Reddit reviews Computability and Logic Fifth Edition
We found 13 Reddit comments about Computability and Logic Fifth Edition. Here are the top ones, ranked by their Reddit score.
Used Book in Good Condition
In response to the same question, my Logic professor suggested:
A few of my favorites:
Computability and Logic by Boolos, Burgess and Jeffrey is good but seems to cover much of the stuff in Hunter. You may want to dig deeper into set theory, model theory, proof theory or recursion theory and look at some references specific to those topics.
That depends on why you're studying Logic.
Do you plan to use Logic as a tool for doing Philosophy? If so, I recommend studying Logic for Philosophy by Theodore Sider. You will get a more rigorous, formal treatment of propositional and predicate logic than what your introductory textbook likely contained. You will be exposed to basic proof theory and model theory. You will also learn, in depth, about several useful extensions to predicate logic, including various modal logics.
Do you want to become a logician, in some capacity? If so, the classic text would be Computability and Logic by Boolos and Jeffrey. This is an extremely rigorous and intensive introduction to metalogical proof. If you want to learn to reason about logics, and gain a basis upon which to go on to study the foundations of mathematics, proof theory, model theory, or computability, then this is probably for you.
Also, perhaps you could tell us what textbook you've just finished? That would give us a better idea of what you've already learned.
If you're already familiar with the standard material in a first logic course (propositional and predicate logic), then most intermediate logic textbooks will give you everything you need to understand the theorems. Some examples are:
http://www.amazon.com/Mathematical-Introduction-Logic-Second-Edition/dp/0122384520
http://www.amazon.com/Computability-Logic-George-S-Boolos/dp/0521701465
If you're interested in non classical logics I'd recommend "An introduction to non classical logic" by Graham Priest (it has modal logic and other very interesting non-classical logics). It's a good overview of the field.
For denser subjects in classical logic like computability, Turing machines, Gödel theorems, proofs for compactness, correctness, completeness, etc.; I'd go for a classical work by now: "Computability and logic" by Boolos, Burgess & Jeffrey. It's not an easy reading though.
I'm glad prof. faux decided to randomly cite an elementary introduction to logic such as hunter (without citing any particular page).
Don't get me wrong, it is a pretty decent introduction afaict, especially for undergrad students, but I'd be really delighted if he could mention what he meant in something a bit more used, if not slightly more rigorous, like boolos: https://www.amazon.com/Computability-Logic-Fifth-George-Boolos/dp/0521701465
And, of course, I'd feel real joy if he could cite a particular page to back up what he meant.
It depends what you're trying to get out of it.
There are literally hundreds of introductory texts for first-order logic. Other posters can cover them. There's so much variety here that I would feel a bit silly recommending one.
For formal tools for philosophy, I would say David Papineau's Philosophical Devices. There's also Ted Sider's Logic for Philosophy but something about his style when it comes to formalism rubs me the wrong way, personally.
For a more mathematical approach to first-order logic, Peter Hinman's Fundamentals of Mathematical Logic springs to mind.
For a semi-mathematical text that is intermediate rather than introductory, Boolos, Burgess, and Jeffrey's Computability and Logic is the gold standard.
Finally, if you want to see some different ways of doing things, check out Graham Priest's An Introduction to Non-Classical Logic.
http://www.amazon.com/Computability-Logic-George-S-Boolos/dp/0521701465
If you want a strong mathematical approach, check out Peter Smith's Teach Yourself Logic Guide. If you don't want to take as heavy of an approach, you can use the suggestions as a roadmap and pick-and-choose from the suggestions. Even the introductory logic book suggestions in that guide might be too math heavy, but you might at least read their reviews on Amazon. A lot of reviewers tend to link to books on either side: easier and harder approaches.
For what it's worth, while I was in University we used Computability and Logic in the second logic course, which is after the introductory course teaching basic propositional and predicate logic. It's not a book for learning logic, but it's an awesome book for tying together a lot of what you initially learn with computability, model and proof theory. In another course we used An Introduction to Non-Classical Logic. I really enjoyed both of these books, and they're relatively cheap, but as I said they are not introductory logic books.
I'll be happy to reply again if you have any further questions.
Goedel's Incompleteness Theorems, by Raymond Smullyan.
From the preface:
> [intended] for the general mathematician, philosopher, computer scientist and any other curious reader who has at least a nodding acquaintance with the symbolism of first-order logic..and who can recognize the logical validity of a few elementary formulas.
I'm guessing most of the people on /r/math meet that description and more. If you want a general introduction to mathematical logic and computation, you should read Computability and Logic by George Boolos. If you can read Boolos, you can probably read Smullyan, and if you read them both you should emerge with some understanding of incompleteness.
The Logic Book is a good text for FOL and the early theorems of meta-logic (soundness and completeness of propositional and first-order logics). It's somewhat slow going though.
A more mathematically inclined text is Herbert Enderton's Introduction to Mathematical Logic. Enderton goes into more of the meta-logic, including incompleteness, Lowenheim-Skolem, and computability. He also touches on second-order logic toward the end.
Along the lines of meta-logic, Boolos and Jeffrey's Computability and Logic is very good as well. (Er, and Burgess. I can only vouch for the 3rd edition, which is pre-Burgess.)
Given that you're already familiar with FOL, I'd lean toward Enderton or Boolos and Jeffrey with the caveat that The Logic Book has endless practice problems and, iirc, answers to many of them in the back of the book (the others have fewer (but more interesting) problems).
If you want to go beyond FOL, I second stoic9's suggestion of Priest's book.
I recommend this to all beginners -- I like the Barwise & Etchemendy book because it's aimed at people with no background at all in logic or upper-level math, it's restricted to propositional and first-order logic (which I think logicians of all stripes should know), and it comes with proof-checker software so that you can check your own understanding instead of needing to find someone to give you feedback.
After that, you'll have some familiarity with the topic and can decide where you want to go. For a more mathematical route, I think Enderton (mentioned previously) or Boolos are good follow-ups. For a more philosophical route, I think Sider or Priest are good next steps.