A mathematical introduction to logic
by Herbert B. Enderton · first published 1972
60% recommend40% neutral
Why HN recommends it
A rigorous, traditional introduction to mathematical logic and the standard text for a first formal course. Suited to those comfortable with mathematical precision who want the foundations.
Summarised by Claude from recommending comments
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…"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,…
on “World's shortest explanation of Gödel's theorem” ↗…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. :-)
on “Ask HN: How should I go about learning CS?” ↗…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
on “Brilliance of Haskell's Maybe type and the Value of Static Type Checking” ↗…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…
on “I deduce you are studying logic” ↗> Mathematical Logic A Mathematical Introduction to Logic, by Herbert Enderton.
on “Ask HN: Mathematicians, what textbooks are best for learning these math topics?” ↗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…
on “Proofs, Computability, Undecidability, Complexity, and the Lambda Calculus [pdf]” ↗I rate Enderton's A Mathematical Introduction to Logic. http://www.math.ucla.edu/~hbe/amil/index.html
on “Ask HN: good math books” ↗…example [1]. The other extreme is Gentzen's sequent calculus [2] which has only one axiom (A |- A), everything else being a rule of inference. Most presentations of FOL are between these extremes. [1] A mathematical introduction to logic, by H. Enderton [2] Untersuchungen über das logische Schliessen I, by G. Gentzen
on “Doing Mathematics Differently” ↗Fair point on "string," though i never really encountered it, i opened up an old goldfarb book, and it's not in the index, but it looks like it is used in my old enderton "mathematical introduction to logic," so, again, fair point. I think "statement" would be a better term, maybe. enderton page 107, 289, etc: http://books.google.com/books?id=dVncCl_EtUkC&printsec=front...
on “My 7-Year Old Daughter’s First Programming Experience” ↗…cannot be deduced from any set of axioms (and therefore, by completeness, are not logically implied by any set of axioms). This is my understanding after having spent a few weeks reading Enderton's "A Mathematical Introduction to Logic." If I am misunderstanding this, I would love input (so please comment). Godel's theorems are something I'm very anxious to wrap my head around.
on “Explaining Gödel's Incompleteness Theorem to a Twelve Year Old” ↗No, they are axioms. Peano arithmetic itself is a first-order theory, and a theory is just a recursively enumerable set of axioms. Enderton, “A Mathematical Introduction to Logic, 2nd Ed.”, p,203,269-270 Kleene, “Mathematical Logic”, p.206 EDIT: It seems like you're talking about Peano's original historical formulation of arithmetic? That's all well and good but it is categorically…
on “Numbering should start at zero (1982)” ↗