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Über dieses Buch

Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Gödel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations of shorthand manuscripts that follow in the right setting. The materials in this book are singular in the way they show the birth and development of Gentzen's central ideas and results, sometimes in a well-developed form, and other times as flashes into the anatomy of the workings of a unique mind.



Part I: A sketch of Gentzen’s life and work

Gerhard Gentzen died on August 4, 1945, in a prison in Prague. His fellow prisoners were professors of the local German university, and there are accounts of his last days and how he was, rendered weak by lack of food, still pondering over the consistency problem of analysis. After the war, some attempts were made to find any manuscripts he might have left behind; a mythical suitcase one letter reports he had been carrying around, filled with papers with a near-proof of the consistency of analysis. Nothing was found, though, in Prague. In Göttingen, instead, there were manuscripts that were preliminary studies for published work, by the account of Arnold Schmidt. He wrote in 1948 to Gentzen’s mother that the papers would be placed and kept together with Hilbert’s papers; yet again, nothing has been found.
Jan von Plato

Part II: An Overview of the shorthand notes

Except for the early thesis manuscript, the correspondence with Bernays and Heyting, and the summary of the series WA of February 1945, all the source materials are written in the unified shorthand. The last-mentioned item was originally written in shorthand, but it got transcribed and typewritten by 1948 (see Menzler-Trott 2007, p. 277). The original has not been found.
Jan von Plato

Part III: The original writings

A result in the small is worth more than no overview at large.
Jan von Plato


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