LEADER 04858nam 22006135 450 001 9910831011603321 005 20251030093404.0 010 $a9783031519710 010 $a303151971X 024 7 $a10.1007/978-3-031-51971-0 035 $a(MiAaPQ)EBC31131996 035 $a(Au-PeEL)EBL31131996 035 $a(OCoLC)1420630820 035 $a(DE-He213)978-3-031-51971-0 035 $a(CKB)30323281700041 035 $a(EXLCZ)9930323281700041 100 $a20240206d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPortrait of Young Gödel $eEducation, First Steps in Logic, the Problem of Completeness /$fby Jan von Plato 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (314 pages) 225 1 $aVienna Circle Institute Library,$x2542-9914 ;$v9 311 08$aPrint version: von Plato, Jan Portrait of Young Gödel Cham : Springer International Publishing AG,c2024 9783031519703 327 $aPART I: AT HIGH SCHOOL AND UNIVERSITY -- 1. At high school -- 1.1. High school extraordinary -- 1.2. The activity of the human mind -- 1.3. Molecular theory -- 1.4. G¨odel?s esoteric side -- At university: from physics to mathematics -- 2.1. The physics student -- 2.2. Mathematics and philosophy -- PART II: FIRST STEPS IN LOGIC -- 1. First encounters with foundational problems -- 2. The Weber-Heft -- 3. The U¨ bungsheft Logik -- 3.1. Exercise in constitutional analysis -- 3.2. Formal derivations in second-order arithmetic and set theory -- 3.3. Beautiful syntax trees and other diversions -- 3.4. Summary overview of the U¨ bungsheft -- 4. Punktmengenlehre -- 4.1. Hilbert?s geometry -- 4.2. Hausdorff?s point set topology -- PART III: THE PROBLEM OF COMPLETENESS -- 1. From Carnap?s exercises to the problem of completeness -- 2. Dissertation draft -- 2.1. Generality -- 2.2. First-order logic -- 2.3. The proof of completeness -- 3. Completeness of the axioms of the narrower function calculus -- 4. Lectures and seminars on completeness. -- 5. Anticipations of incompleteness -- PART IV: THE SHORTHAND NOTEBOOKS -- 1. The Weber-Heft -- 2. U¨ bungsheft Logik: formal derivations -- 3. Punktmengenlehre: Hilbert?s geometry -- 4. Punktmengenlehre and U¨ bungsheft: set theory and topology -- 6. Completeness of the axioms of the narrower function calculus -- PART V: LECTURES AND SEMINARS ON COMPLETENESS -- 1. On the completeness of the axioms of the logical function calculus -- 2. Lecture in K¨onigsberg -- 3. Lecture in Vienna (plan of contents) -- 4. Report on G¨odel?s work -- 5. Completeness of the function calculus. 330 $aIn the summer of 1928, Kurt Gödel (1906?1978) embarked on his logical journey that would bring him world fame in a mere three years. By early 1929, he had solved an outstanding problem in logic, namely the question of the completeness of the axioms and rules of quantificational logic. He then went on to extend the result to the axiom system of arithmetic but found, instead of completeness, his famous incompleteness theorem that got published in 1931. It belongs to the most iconic achievements of 20th century science and has been instrumental in the development of theories of formal languages and algorithmic computability ? two essential components in the birth of the information society. This book explores Gödel?s way from an exceptional high-school student to a firmly established young logician. Essays in Gödel?s hand from the high school show that his central philosophical and scientific convictions were formed early on, before his university studies. Particular emphasis is laid on the course that made Gödel one of the foremost logicians of all times. The scientific biography of young Gödel is followed by English translations from Gödel?s German Gabelsberger shorthand of all his early preserved notebooks on logic and related topics. 410 0$aVienna Circle Institute Library,$x2542-9914 ;$v9 606 $aIntellectual life$xHistory 606 $aLogic 606 $aPhysicists$vBiography 606 $aAstronomers$vBiography 606 $aIntellectual History 606 $aLogic 606 $aBiographies of Physicists and Astronomers 615 0$aIntellectual life$xHistory. 615 0$aLogic. 615 0$aPhysicists 615 0$aAstronomers 615 14$aIntellectual History. 615 24$aLogic. 615 24$aBiographies of Physicists and Astronomers. 676 $a001.09 700 $avon Plato$b Jan$0766770 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910831011603321 996 $aPortrait of Young Gödel$93970425 997 $aUNINA