Godel Editorial Project

1931年，库尔特·戈德尔发表了一篇文章，结束了近一个世纪来试图建立公理的尝试，这些公理将为所有数学提供严格的基础。他证明，在任何严格逻辑的数学系统中，都有一些命题不能根据该系统的公理来证明或反驳。因此，寻求证明数学的自我一致性的努力遭到了毁灭性的打击。如果数学实际上是一致的，戈德尔指出，这种一致性的事实不能在数学本身的规则内得到证明。数学家永远不能确定算术的基本公理不会引起矛盾，数学的基础最终必须始终是一个谜。哥德尔从这一辉煌的开端继续作出贡献，这将深刻地影响逻辑、物理、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·戈德尔的作品，并使更多的数学家、哲学家和历史学家能够获得这些作品。根据NSF之前的拨款，费弗曼教授和他的编辑人员已经出版了第一卷，现在预计是数学家和逻辑学家库尔特·戈德尔的四卷本论文集。第一卷收录了戈德尔1929-1936年的出版物集。目前正在完成的第二卷收录了他从1936年到1974年的出版物。在这笔新的拨款下，戈德尔的课程笔记、信件、讲座、科学笔记本和未出版手稿的草稿将被准备出版。这些论文将在另外两卷中出版。编辑工作包括将许多文件从德语翻译成英语，并准备文件的导言和注释，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 Under this new grant, Godel's notes from his courses, letters, lectures, scientific notebooks and drafts of unpublished manuscripts will be prepared for publication.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.