, Kurt (1950). "Rotating universes in general relativity theory". In: Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, August 30–September 6, 1950. 1. pp. 175–81. http://www.mathunion.org/ICM/ICM1950.1/Main/icm1950.1.0175.0181.ocr.pdf. Retrieved December 4, 2017.
53. ↑ Brewer, William D. "Kurt Gödel: The Genius of Metamathematics". Springer Nature. 2022. Pages 209-210
54. ↑ Bausek, Nina; Stefan Washietl (February 20, 2018). "Tragic deaths in science: Kurt Gödel — looking over the edge of reason". https://paperpile.com/blog/kurt-goedel/.
55. ↑ Davis, Martin (May 4, 2005). "Gödel's universe". Nature 435 (7038): 19–20. doi:10.1038/435019a. Bibcode: 2005Natur.435...19D.
56. ↑ Toates, Frederick; Olga Coschug Toates (2002). Obsessive Compulsive Disorder: Practical Tried-and-Tested Strategies to Overcome OCD. Class Publishing. p. 221. ISBN 978-1-85959-069-0.
57. ↑ Dawson, John W. (June 1, 2006). "Gödel and the limits of logic" (in en). University of Cambridge. https://plus.maths.org/content/goumldel-and-limits-logic.
58. ↑ Tucker McElroy (2005). A to Z of Mathematicians. Infobase Publishing. p. 118. ISBN 978-0-8160-5338-4. https://archive.org/details/tozofmathematici0000mcel/page/118. "Gödel had a happy childhood, and was called "Mr. Why" by his family, due to his numerous questions. He was baptized as a Lutheran, and remained a theist (a believer in a personal God) throughout his life."
59. ↑ Wang 1996, p. 8.
60. ↑ Wang 1996, p. 104-105.
61. ↑ Feldman, Burton. 112 Mercer Street: Einstein, Russell, Gödel, Pauli, and the End of Innocence in Science. Arcade Publishing. 2007. Page 7.
62. ↑ Gödel's answer to a special questionnaire sent him by the sociologist Burke Grandjean. This answer is quoted directly in Wang 1987, p. 18, and indirectly in Wang 1996, p. 112\. It is also quoted directly in Dawson 1997, p. 6, who cites Wang 1987. The Grandjean questionnaire is perhaps the most extended autobiographical item in Gödel's papers. Gödel filled it out in pencil and wrote a cover letter, but did not return it. "Theistic" is italicized in both Wang 1987 and Wang 1996. It is possible that this italicization is Wang's and not Gödel's. The quote follows Wang 1987, with two corrections taken from Wang 1996. Wang 1987 reads "Baptist Lutheran" where Wang 1996 has "baptized Lutheran". Wang 1987 has "rel. cong.", which in Wang 1996 is expanded to "religious congregation".
63. ↑ Gödel, Kurt (2003). "Marianne Gödel". in Feferman, Solomon (in en). Kurt Gödel: Collected Works: Volume IV. OUP Oxford. p. 425. doi:10.1093/oso/9780198500735.003.0018. ISBN 978-0-19-968961-3. https://books.google.com/books?id=UZnlAgAAQBAJ&dq=“Religions+are,+for+the+most+part,+bad"&pg=PA425. "Godel was not unmoved by religious concerns. On the contrary, his library included many books and tracts devoted to various religious sects; among his notebooks are two devoted to theology; and in a shorthand manuscript found in his Nachlaß he wrote, "Die Religionen sind zum größten Teil schlecht, aber nicht die Religion." ("Religions are for the most part bad, but not religion itself.")"
64. ↑ Wang 1996, p. 51.
65. ↑ Wang 1996, p. 148, 4.4.3. It is one of Gödel's observations, made between November 16 and December 7, 1975, that Wang found hard to classify under the main topics considered elsewhere in the book.
66. ↑ A. K. Peters, Wellesley, MA, ISBN 1-56881-256-6
67. ↑ W. W. Norton & Company, New York City, ISBN 978-0-393-35820-9
68. ↑ "Times Critics' Top Books of 2021". The New York Times. December 15, 2021. https://www.nytimes.com/2021/12/15/books/critics-top-books-2021.html.
69. ↑ "Dangerous Knowledge". BBC. June 11, 2008. https://www.bbc.co.uk/bbcfour/documentaries/features/dangerous-knowledge.shtml.
70. ↑ "Kurt-Gödel-Forschungsstelle: die "Philosophischen Bemerkungen" Kurt Gödels (Kurt Gödel Research Centre: The 'Philosophical Remarks' of Kurt Gödel) – Berlin-Brandenburg Academy of Sciences and Humanities". https://www.bbaw.de/en/research/kurt-goedel-forschungsstelle-die-philosophischen-bemerkungen-kurt-goedels-kurt-goedel-research-centre-the-philosophical-remarks-of-kurt-goedel.
71. ↑ "The Academy – Berlin-Brandenburg Academy of Sciences and Humanities". https://www.bbaw.de/en/the-academy.
72. ↑ Kurt Godel (1931). "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I". Monatshefte für Mathematik und Physik 38: 173–98. doi:10.1007/BF01700692. http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf.

