逻辑的数学引论

Hacker News 上怎么说

• anatoly · 2009 年

  ……“被反驳”，而且对它们的含义理解得一塌糊涂。这些词其实都有明确的专业定义。如果你对这些感兴趣并且能啃得下数学的严谨性，我强烈推荐 Enderton 的《A Mathematical Introduction to Logic》作为数理逻辑的通识书，以及 Smullyan 自己写的《Goedel's Incompleteness Theorems》来了解这个专题。现在，稍微为我刚才刺耳的话找点依据。在哥德尔不完备定理的语境下，一个公理系统……

  …"refuted", with confused understanding of what they mean. They all have clear technical meanings. If you're interested in this stuff and can stomach mathematical rigor, I highly recommend Enderton's _A Mathematical Introduction to Logic_ for mathematical logic in general, and Smullyan's own _Goedel's Incompleteness Theorems_ for this topic. Now, to back my harsh words a little. An axiomatic system, in the context of Goedel's theorems,…

• azanar · 2008 年

  ……是我上过的那门相关课程的教材，在亚马逊上的评价也挺不错：Karel Hrbacek 和 Thomas Jech 的《Introduction to Set Theory》，ISBN-13: 978-0824779153。Herbert Enderton 的《A Mathematical Introduction to Logic》，ISBN-13: 978-0122384523。希望能帮到你。:-)

  …were the basis for the course I took on the topic, and recieved pretty good reviews on Amazon: Karel Hrbacek and Thomas Jech, Introduction to Set Theory. ISBN-13: 978-0824779153. Herbert Enderton, A Mathematical Introduction to Logic. ISBN-13: 978-0122384523. Hope this helps. :-)

• ionfish · 2010 年

  ……返回一个类型为 a 的值。如果你想更好地理解文章中用到的逻辑概念和记号，不妨找一本逻辑学入门教材来看看。我推荐 Enderton 的《A Mathematical Introduction to Logic》。http://www.math.ucla.edu/~hbe/amil/index.html

  …returns a value of type a. If you want to attain a better understanding of the logical concepts and notation used in the article, try getting hold of an introductory logic text. I recommend Enderton's 'A Mathematical Introduction to Logic'. http://www.math.ucla.edu/~hbe/amil/index.html

• danharaj · 2015 年

  ……哲学；这篇文章是个极好的切入点：http://plato.stanford.edu/entries/logic-classical/。当然，内容非常硬核密集！Enderton 写的《A Mathematical Introduction to Logic》以一种兼具教学法且十分优美的方式涵盖了这篇的内容。但话说回来，这些都属于形式逻辑（formal logic）。它处于许多学科和思维方式的交汇点，而且有太多太多的形式逻辑值得去探索。正是形式逻辑这一思想……

  …Philosophy; this article is a perfect start: http://plato.stanford.edu/entries/logic-classical/ Of course, this is extremely dense! A book that covers this article in a pedagogical and beautiful manner is A Mathematical Introduction to Logic by Enderton. But still, this is all formal logic. It lies at the locus of many disciplines and ways of thinking, and there are many, many formal logics to explore. It is the idea of formal logic which…

• fnrslvr · 2019 年

  > 数理逻辑（Mathematical Logic）：《A Mathematical Introduction to Logic》，Herbert Enderton 著。

  > Mathematical Logic A Mathematical Introduction to Logic, by Herbert Enderton.

• throwaway81523 · 2021 年

  嗯，这取决于你想找什么样的书，不过我习惯的传统风格教材是 H. B. Enderton 的《A Mathematical Introduction to Logic》，而且 Enderton 还配有一本关于集合论的书。我觉得与其用它们替代 Gallier 和 Quaintance 的书，不如把它们当作配套参考。在我看来，G&Q 那本书更现代，而且……

  Well, it depends on what you are looking for, but the traditional-style book that I'm used to is H. B. Enderton, "A Mathematical Introduction to Logic", and Enderton also has an accompanying book on set theory. I guess I'd suggest those as a companion rather than an alternative to the Gallier and Quaintance book. The G&Q book is imho more modern and…

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