Godel Editorial Project

1931年，库尔特·哥德尔发表了一篇文章，结束了近一个世纪以来建立公理的尝试，这些公理将为所有数学提供严格的基础。他证明了，在任何严格的逻辑数学系统中，都存在不能根据该系统的公理来证明或证伪的命题。因此，对数学自洽性的论证的探索受到了毁灭性的打击。如果数学实际上是一致的，哥德尔表明，这种一致性的事实不能在数学本身的规则内证明。数学家们永远不能确定算术的基本公理不会引起矛盾，数学的基础最终必定永远是一个谜。哥德尔从这个辉煌的开端开始，做出了深远的贡献，影响了逻辑学、物理学、哲学、计算机科学的基础以及数学基础的其他方面。这个项目的目的是出版库尔特·哥德尔的著作，并使它们能够提供给数学家、哲学家和历史学家等更广泛的受众。在以前的国家科学基金资助下，费尔曼教授和他的编辑人员已经出版了数学家和逻辑学家库尔特·哥德尔的四卷文集的第一卷。第一卷包含哥德尔1929-1936年的出版物。目前正在完成的第二卷载有他1936年至1974年的出版物。在这项新的资助下，哥德尔的课程笔记、信件、讲座、科学笔记和未发表手稿的草稿将被准备出版。这些文件将以另外两卷的形式出版。编辑工作包括将许多文件从德语翻译成英语，并编写文件的介绍和注释，以使这些材料具有最大的科学、历史和哲学意义。

In 1931, Kurt Godel published an article which ended nearly a century of attempts to establish axioms which would provide a rigorous basis for all of mathematics. He proved that within any rigidly logical mathematical system, there are propositions that cannot be proved or disproved on the basis of the axioms of that system. Thus, the search for a demonstration of the self- consistency of mathematics was dealt a shattering blow. If mathematics is actually consistent, Godel showed that the fact of this consistency cannot be proved within the rules of mathematics itself. Mathematicians can never be certain that the basic axioms of arithmetic will not give rise to contradictions and the foundations of mathematics must ultimately always remain a mystery. Godel went on from this brilliant start to make contributions which would profoundly affect logic, physics, philosophy, the foundations of computer science, and other aspects of the foundations of mathematics. The purpose of this project is to publish the works of Kurt Godel and make them available to a wider audience of mathematicians, philosophers and historians. Under previous NSF grants, Professor Feferman and his editorial staff have published the first volume of what is now projected to be a four volume collection of the papers of the mathematician and logician, Kurt Godel. Volume one contains Godel's collected publications of 1929-1936. Volume two, which is currently being finished, contains his publications form 1936 to 1974. Under this new grant, Godel's notes from his courses, letters, lectures, scientific notebooks and drafts of unpublished manuscripts will be prepared for publication. These papers will be published in an additional two volumes. The editorial work includes translations of many documents from the German to English and the preparation of introductions and notes to the documents in order to make these materials of maximum scientific, historical and philosophical significance.