## Sources

* Dawson, John W (1997), Logical dilemmas: The life and work of Kurt Gödel, Wellesley, MA: AK Peters, https://archive.org/details/logicaldilemmasl0000daws .
* Goldstein, Rebecca (2005), Incompleteness: The Proof and Paradox of Kurt Gödel, New York: W.W. Norton & Co, ISBN 978-0-393-32760-1, https://books.google.com/books?id=tXk2AAAAQBAJ .
* Wang, Hao (1987), Reflections on Kurt Gödel, Cambridge: MIT Press, ISBN 0-262-73087-1, https://books.google.com/books?id=wLLePwhDOMYC
* Wang, Hao (1996), A Logical Journey: From Gödel to Philosophy, Cambridge: MIT Press, ISBN 0-262-23189-1, https://books.google.com/books?id=pckvCy6L_ocC

## Further reading

* Brewer, William D. (2022). Kurt Gödel: The Genius of Metamathematics. Cham: Springer. ISBN 978-3-031-11308-6.
* Stephen Budiansky, 2021. Journey to the Edge of Reason: The Life of Kurt Gödel. W.W. Norton & Company.
* Casti, John L; DePauli, Werner (2000), Gödel: A Life of Logic, Cambridge, MA: Basic Books (Perseus Books Group), ISBN 978-0-7382-0518-2 .
* Dawson, John W Jr (1999), "Gödel and the Limits of Logic", Scientific American 280 (6): 76–81, doi:10.1038/scientificamerican0699-76, PMID 10048234, Bibcode: 1999SciAm.280f..76D .
* Franzén, Torkel (2005), Gödel's Theorem: An Incomplete Guide to Its Use and Abuse, Wellesley, MA: AK Peters .
* Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870–1940. Princeton Univ. Press.
* Hämeen-Anttila, Maria (2020). Gödel on Intuitionism and Constructive Foundations of Mathematics (Ph.D. thesis). Helsinki: University of Helsinki. ISBN 978-951-51-5922-9. http://urn.fi/URN:ISBN:978-951-51-5923-6.
* Jaakko Hintikka, 2000. On Gödel. Wadsworth.
* Dirk W. Hoffmann (2024). Gödel's Incompleteness Theorems. Berlin, Heidelberg: Springer. ISBN 978-3-662-69549-4.
* Douglas Hofstadter, 1980. Gödel, Escher, Bach. Vintage.
* Stephen Kleene, 1967. Mathematical Logic. Dover paperback reprint c. 2001.
* Stephen Kleene, 1980. Introduction to Metamathematics. North Holland ISBN 0-7204-2103-9 (Ishi Press paperback. 2009. ISBN 978-0-923891-57-2)
* J.R. Lucas, 1970. The Freedom of the Will. Clarendon Press, Oxford.
* Ernest Nagel and Newman, James R., 1958. Gödel's Proof. New York Univ. Press.
* Hal Prince (2022). The Annotated Gödel. Homebred Press. ISBN 979-8-9864142-0-1.
* Ed Regis, 1987. Who Got Einstein's Office? Addison-Wesley Publishing Company, Inc.
* Raymond Smullyan, 1992. Godel's Incompleteness Theorems. Oxford University Press.
* Olga Taussky-Todd, 1983. Remembrances of Kurt Gödel. Engineering & Science, Winter 1988.
* Yourgrau, Palle, 1999. Gödel Meets Einstein: Time Travel in the Gödel Universe. Chicago: Open Court.
* Yourgrau, Palle, 2004. A World Without Time: The Forgotten Legacy of Gödel and Einstein. Basic Books. ISBN 978-0-465-09293-2. (Reviewed by John Stachel in the Notices of the American Mathematical Society (54 (7), pp. 861–68).

