Briefly Gödel

Kurt Gödel
briefly Gödel

briefly Gödel (* 28. April 1906 in Brünn, Austria Hungary, today Brno, Tschechien; † 14. January 1978 in Princeton, new jersey) was a mathematician and logician. Gödel becomes of many as thatmost important logicians 20. Century outstandingly. It has relevant contributions within the range of the predicate calculus (decision problem) as well as carried out to the classical and intuitionistic statement calculation.

Table of contents

youth and study

Gödel originated from a wealthy largecivil family in Brünn in Mähren. The city had a German-language population majority at the birth time Gödels and lay until 1918 in the Austrian part of the Austrian-Hungarian monarchy (today: Tschechien). Its parents were Marianne (geb. Glove) and Rudolf August Gödel. Its father was to prosperity of arrived textile entrepreneurs. The father was catholic, the nut/mother Evangelist, the children of the familywere Evangelist educated. Gödel, which, caused through rheumatism table fever, often suffered in its childhood from a bad state of health, showed nevertheless school best performances. 1912 occurred Gödel the private-people and citizen school, four years later the German-language imperial andRoyal state material High School. After the First World War the city became Brünn 1918/19 part of the again created Czechoslovakian republic. Gödel, which spoke hardly Czech, did not feel domestic in the again-created state and, like it his later bio count JohnD. Dawson said, like a “Austrian banishing in Tschechoslowakien”. It accepted 1923 the Austrian nationality, pulled to the autumn 1924 to Vienna and wrote themselves there first in the course of studies for theoretical physics. It was occupied in the following year mainlywith physical topics. In addition it visited also the philosophical lecture of Heinrich Gomperz as well as the lecture on the number theory of Philipp Furtwängler. These two professors gave the crucial impulses to Gödel to argue intensively with the bases of mathematics whichon the formal logic as well as the set theory are based. Briefly after beginning of its course of studies it began to visit the Viennese circle, an academic circle, that by Moritz mud in the life called itself and with the methodical bases of thinking andthus the bases of jedweder philosophy argued. The discussions with the other members of the group, of which in particular Hans's cock, Karl Menger as well as Olga Taussky for Gödel of special importance were, led likewise to the extension of its mathematical knowledge. Also infamily regard were the meetings of the circle for it of importance, since it met here 1927 for the first time its later Mrs ennobling Porkert. When it pulled in July 1928 with its brother into a new dwelling within Vienna, foundthis coincidentally directly opposite the dwelling of ennobles itself Porkert. Under this neighbourhood the two were received only now a relationship, which was disturbed however by Kurts parents due to social reservations.

Gödels innovative scientific achievements (1929-1938)

Fascinated of the discussions in the Viennese circle visited Gödel the mathematical colloquium of Karl Menger and was in particular made familiar with the current basic problems of mathematics and logic as well as with the Hilbertprogramm the complete provableness of mathematics here. Among other thingsbelonged therefore the first edition of the writing of fundamentals of the theoretical logic of David Hilbert and William field man to its reading, those the main basis for its own thesis over the completeness of the closer calculation of the predicate calculus of first stage (exact title: Over the completeness of the logic calculus) of 1929 will should. Those became briefly Gödel for this first-class work to 6. February 1930 lent.

The thirties were mainly coined/shaped of scientific work for Gödel, those first in connection alsostood for the feasibility of the Hilbert program. If Gödels first work could have been considered still as a reference to the feasibility of the project to a complete logical proof of mathematics, then its most important work, which it published in the year 1931, was the endthe dream by David Hilbert. In the work, which carried the title over formally unentscheidbare sets of the Principia mathematica and related systems, Gödel proved the incompleteness set. This means that any class of formulas k not logically completely withinthe formula system formed by k to be proven can, because otherwise k would not be assertible. That means in other words that there are formally unentscheidbare sentences within the system k. (Simple paradox, which clarifies the logical Grundproblem: „This sentence is not provably. “) Only by the introduction of a more powerful formula system ω, which covers k, k can be completely proven. The meant that all sets of mathematics could be proven only by a system, which powerful than the quantity all mathematicalSentences was. Thus the Hilbert program for the complete provableness of mathematics had failed, since it could be based only on mathematical formulas.

The logician Paul Cohen could show 1963 that both the axiom of choice and the continuum hypothesis on basis of the axioms the Zermelo Fraenkel set theory are formally unentscheidbar.

By its innovative work and the astonishing results, which followed from it, Gödel was finally recognized as one of the prominent logicians of its time. That led among other things to the fact that Gödel of its American colleague Oswald Veblen after Princeton was invited into again-created institutes for the Advanced Study. From 1933 to 1934 it traveled for the first time to America and became there common with James Alexander, John von Neumann and Oswald Veblen initial member thatFaculty. However its psychological illness, which it carried probably latently since its childhood days in itself began itself, to make noticeable for the first time in the form of depressive tendencies and hypochondrischen obsessions in this time. This mental load was howeverto attribute only to personal influences. Out our current view ever more threateningly becoming political situation in Europe only by the few was registered and Gödel was interested at that time in it not at all.

When Gödel returned in the spring 1934 to Vienna, hadit already receive the invitation for a further lecturer activity in Princeton. The death of his Mentors Hans cock and the increasing purge of its health by its incomplete nutrition led to the fact that it itself instead of its in the autumn 1934 for one weekinto a sanatorium gone had. After this stay, which brought him sufficient recovery, Gödel began itself to employ with the continuum hypothesis, whose relative compatibility he could prove 1940. To this topic Gödel co-operated among other things with John von Neumann .

