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首页> 外文期刊>Jahresbericht der Deutschen Mathematiker-Vereinigung >Reinhard Kahle, Michael Rathjen (eds.): 'Gentzen's Centenary, The Quest for Consistency' Springer, 2015, 561 pp.
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Reinhard Kahle, Michael Rathjen (eds.): 'Gentzen's Centenary, The Quest for Consistency' Springer, 2015, 561 pp.

机译：莱因哈德·卡勒（Reinhard Kahle），迈克尔·拉特恩（Michael Rathjen）（编辑）：“根岑百年纪念，《寻求一致性》”，施普林格，2015年，561页。

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摘要

The origins of this informative and important volume go back to a conference in Leeds and a workshop in Coim-bra that were both celebrating the 100th birthday of "one of the greatest logicians ever to whom we owe the most profound investigation of the nature of proofs since Aristotle and Frege". That's how the editors characterize Gerhard Gentzen in their Preface. Gentzen was born in 1909 three years after Kurt Godel and three years before Alan Turing. What a constellation of logical, mathematical and philosophical genius. Godel and Turing are widely known: Godel through his incompleteness theorems, the first of which establishes limits of formal provability, and Turing through his undecidability theorem, which crucially uses his profound analysis of computations (carried out by humans). Gentzen became famous through his consistency proof for arithmetic. Evaluating the significance of that proof is, however, a much more subtle task than judging the "negative" results of Godel and Turing, both with distinctive mathematical underpinnings and striking philosophical consequences. This subtlety is undoubtedly one part of the reason why Gentzen has not yet achieved the wide recognition of his contemporaries; another part is his direct involvement in the "failed" Hilbert Program. That's why I will describe also the program's emergence, its broad goals and the directions of contemporary work in its tradition.
机译：这本翔实而重要的书的起源可以追溯到在利兹举行的一次会议和在科英布拉举行的一次研讨会，这两场研讨会都是为了庆祝“有史以来最伟大的逻辑学家之一，我们对他们对证据性质的最深刻的研究而感到震惊”。自亚里斯多德和弗雷格”。这就是编辑在前言中刻画Gerhard Gentzen的方式。根岑（Kentzen）于1909年出生，比库尔特·戈德尔（Kurt Godel）落后三年，比艾伦·图灵（Alan Turing）早三年。逻辑，数学和哲学天才的星座。 Godel和Turing广为人知：Godel通过他的不完备性定理（第一个建立形式可证明性的极限），以及Turing通过他的不确定性定理（至关重要的是使用他对计算的深刻分析）（人类进行）。 Gentzen通过他的算术一致性证明而闻名。然而，评估该证据的重要性是比判断Godel和Turing的“负”结果更为微妙的任务，这两者都有独特的数学基础和惊人的哲学后果。毫无疑问，这种微妙之处是根岑尚未获得当代人的广泛认可的原因之一。另一部分是他直接参与了“失败的”希尔伯特计划。这就是为什么我还要描述该程序的出现，其广泛的目标以及其传统中当代作品的发展方向。

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