希尔伯特纲领的过去与现在
Hilbert's Program Then and Now
摘要：
希尔伯特的计划是一个雄心勃勃的和广泛的项目在哲学和数学基础。为了“一劳永逸地解决数学中的基本问题”，希尔伯特在1921年提出了一个双管齐下的方法：首先，经典数学应该在公理系统中形式化;其次，只使用限制性的“有限”方法，应该证明这些公理系统的一致性。虽然哥德尔的不完备性定理表明，最初设想的程序无法执行，但它有许多部分成功，并在当时和之后的逻辑理论和元理论中产生了重要的进展。本文讨论了希尔伯特纲领的历史背景和发展，它的哲学基础和后果，以及它自20世纪30年代以来的发展和影响。
英文摘要：
Hilbert's program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to "dispose of the foundational questions in mathematics once and for all, "Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, "finitary" means, one should give proofs of the consistency of these axiomatic systems. Although Godel's incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial successes, and generated important advances in logical theory and meta-theory, both at the time and since. The article discusses the historical background and development of Hilbert's program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