## External links

* Weisstein, Eric Wolfgang, ed. "Gödel, Kurt (1906–1978)". http://scienceworld.wolfram.com/biography/Goedel.html.
* Kennedy, Juliette. "Kurt Gödel". in Zalta, Edward N.. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/goedel/.
* Time Bandits: an article about the relationship between Gödel and Einstein by Jim Holt
* Notices of the AMS, April 2006, Volume 53, Number 4 Kurt Gödel Centenary Issue
* Paul Davies and Freeman Dyson discuss Kurt Godel (transcript)
* "Gödel and the Nature of Mathematical Truth" Edge: A Talk with Rebecca Goldstein on Kurt Gödel.
* It's Not All In The Numbers: Gregory Chaitin Explains Gödel's Mathematical Complexities.
* Gödel photo gallery. (archived)
* Kurt Gödel MacTutor History of Mathematics archive page
* National Academy of Sciences Biographical Memoir

* v
* t
* e

United States National Medal of Science laureates

Behavioral and social science

| 1960s|

1964
Roger Adams
Othmar H. Ammann
Theodosius Dobzhansky
Neal Elgar Miller

|

1980s|

1986
Herbert A. Simon
1987
Anne Anastasi
George J. Stigler
1988
Milton Friedman

1990s|

1990
Leonid Hurwicz
Patrick Suppes
1991
Robert W. Kates
George A. Miller
1992
Eleanor J. Gibson
1994
Robert K. Merton
1995
Roger N. Shepard
1996
Paul Samuelson
1997
William K. Estes
1998
William Julius Wilson
1999
Robert M. Solow

2000s|

2000
Gary Becker
2001
George Bass
2003
R. Duncan Luce
2004
Kenneth Arrow
2005
Gordon H. Bower
2008
Michael I. Posner
2009
Mortimer Mishkin

2010s|

2011
Anne Treisman
2014
Robert Axelrod
2015
Albert Bandura

Biological sciences

| 1960s|

1963
C. B. van Niel
1964
Marshall W. Nirenberg
1965
Francis P. Rous
George G. Simpson
Donald D. Van Slyke
1966
Edward F. Knipling
Fritz Albert Lipmann
William C. Rose
Sewall Wright
1967
Kenneth S. Cole
Harry F. Harlow
Michael Heidelberger
Alfred H. Sturtevant
1968
Horace Barker
Bernard B. Brodie
Detlev W. Bronk
Jay Lush
Burrhus Frederic Skinner
1969
Robert Huebner
Ernst Mayr

|

1970s|

1970
Barbara McClintock
Albert B. Sabin
1973
Daniel I. Arnon
Earl W. Sutherland Jr.
1974
Britton Chance
Erwin Chargaff
James V. Neel
James Augustine Shannon
1975
Hallowell Davis
Paul Gyorgy
Sterling B. Hendricks
Orville Alvin Vogel
1976
Roger Guillemin
Keith Roberts Porter
Efraim Racker
E. O. Wilson
1979
Robert H. Burris
Elizabeth C. Crosby
Arthur Kornberg
Severo Ochoa
Earl Reece Stadtman
George Ledyard Stebbins
Paul Alfred Weiss

