希尔伯特的“Verunglueckter Beweis”，第一定理和一致性证明
Hilbert's "Verunglueckter Beweis," the first epsilon theorem, and consistency proofs
摘要：
在20世纪20年代，阿克曼和冯诺依曼，在追求希尔伯特的纲领，工作的一致性证明算术系统。一种提出的方法给出这样的证明是希尔伯特的ε替代方法。然而，还有第二种方法，这在20世纪20年代的希尔伯特学派的出版物中没有反映出来，它是希尔伯特第一定理的直接先驱，也是伯奈斯的某种“一般一致性结果”。对这种所谓的“失败证明”的形式的分析进一步阐明了希尔伯特纲领作为一种工具主义事业的解释，其目的是表明，只要一个“真实”命题可以用“理想”手段证明，它也可以用“真实”的有限手段证明。
英文摘要：
In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's Programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain 'general consistency result' due to Bernays. An analysis of the form of this so-called 'failed proof' sheds further light on an interpretation of Hilbert's Programme as an instrumentalist enterprise with the aim of showing that whenever a `real' proposition can be proved by 'ideal' means, it can also be proved by 'real', finitary means.
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