Its health worsened with increasing age ever more. Already 1935 spent Gödel several months in a psychiatric hospital. When the Moritz mud very respected of Gödel was murdered 1936 by a former student, Gödel suffered a Nervenzusammenbruch.

Work on []

America

1938 married briefly Gödel finally ennobles Porkert. When Austria was attached to the third realm, Gödel lost its Austrian Dozentur due to the conversion of the Bildungsystems. It tried to receive an adequate academic place in the now German education system, thoseappropriate requests were however sluggishly worked on very. When it was angepöbelt in Vienna as a Jew and one it in addition into the service in the German armed forces called up, it seized the final resolution to leave its past homeland and emigrate to America.Owing to its American friends and the efforts of its wife he could leave the third realm in the spring 1940 over the Trans-Siberian railway by the Soviet Union and Japan.

After its entry into the USA and the beginning of its work in PrincetonGödel began itself to employ ever more with philosophical problems and turn away from the formal logic.1941 he wrote his last work to a logical problem, which he however only 1958 published. 1942 became acquainted with Gödel Albert Einstein more nearand began to discuss with it physical problems like relativity theory or philosophical topics. Between both developed itself a close friendship, which continued up to the death of Einstein. Beside few further acquaintances office for association Gödel however into thatand fifties forties due to its progressive mental disorder ever more. It received only a Professur in Princeton to 1953, since it was regarded particularly of Hermann Weyl and Carl Ludwig seal because of its strange behavior as unsuitable. In the sixtiesYears stopped it giving lectures and its illness left to it less and less the possibility of working or socially of interacting. Although it during this entire time further as one of the prominent logicians applied and one for it appropriate academicAcknowledgment in the form of honors granted, could not that naturally its condition not improve.it tried to publish 1970 for the last time. The writing had to be taken back however, since it had ignored many errors simple due to the effect of psychopharmacologic drugs.

Its last Lebensjahre, which must have been terrible for him, Gödel spent at home in Princeton or in different sanatoriums, from which he fled several times. Only the welfare service of its wife, who ensured that he itself at least halfway normallynourished, held it alive. As if ennoble Gödel 1978 even to a hospital to be in-supplied had, died briefly Gödel at malnutrition.

mathematical work

Gödel proved the following fundamental theorems of the logic:

See also Gödel, E, to brook

literature

Writings

(selection)
  • short Gödel: Over the completeness of the axioms of the logical function calculation. Thesis 1929. In: Monthly magazines for mathematics and physics academic publishing house company, Leipzig 36,1930, 2, S.349-360. (Also in: Suppl. 3.1932, S. 12 - 13)
  • short Gödel: Over formally unentscheidbareSets of the Principia Mathematica and related systems I. in: Monthly magazine for mathematics and physics. Academic publishing house company, Leipzig 38,1931, S.173-198.
  • Briefly Gödel: Discussion for the foundation of mathematics, realization 2. in:Monthly magazine for Math. and physics.Academic publishing house company, Leipzig 39.1931-32,S.147-148.
  • (Hrsg.) Solomon Feferman and. A.: Briefly Gödel. Collected Works. Volume. I-III. Clarendon press, Oxford 1986. ISBN 0-1951-4720-0, ISBN 0-1951-4721-9, ISBN 0-1951-4722-7 (the complete collection of all of Gödel published and unpublished writings into German ever wrote andEnglish)

secondary literature

  • Karl victory mouth, John Dawson, briefly Mühlberger: Briefly Gödel - the album/The album. Vieweg 2006. ISBN 3-8348-0173-9
  • Ernest nail, James R. New man: The Gödel proof. Scientia new facts, Oldenbourg 2003. ISBN 3-486-45214-2
  • Douglas R.Hofstadter: Gödel, E, brook. An endless twisting volume. Dt. Paperback publishing house, Munich 1991. ISBN 3-423-30017-5
  • max of Woitschach: Gödel, Götzen and computer. A criticism of the impure reason. Poller, Stuttgart 1986. ISBN 3-87959-294-2
  • Wolfgang bar Mueller: Incompleteness and Unentscheidbarkeit.The metamathematischen results of Goedel, Church, Kleene, Rosser and their epistemological importance. Springer, Vienna 1973. ISBN 3-211-81208-3
  • Sybille shopkeepers: Symbolic machines. The idea of formalizing in historical outline. Scientific book company, Darmstadt 1988. ISBN 3-534-03207-1
  • Ludwig Fischer: The basesphilosophy and mathematics. Felix mine, Leipzig 1933.
  • John W. Dawson jr.: Briefly Gödel. Life and work. Springer, Vienna 1999. ISBN 3-211-83195-9
  • Gianbruno Guerrerio: Briefly Gödel. Logical paradoxes and mathematical truth. Spektrum der Wissenschaft, Biografie. Spectrum,Heidelberg 2002, 1.ISBN 3-936278-04-0
  • Palle Yourgrau: Gödel, Einstein and the consequences. Legacy of an unusual friendship. C.H. Beck, Munich 2005. ISBN 3-406-52914-3
  • Jaakko Hintikka: On Gödel. Wadsworth Philosophers Series, 2000. (English) ISBN 0-534-57595-1

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