1980s|

1981
Philip Handler
1982
Seymour Benzer
Glenn W. Burton
Mildred Cohn
1983
Howard L. Bachrach
Paul Berg
Wendell L. Roelofs
Berta Scharrer
1986
Stanley Cohen
Donald A. Henderson
Vernon B. Mountcastle
George Emil Palade
Joan A. Steitz
1987
Michael E. DeBakey
Theodor O. Diener
Harry Eagle
Har Gobind Khorana
Rita Levi-Montalcini
1988
Michael S. Brown
Stanley Norman Cohen
Joseph L. Goldstein
Maurice R. Hilleman
Eric R. Kandel
Rosalyn Sussman Yalow
1989
Katherine Esau
Viktor Hamburger
Philip Leder
Joshua Lederberg
Roger W. Sperry
Harland G. Wood

1990s|

1990
Baruj Benacerraf
Herbert W. Boyer
Daniel E. Koshland Jr.
Edward B. Lewis
David G. Nathan
E. Donnall Thomas
1991
Mary Ellen Avery
G. Evelyn Hutchinson
Elvin A. Kabat
Salvador Luria
Paul A. Marks
Folke K. Skoog
Paul C. Zamecnik
1992
Maxine Singer
Howard Martin Temin
1993
Daniel Nathans
Salome G. Waelsch
1994
Thomas Eisner
Elizabeth F. Neufeld
1995
Alexander Rich
1996
Ruth Patrick
1997
James Watson
Robert A. Weinberg
1998
Bruce Ames
Janet Rowley
1999
David Baltimore
Jared Diamond
Lynn Margulis

2000s|

2000
Nancy C. Andreasen
Peter H. Raven
Carl Woese
2001
Francisco J. Ayala
Mario R. Capecchi
Ann Graybiel
Gene E. Likens
Victor A. McKusick
Harold Varmus
2002
James E. Darnell
Evelyn M. Witkin
2003
J. Michael Bishop
Solomon H. Snyder
Charles Yanofsky
2004
Norman E. Borlaug
Phillip A. Sharp
Thomas E. Starzl
2005
Anthony S. Fauci
Torsten N. Wiesel
2006
Rita R. Colwell
Nina Fedoroff
Lubert Stryer
2007
Robert J. Lefkowitz
Bert W. O'Malley
2008
Francis S. Collins
Elaine Fuchs
J. Craig Venter
2009
Susan L. Lindquist
Stanley B. Prusiner

2010s|

2010
Ralph L. Brinster
Shu Chien
Rudolf Jaenisch
2011
Lucy Shapiro
Leroy Hood
Sallie Chisholm
2014
May Berenbaum
Bruce Alberts
2015
Stanley Falkow
Rakesh K. Jain
Mary-Claire King
Simon Levin

Chemistry

| 1980s|

1982
F. Albert Cotton
Gilbert Stork
1983
Roald Hoffmann
George C. Pimentel
Richard N. Zare
1986
Harry B. Gray
Yuan Tseh Lee
Carl S. Marvel
Frank H. Westheimer
1987
William S. Johnson
Walter H. Stockmayer
Max Tishler
1988
William O. Baker
Konrad E. Bloch
Elias J. Corey
1989
Richard B. Bernstein
Melvin Calvin
Rudolph A. Marcus
Harden M. McConnell

|

1990s|

1990
Elkan Blout
Karl Folkers
John D. Roberts
1991
Ronald Breslow
Gertrude B. Elion
Dudley R. Herschbach
Glenn T. Seaborg
1992
Howard E. Simmons Jr.
1993
Donald J. Cram
Norman Hackerman
1994
George S. Hammond
1995
Thomas Cech
Isabella L. Karle
1996
Norman Davidson
1997
Darleane C. Hoffman
Harold S. Johnston
1998
John W. Cahn
George M. Whitesides
1999
Stuart A. Rice
John Ross
Susan Solomon

