Goldilocks的哥德尔：哥德尔第一不完全性定理（的一个变体）的严格简化证明
Gödel for Goldilocks: A Rigorous, Streamlined Proof of (a variant of) Gödel's First Incompleteness Theorem
摘要：
大多数关于哥德尔定理的讨论都属于两种类型之一：要么他们强调定理的哲学和文化意义，也许只是粗略地描述证明的一些想法，通常把哥德尔的证明与谜语和悖论联系起来，但并不试图提出严格的、完整的证明;或者他们确实提出了严格的证明，但在传统的数理逻辑中，所有的符号和困难的定义，反映哥德尔原始方法和更广泛的逻辑问题的技术问题。许多非专业人士对这两种极端类型的论述感到沮丧，并希望得到一个完整的，严格的证明，他们可以理解。这样的阐述是可能的，因为许多人已经意识到哥德尔第一不完备性定理的变体可以用一种更简单的中间方法严格证明，在一个极端避免了哲学讨论和手工放弃;在另一个极端也避免了传统数理逻辑的重型机器，以及哥德尔原始证明的许多更难的细节。这就是最好的金发女孩方法。在这个博览会中，我们给出了一个简短的，独立的哥德尔第一定理的金发姑娘博览会，针对广泛的本科观众。
英文摘要：
Most discussions of Gödel's theorems fall into one of two types: either they emphasize perceived philosophical, cultural "meanings" of the theorems, and perhaps sketch some of the ideas of the proofs, usually relating Gödel's proofs to riddles and paradoxes, but do not attempt to present rigorous, complete proofs; or they do present rigorous proofs, but in the traditional style of mathematical logic, with all of its heavy notation and difficult definitions, and technical issues which reflect Gödel's original approach and broader logical issues. Many non-specialists are frustrated by these two extreme types of expositions and want a complete, rigorous proof that they can understand. Such an exposition is possible, because many people have realized that variants of Gödel's first incompleteness theorem can be rigorously proved by a simpler middle approach, avoiding philosophical discussions and hand-waiving at one extreme; and also avoiding the heavy machinery of traditional mathematical logic, and many of the harder detail's of Gödel's original proof, at the other extreme. This is the just-right Goldilocks approach. In this exposition we give a short, self-contained Goldilocks exposition of Gödel's first theorem, aimed at a broad, undergraduate audience.
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