Kurt Gödel
Kurt Friedrich Gödel (/ˈɡɜːrdəl/ GUR-dəl, German: [kʊʁt ˈɡøːdl̩] (Afrilu 28, 1906 -Janairu 14, 1978) masanin dabaru, mathematician, kuma masanin falsafa. An yi la'akari da shi tare da Aristotle da Gottlob Frege a matsayin daya daga cikin manyan masana a tarihi, Gödel yana da tasiri mai yawa akan tunanin kimiyya da falsafa a karni na 20, lokacin da wasu irin su Bertrand Russell, Alfred North Whitehead, da David Hilbert suna amfani da dabaru da kafa ka'idar don bincika tushen ilimin lissafi, ginawa a kan aikin farko ta irin su Richard Dedekind, Georg Cantor da Frege.
Gödel ya buga first incompleteness theorem a cikin shekarar 1931, lokacin yana ɗan shekara 25, shekara ɗaya bayan kammala karatun digirinsa a Jami'ar Vienna. Ka'idar rashin cikawa ta farko ta bayyana cewa ga kowane tsarin ω-daidaitacce recursive axiomatic tsarin iko wanda ya isa ya bayyana lissafin lissafin lambobi na halitta (misali Peano ilmin lissafi ), akwai shawarwari na gaskiya game da lambobi na halitta waɗanda ba za a iya tabbatar da su ba kuma ba za a iya warware su daga axioms ba. [1] Don tabbatar da hakan, Gödel ya ɓullo da wata dabara a yanzu da aka fi sani da lambar Gödel, wadda ke ƙididdige kalmomi na yau da kullun azaman lambobi. Ka'idar rashin cikawa ta biyu, wacce ta biyo baya daga farko, ta bayyana cewa tsarin ba zai iya tabbatar da daidaitonsa ba. [2]
Gödel ya kuma nuna cewa ba za a iya karyata ra'ayin axiom na zabi ko hasashen ci gaba ba daga ka'idar saiti na Zermelo-Fraenkel da aka yarda, yana zaton cewa axioms din sun daidaita. Sakamakon da ya gabata ya buɗe kofa ga masu ilimin lissafi su ɗauka axiom ɗin zaɓi a cikin hujjojinsu. Ya kuma ba da gudummawa mai mahimmanci ga ka'idar hujja ta hanyar fayyace alaƙa tsakanin dabaru na gargajiya, dabaru na fahimta, da dabaru na modal.
Ƙuruciya da ilimi
gyara sasheYarantaka
gyara sasheAn haifi Gödel a ranar 28 ga watan Afrilu, shekara ta, 1906, a Brünn, Austria-Hungary (now Brno, Jamhuriyar Czech) a cikin dangin Jamusanci na Rudolf Gödel a shekara ta
(1974 zuwa 1929), darektan gudanarwa kuma mai mallakar babban kamfanin masaku, da Marianne. Gödel a shekara ta (née Handschuh, 1879 zuwa1966). [3] A lokacin da aka haife shi birnin yana da rinjaye na Jamusanci wanda ya hada da iyayensa. [4] Mahaifinsa ɗan Katolika ne kuma mahaifiyarsa 'yar Furotesta ce kuma yaran Furotesta ne. Kakannin Kurt Gödel sun kasance da yawa a cikin rayuwar al'adun Brünn. Alal misali, kakansa Joseph Gödel ya kasance sanannen mawaƙi a lokacinsa kuma na wasu shekaru yana memba na Brünner Männergesangverein. (Men's Choral Union of Brünn). [5]
Gödel ya zama ɗan ƙasar Czechoslovakia kai tsaye yana ɗan shekara 12 lokacin da daular Austro-Hungary ta ruguje bayan shan kaye a yakin duniya na farko. A cewar abokin karatunsa Klepetař , kamar yawancin mazauna yankin Sudetenländer na Jamus, "Gödel ya ɗauki kansa ko da yaushe dan Austriya kuma ɗan gudun hijira a Czechoslovakia". [6] A watan Fabrairun shekara ta (1929) an sake shi daga zama ɗan ƙasar Czechoslovakia sannan kuma, a cikin Afrilu, ya ba da izinin zama ɗan ƙasar Austriya. Lokacin da Jamus ta mamaye Ostiriya a cikin shekara ta (1938) Gödel ya zama ɗan ƙasar Jamus kai tsaye yana ɗan shekara 32. A shekara ta (1948) bayan yakin duniya na biyu, yana da shekaru 42, ya zama dan kasar Amurka.