2000s|

2000
John D. Baldeschwieler
Ralph F. Hirschmann
2001
Ernest R. Davidson
Gábor A. Somorjai
2002
John I. Brauman
2004
Stephen J. Lippard
2006
Marvin H. Caruthers
Peter B. Dervan
2007
Mostafa A. El-Sayed
2008
Joanna Fowler
JoAnne Stubbe
2009
Stephen J. Benkovic
Marye Anne Fox

2010s|

2010
Jacqueline K. Barton
Peter J. Stang
2011
Allen J. Bard
M. Frederick Hawthorne
2014
Judith P. Klinman
Jerrold Meinwald
2015
A. Paul Alivisatos
Geraldine L. Richmond

Engineering sciences

| 1960s|

1962
Theodore von Kármán
1963
Vannevar Bush
John Robinson Pierce
1964
Charles S. Draper
1965
Hugh L. Dryden
Clarence L. Johnson
Warren K. Lewis
1966
Claude E. Shannon
1967
Edwin H. Land
Igor I. Sikorsky
1968
J. Presper Eckert
Nathan M. Newmark
1969
Jack St. Clair Kilby

|

1970s|

1970
George E. Mueller
1973
Harold E. Edgerton
Richard T. Whitcomb
1974
Rudolf Kompfner
Ralph Brazelton Peck
Abel Wolman
1975
Manson Benedict
William Hayward Pickering
Frederick E. Terman
Wernher von Braun
1976
Morris Cohen
Peter C. Goldmark
Erwin Wilhelm Müller
1979
Emmett N. Leith
Raymond D. Mindlin
Robert N. Noyce
Earl R. Parker
Simon Ramo

1980s|

1982
Edward H. Heinemann
Donald L. Katz
1983
Bill Hewlett
George Low
John G. Trump
1986
Hans Wolfgang Liepmann
Tung-Yen Lin
Bernard M. Oliver
1987
Robert Byron Bird
H. Bolton Seed
Ernst Weber
1988
Daniel C. Drucker
Willis M. Hawkins
George W. Housner
1989
Harry George Drickamer
Herbert E. Grier

1990s|

1990
Mildred Dresselhaus
Nick Holonyak Jr.
1991
George H. Heilmeier
Luna B. Leopold
H. Guyford Stever
1992
Calvin F. Quate
John Roy Whinnery
1993
Alfred Y. Cho
1994
Ray W. Clough
1995
Hermann A. Haus
1996
James L. Flanagan
C. Kumar N. Patel
1998
Eli Ruckenstein
1999
Kenneth N. Stevens

2000s|

2000
Yuan-Cheng B. Fung
2001
Andreas Acrivos
2002
Leo Beranek
2003
John M. Prausnitz
2004
Edwin N. Lightfoot
2005
Jan D. Achenbach
Tobin J. Marks
2006
Robert S. Langer
2007
David J. Wineland
2008
Rudolf E. Kálmán
2009
Amnon Yariv

2010s|

2010
Shu Chien
2011
John B. Goodenough
2014
Thomas Kailath

Mathematical, statistical, and computer sciences

| 1960s|

1963
Norbert Wiener
1964
Solomon Lefschetz
H. Marston Morse
1965
Oscar Zariski
1966
John Milnor
1967
Paul Cohen
1968
Jerzy Neyman
1969
William Feller

|

1970s|

1970
Richard Brauer
1973
John Tukey
1974
Kurt Gödel
1975
John W. Backus
Shiing-Shen Chern
George Dantzig
1976
Kurt Otto Friedrichs
Hassler Whitney
1979
Joseph L. Doob
Donald E. Knuth

1980s|

1982
Marshall Harvey Stone
1983
Herman Goldstine
Isadore Singer
1986
Peter Lax
Antoni Zygmund
1987
Raoul Bott
Michael Freedman
1988
Ralph E. Gomory
Joseph B. Keller
1989
Samuel Karlin
Saunders Mac Lane
Donald C. Spencer

