……“另一方面，如果你能证明你最喜欢的 Neveu 微积分根据某种可计算逻辑是可靠的（sound），那确实会有帮助。”废话。Neveu 只不过是建立在集合论之上的，你想说是公理集合论（axiomatic set theory）也行，想说是布尔巴基学派的基础或者 P. Suppes 的体系也行，本质上和过去 100 年左右的所有数学没什么两样。就那些内容的重要性而言，没有任何人应该……
…"On other hand if you can show that your favorite Neveu calculus can be proved sound according to some computable logic, that would indeed be helpful." Nonsense. Neveu is based just on set theory, axiomatic set theory if you wish, the foundations as in Bourbaki if you wish, or P. Suppes, essentially the same as all of math for the past 100 years or so. For the importance of that material, there is nothing anyone should…
……罗素等人试图仅从集合出发来重新定义数学中的一切。随后，所有的东西都从最底层的集合概念开始构建。其严肃的成果就是公理集合论，例如 P. Suppes 的《Axiomatic Set Theory》。因此，数、函数、微积分、线、面、球、群、环、域、向量空间等等，全都是基于集合来定义的。勒贝格的……也是如此。
…Russell, etc. there was an effort to redefine everything in mathematics starting with just sets. Then everything was constructed starting with just the low level ideas of sets. The serious result was axiomatic set theory, e.g., as in P. Suppes, Axiomatic Set Theory. So, numbers, functions, calculus, lines, planes, spheres, groups, rings, fields, vector spaces. etc. were all defined based on sets. And similarly for Lebesgue's…
Part I I tried a grad math department and didn't like it: (1) In a course in real analysis, early on the prof discussed some set theory. The summer before I'd had an NSF thing in axiomatic set theory, Suppes, von Neumann, an appendix in Kelley, etc. His first test had a problem, and at the last minute I saw a solution and wrote it down. He called me on the carpet -- nasty guy. I apologized for using…
……想了解更多，有优雅且长盛不衰的 P. Halmos 的《Naive Set Theory》（朴素集合论），现在已有 PDF、LaTeX 等版本。想看更多，有 J. Kelley 的《General Topology》（点集拓扑）的附录。想看更多，有 P. Suppes 的《Axiomatic Set Theory》。还想看更多？你确定还想要更多？？？？
…For more, there is the elegant, long popular, P. Halmos Naive Set Theory, now available in PDF, LaTeX, etc. For more there is the appendix to J. Kelley, General Topology. For more there is P. Suppes, Axiomatic Set Theory. For more, sure you want more????
……“另一方面，如果你能证明你最喜欢的 Neveu 微积分根据某种可计算逻辑是可靠的（sound），那确实会有帮助。”废话。Neveu 只不过是建立在集合论之上的，你想说是公理集合论（axiomatic set theory）也行，想说是布尔巴基学派的基础或者 P. Suppes 的体系也行，本质上和过去 100 年左右的所有数学没什么两样。就那些内容的重要性而言，没有任何人应该……
…"On other hand if you can show that your favorite Neveu calculus can be proved sound according to some computable logic, that would indeed be helpful." Nonsense. Neveu is based just on set theory, axiomatic set theory if you wish, the foundations as in Bourbaki if you wish, or P. Suppes, essentially the same as all of math for the past 100 years or so. For the importance of that material, there is nothing anyone should…
……罗素等人试图仅从集合出发来重新定义数学中的一切。随后，所有的东西都从最底层的集合概念开始构建。其严肃的成果就是公理集合论，例如 P. Suppes 的《Axiomatic Set Theory》。因此，数、函数、微积分、线、面、球、群、环、域、向量空间等等，全都是基于集合来定义的。勒贝格的……也是如此。
…Russell, etc. there was an effort to redefine everything in mathematics starting with just sets. Then everything was constructed starting with just the low level ideas of sets. The serious result was axiomatic set theory, e.g., as in P. Suppes, Axiomatic Set Theory. So, numbers, functions, calculus, lines, planes, spheres, groups, rings, fields, vector spaces. etc. were all defined based on sets. And similarly for Lebesgue's…
第一部分 我去读过数学研究生院，但并不喜欢：(1) 在一门实分析课上，教授很早就讲了一些集合论。在此前那个夏天，我刚参加了一个公理集合论方面的 NSF 项目，学了 Suppes、冯·诺伊曼、Kelley 书里的附录等等。他的第一次测验有一道题，我在最后一刻想出了一个解法并写了下来。他把我叫去训了一顿——这家伙真恶心。我为自己使用了……而道歉
Part I I tried a grad math department and didn't like it: (1) In a course in real analysis, early on the prof discussed some set theory. The summer before I'd had an NSF thing in axiomatic set theory, Suppes, von Neumann, an appendix in Kelley, etc. His first test had a problem, and at the last minute I saw a solution and wrote it down. He called me on the carpet -- nasty guy. I apologized for using…
这让我想起了 Suppes 写的教材《Axiomatic Set Theory》（公理集合论），里面在第 137 页给出了 3 + 1 = 4 的证明。
I'm reminded of the textbook Axiomatic Set Theory by Suppes, which has on page 137 a proof that 3 + 1 = 4.
……想了解更多，有优雅且长盛不衰的 P. Halmos 的《Naive Set Theory》（朴素集合论），现在已有 PDF、LaTeX 等版本。想看更多，有 J. Kelley 的《General Topology》（点集拓扑）的附录。想看更多，有 P. Suppes 的《Axiomatic Set Theory》。还想看更多？你确定还想要更多？？？？
…For more, there is the elegant, long popular, P. Halmos Naive Set Theory, now available in PDF, LaTeX, etc. For more there is the appendix to J. Kelley, General Topology. For more there is P. Suppes, Axiomatic Set Theory. For more, sure you want more????
1. Suppes 的《Axiomatic Set Theory》 2. 菲利普·K·迪克（Philip K. Dick）的《太阳乐透》（Solar Lottery）
1. Axiomatic Set Theory by Suppes 2. Solar Lottery by Philip K. Dick