不完整性Ex Machina
Incompleteness Ex Machina
摘要：
在这篇文章中，我们将证明哥德尔的不完全性定理两次。首先，我们要用传统的方法证明他们。然后我们将在计算的设置中重复这一壮举。在这个过程中，我们会发现，正确地看，哥德尔的工作需要分为两部分：一方面是将计算转移到算术领域，另一方面是实际的不完备性定理。吃完后会有蛋糕。
英文摘要：
In this essay we'll prove Gödel's incompleteness theorems twice. First, we'll prove them the good old-fashioned way. Then we'll repeat the feat in the setting of computation. In the process we'll discover that Gödel's work, rightly viewed, needs to be split into two parts: the transport of computation into the arena of arithmetic on the one hand and the actual incompleteness theorems on the other. After we're done there will be cake.
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。