1990s|

1990
George F. Carrier
Stephen Cole Kleene
John McCarthy
1991
Alberto Calderón
1992
Allen Newell
1993
Martin David Kruskal
1994
John Cocke
1995
Louis Nirenberg
1996
Richard Karp
Stephen Smale
1997
Shing-Tung Yau
1998
Cathleen Synge Morawetz
1999
Felix Browder
Ronald R. Coifman

2000s|

2000
John Griggs Thompson
Karen Uhlenbeck
2001
Calyampudi R. Rao
Elias M. Stein
2002
James G. Glimm
2003
Carl R. de Boor
2004
Dennis P. Sullivan
2005
Bradley Efron
2006
Hyman Bass
2007
Leonard Kleinrock
Andrew J. Viterbi
2009
David B. Mumford

2010s|

2010
Richard A. Tapia
S. R. Srinivasa Varadhan
2011
Solomon W. Golomb
Barry Mazur
2014
Alexandre Chorin
David Blackwell
2015
Michael Artin

Physical sciences

| 1960s|

1963
Luis W. Alvarez
1964
Julian Schwinger
Harold Clayton Urey
Robert Burns Woodward
1965
John Bardeen
Peter Debye
Leon M. Lederman
William Rubey
1966
Jacob Bjerknes
Subrahmanyan Chandrasekhar
Henry Eyring
John H. Van Vleck
Vladimir K. Zworykin
1967
Jesse Beams
Francis Birch
Gregory Breit
Louis Hammett
George Kistiakowsky
1968
Paul Bartlett
Herbert Friedman
Lars Onsager
Eugene Wigner
1969
Herbert C. Brown
Wolfgang Panofsky

|

1970s|

1970
Robert H. Dicke
Allan R. Sandage
John C. Slater
John A. Wheeler
Saul Winstein
1973
Carl Djerassi
Maurice Ewing
Arie Jan Haagen-Smit
Vladimir Haensel
Frederick Seitz
Robert Rathbun Wilson
1974
Nicolaas Bloembergen
Paul Flory
William Alfred Fowler
Linus Carl Pauling
Kenneth Sanborn Pitzer
1975
Hans A. Bethe
Joseph O. Hirschfelder
Lewis Sarett
Edgar Bright Wilson
Chien-Shiung Wu
1976
Samuel Goudsmit
Herbert S. Gutowsky
Frederick Rossini
Verner Suomi
Henry Taube
George Uhlenbeck
1979
Richard P. Feynman
Herman Mark
Edward M. Purcell
John Sinfelt
Lyman Spitzer
Victor F. Weisskopf

1980s|

1982
Philip W. Anderson
Yoichiro Nambu
Edward Teller
Charles H. Townes
1983
E. Margaret Burbidge
Maurice Goldhaber
Helmut Landsberg
Walter Munk
Frederick Reines
Bruno B. Rossi
J. Robert Schrieffer
1986
Solomon J. Buchsbaum
H. Richard Crane
Herman Feshbach
Robert Hofstadter
Chen-Ning Yang
1987
Philip Abelson
Walter Elsasser
Paul C. Lauterbur
George Pake
James A. Van Allen
1988
D. Allan Bromley
Paul Ching-Wu Chu
Walter Kohn
Norman F. Ramsey
Jack Steinberger
1989
Arnold O. Beckman
Eugene Parker
Robert Sharp
Henry Stommel

1990s|

1990
Allan M. Cormack
Edwin M. McMillan
Robert Pound
Roger Revelle
1991
Arthur L. Schawlow
Ed Stone
Steven Weinberg
1992
Eugene M. Shoemaker
1993
Val Fitch
Vera Rubin
1994
Albert Overhauser
Frank Press
1995
Hans Dehmelt
Peter Goldreich
1996
Wallace S. Broecker
1997
Marshall Rosenbluth
Martin Schwarzschild
George Wetherill
1998
Don L. Anderson
John N. Bahcall
1999
James Cronin
Leo Kadanoff