A cikin iyalinsa, an yi wa matashin Gödel lakabi Herr Warum ("Mr. Me ya sa") saboda rashin koshi. A cewar ɗan'uwansa Rudolf, yana da shekaru shida ko bakwai, Kurt ya sha wahala daga zazzabin rheumatic; ya murmure gaba daya, amma har tsawon rayuwarsa ya kasance yana da yakinin cewa zuciyarsa ta yi rauni na dindindin. Tun yana da shekaru huɗu, Gödel ya sha fama da "sau da yawa na rashin lafiya", wanda zai ci gaba har tsawon rayuwarsa.
Gödel ya halarci Evangelische Volksschule , makarantar Lutheran a Brünn daga shekara ta (1912 zuwa 1916) kuma an yi rajista a Deutsches Staats-Realgymnasium daga shekarar (1916 zuwa 1924) ya yi fice tare da karramawa a dukkan batutuwansa, musamman a fannin lissafi, harsuna da addini. Ko da yake Gödel ya yi fice a cikin harsuna da farko, amma daga baya ya fi sha'awar tarihi da lissafi. Sha'awar ilimin lissafi ya karu lokacin da a cikin shekara ta (1920) ɗan'uwansa Rudolf (an haife shi a shekara ta 1902) ya tafi Vienna, inda ya halarci makarantar likitanci a Jami'ar Vienna. A lokacin ƙuruciyarsa, Gödel ya yi nazarin Gabelsberger shorthand, Goethe's Theory of Colors da kuma sukar Isaac Newton, da rubuce-rubucen Immanuel Kant .[ana buƙatar hujja]
Karatu a Vienna
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Lokacin da yake da shekaru 18, Gödel ya shiga da ɗan'uwansa a Jami'ar Vienna. A lokacin, ya riga ya kware a fannin lissafi a matakin jami'a. [7] Ko da yake da farko yana da niyyar karanta ilimin kimiyyar lissafi, ya kuma halarci kwasa-kwasan ilimin lissafi da falsafa. A wannan lokacin, ya ɗauki ra'ayoyin gaskiyar ilimin lissafi. Ya karanta Metaphysische Anfangsgründe der Naturwissenschaft Kant, kuma ya shiga cikin da'irar Vienna tare da Moritz Schlick, Hans Hahn, da Rudolf Carnap. Daga nan Gödel ya karanci ka'idar lamba, amma lokacin da ya shiga wani taron karawa juna sani da Moritz Schlick ya gudanar wanda ya nazarci littafin Bertrand Russell na Gabatarwa ga Falsafar Lissafi, ya fara sha'awar ilimin lissafi. A cewar Gödel, ilimin lissafi shine "kimiyya kafin sauran duka, wanda ya ƙunshi ra'ayoyi da ka'idodin da ke ƙarƙashin dukan kimiyya." [8]
Manazarta
gyara sashe- ↑ Smullyan, R. M. (1992). Gödel's Incompleteness Theorems. New York, Oxford: Oxford University Press, ch. V.
- ↑ Smullyan, R. M. (1992). Gödel's Incompleteness Theorems. New York, Oxford: Oxford University Press, ch. IX.
- ↑ Dawson 1997, pp. 3–4.
- ↑ Dawson 1997, p. 12
- ↑ Procházka 2008, pp. 30–34.
- ↑ Dawson 1997, p. 15.
- ↑ Dawson 1997, p. 24.
- ↑ Gleick, J. (2011) The Information: A History, a Theory, a Flood, London, Fourth Estate, p. 181.