04953nam a22005535i 4500 978-3-031-51971-0 DE-He213 20251030111418.0 cr nn 008mamaa 240206s2024 sz | s |||| 0|eng d 9783031519710 978-3-031-51971-0 10.1007/978-3-031-51971-0 doi D1-2027 JFCX bicssc HIS000000 bisacsh JBCC9 thema von Plato, Jan. author. (orcid)0000-0002-8370-9255 https://orcid.org/0000-0002-8370-9255 aut http://id.loc.gov/vocabulary/relators/aut 70672 Portrait of Young Gödel [electronic resource] : Education, First Steps in Logic, the Problem of Completeness / by Jan von Plato. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 307 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Vienna Circle Institute Library ; 9 PART 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. In 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. Intellectual life History. 70673 Logic. 70674 Physicists Biography. 68034 Astronomers Biography. 68035 Intellectual History. 70675 Logic. 70674 Biographies of Physicists and Astronomers. 68038 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031519703 Printed edition: 9783031519727 Printed edition: 9783031519734 Vienna Circle Institute Library ; 9 70676 https://doi.org/10.1007/978-3-031-51971-0 ZDB-2-HTY ZDB-2-SXH 57512 57512