2000s|

2000
Willis E. Lamb
Jeremiah P. Ostriker
Gilbert F. White
2001
Marvin L. Cohen
Raymond Davis Jr.
Charles Keeling
2002
Richard Garwin
W. Jason Morgan
Edward Witten
2003
G. Brent Dalrymple
Riccardo Giacconi
2004
Robert N. Clayton
2005
Ralph A. Alpher
Lonnie Thompson
2006
Daniel Kleppner
2007
Fay Ajzenberg-Selove
Charles P. Slichter
2008
Berni Alder
James E. Gunn
2009
Yakir Aharonov
Esther M. Conwell
Warren M. Washington

2010s|

2011
Sidney Drell
Sandra Faber
Sylvester James Gates
2012
Burton Richter
Sean C. Solomon
2014
Shirley Ann Jackson

* v
* t
* e

Analytic philosophy

Related articles|

| Areas of focus|

* Epistemology
* Language
* Mathematics
* Science

|

Turns|

* Aretaic
* Linguistic

Logic|

* Classical
* Mathematical
* Non-classical
* Philosophical

Theories|

* Anti-realism
* Australian realism
* Descriptivist theory of names
* Emotivism
* Functionalism
* Analytical feminism
* Logical atomism
* Logical positivism
* Analytical Marxism
* Neopragmatism
* Neurophilosophy
* Ordinary language
* Quietism
* Scientific structualism
* Sense data

Concepts|

* Analysis (Paradox)
* Analytic–synthetic distinction
* Counterfactual
* Natural kind
* Reflective equilibrium
* Supervenience

| Modality|

* Actualism
* Necessity
* Possibility
* Possible world
* Realism
* Rigid designator

|

Philosophers|

* Nick Bostrom
* Noam Chomsky
* Patricia Churchland
* David Chalmers
* James F. Conant
* Alice Crary
* Daniel Dennett
* Cora Diamond
* Keith Donnellan
* Paul Feyerabend
* Bas van Fraassen
* Gottlob Frege
* Jerry Fodor
* Ian Hacking
* Jaegwon Kim
* Alasdair MacIntyre
* J. L. Mackie
* Ruth Millikan
* Ernest Nagel
* Thomas Nagel
* Derek Parfit
* Karl Popper
* Graham Priest
* John Searle
* Peter Singer
* J. J. C. Smart
* Ernest Sosa
* Barry Stroud
* Charles Taylor
* Michael Walzer

| Cambridge|

* Charlie Broad
* Norman Malcolm
* G. E. Moore
* Bertrand Russell
* Frank P. Ramsey
* Ludwig Wittgenstein

|

Oxford|

* G. E. M. Anscombe
* J. L. Austin
* A. J. Ayer
* Michael Dummett
* Antony Flew
* Philippa Foot
* Peter Geach
* Paul Grice
* R. M. Hare
* Gilbert Ryle
* P. F. Strawson
* Richard Swinburne
* Bernard Williams
* Timothy Williamson

Berlin Circle|

* Carl Gustav Hempel
* Hans Reichenbach

Vienna Circle|

* Rudolf Carnap
* Kurt Gödel
* Otto Neurath
* Moritz Schlick

Harvard|

* Roderick Chisholm
* Donald Davidson
* Nelson Goodman
* Christine Korsgaard
* Thomas Kuhn
* Robert Nozick
* Hilary Putnam
* W. V. O. Quine
* John Rawls

Pittsburgh School|

* Robert Brandom
* John McDowell
* Nicholas Rescher
* Wilfrid Sellars

Princeton|

* David Lewis
* Saul Kripke
* Richard Rorty

Notre Dame|

* Robert Audi
* Peter van Inwagen
* Alvin Plantinga

* Category
* Index

* v
* t
* e

Platonists

Academics|

| Old|

* Plato
* Aristotle
* Eudoxus
* Philip of Opus
* Aristonymus
* Coriscus and Erastus of Scepsis
* Demetrius of Amphipolis
* Euaeon of Lampsacus
* Heraclides and Python of Aenus
* Hestiaeus of Perinthus
* Lastheneia of Mantinea
* Timolaus of Cyzicus
* Speusippus
* Axiothea of Phlius
* Heraclides Ponticus
* Menedemus of Pyrrha
* Xenocrates
* Crantor
* Polemon
* Crates of Athens

|

Skeptics|

| Middle|

* Arcesilaus
* Diocles of Cnidus
* Lacydes
* Telecles and Evander
* Hegesinus

|

New|

* Carneades
* Hagnon of Tarsus
* Metrodorus of Stratonicea
* Clitomachus
* Charmadas
* Aeschines of Neapolis
* Philo of Larissa
* Cicero
* Dio of Alexandria

Middle Platonists|

* Antiochus
* Philo of Alexandria
* Plutarch
* Justin Martyr
* Gaius
* Albinus
* Alcinous
* Apuleius
* Atticus
* Maximus of Tyre
* Numenius of Apamea
* Longinus
* Clement of Alexandria
* Origen the Pagan
* Calcidius

Neoplatonists|

| Ancient|

* Ammonius Saccas
* Plotinus
* Disciples
* Origen
* Amelius
* Porphyry
* Iamblichus
* Sopater
* Eustathius of Cappadocia
* Sosipatra
* Aedesius
* Dexippus
* Chrysanthius
* Theodorus of Asine
* Julian
* Sallustius
* Maximus of Ephesus
* Eusebius of Myndus
* Priscus of Epirus
* Antoninus
* Gregory of Nyssa
* Hypatia
* Augustine
* Macrobius

| Academy|

* Plutarch of Athens
* Asclepigenia
* Hierocles
* Syrianus
* Hermias
* Aedesia
* Proclus
* Ammonius Hermiae
* Asclepiodotus
* Hegias
* Zenodotus
* Marinus
* Agapius
* Isidore
* Damascius
* Simplicius
* Priscian

|

Medieval|

* Boethius
* John Philoponus
* Olympiodorus
* Pseudo-Dionysius the Areopagite
* John Scotus Eriugena

| Islamic Golden Age|

* Al-Farabi

|

* Anselm
* Peter Abelard

Chartres|

* Bernard
* Gilbert
* Thierry

|

* Henry of Ghent
* Bonaventure
* Meister Eckhart
* Paul of Venice

Modern|

| Renaissance|

| Florentine Academy|

* Plethon
* Marsilio Ficino
* Cristoforo Landino
* Giovanni Pico della Mirandola

|

Cambridge|

* Ralph Cudworth
* Henry More
* Anne Conway

* Petrus Ramus
* Giordano Bruno
* Blaise Pascal
* Emanuel Swedenborg

German idealists|

* Gottfried Wilhelm Leibniz
* Christian Wolff
* Moses Mendelssohn
* Immanuel Kant
* Johann Gottlieb Fichte
* Friedrich Wilhelm Joseph Schelling
* G. W. F. Hegel
* Hermann Lotze

|

* Thomas Taylor
* Ralph Waldo Emerson
* Josiah Royce
* Søren Kierkegaard
* Henri Bergson
* Aleksei Losev

Contemporary|

* Bernard Bolzano
* Philip K. Dick
* Joseph Ratzinger

| Analytic|

* Gottlob Frege
* G. E. Moore
* Kurt Gödel
* Alonzo Church
* Roderick Chisholm
* Michael Dummett
* W. V. O. Quine
* David Kaplan
* Saul Kripke
* Alvin Plantinga
* Peter van Inwagen
* Nicholas Wolterstorff
* Crispin Wright
* Edward N. Zalta

|

Continental|

* Edmund Husserl
* Roman Ingarden
* Leo Strauss

Categories|

Platonism

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Kurt Gödel. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Biography:Kurt_Gödel&oldid=4223752"
*[c.]: circa
*[m.]: married
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template