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I was reading my daily reddit and came accross this link to a new double major at Oxford, Computer Science and Philosophy.

http://www.comlab.ox.ac.uk/admissions/ugrad/Computer_Science_and_Philosophy

I just wish my university had a double major like this, i would have taken it as an undergrad for sure (I am now doing graduate research in CS). Anyways, i wanted to ask what books are good for beginning and intermediate levels in Logic. I know theres like Deductive Logic, Set Theory, but the actual books i don't know any.

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I'm using the following textbook in my current Symbolic Logic course. I think it's honestly the best book for a beginner, and the book gets to a pretty intermediate level towards the end. ggww.stanford.edu/NGUS/lpl. Also, it comes with a great set of software and tons of really exciting exercises. –  KerxPhilo Apr 24 '11 at 8:34

5 Answers 5

up vote 6 down vote accepted

My preferred intro logic text is Enderton's "A mathematical introduction to logic." Smullyan's book on first-order logic is very nice, though it uses proof trees, which is (awesome but) somewhat unusual. I'm also a fan of Peter Smith's "An Introduction to Godel's Theorems." As far as set theory goes, it really depends how far you'd like to go. I imagine that if you're doing graduate research in CS you know the "basics" that would be covered in Halmos' "Naive Set Theory." If you're looking for more, I also like Enderton's "Set Theory," and after that a big standard text is Jech's.

There's obviously more. You need a good textbook for modal logic, and I don't know any. Hopefully someone else can help fill in the picture.

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Thanks, i will check these out –  gprime Jan 30 '11 at 14:18
    
Among modal logicians who are mathematically inclined, Blackburn & Venema's Modal Logic is very well regarded. I recall it was published in a theoretical CS series of text books. –  student May 22 '12 at 17:23

Lectures in Logic and Set Theory (Volumes 1 and 2) by George Tourlakis. This is (in my opinion) a good beginner-intermediate book. I flipped through both volumes and liked the writing style and presentation. It's not too verbose or too terse.

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Why the down vote? –  PEV Jan 30 '11 at 2:26
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I think some people dislike your tendency to post short answers containing solely links or the titles of books. It was not me. –  Harry Stern Jan 30 '11 at 5:14
    
I thought it was a good post, short but good. I upvoted. –  gprime Jan 30 '11 at 14:17
    
@PEV: Why do you suggest it? Is it beginning or intermediate? (I don't mind the shortness but a little extra might help) –  Mitch Jan 31 '11 at 1:05
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See jstor.org/pss/1556753 and jstor.org/pss/1556754 for my review of this book in the BSL. (click on both for 2 pages) –  JDH Jan 31 '11 at 4:01

I second the recommendations for Enderton's texts: Both "A mathematical introduction to logic" and his text on set theory. If you want something to peruse right now, Paul Teller has a fairly good introduction to logic, available on-line (free, no strings attached) here or, more directly, there.
The first volume is pretty elementary, but the second gets slightly more complex. It's a good start, depending on your background in logic.

Another "starter" book, a bit more rigorous than the usual "Intro to Logic" text, is the classic by Benson Mates, "Elementary Logic", 2nd edition. It's not nearly as "elementary" as some introductory texts, and would be a great start if you're just getting your "feet wet".

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Thanks, Amzoti. I love logic! –  amWhy Apr 30 '13 at 0:53
    
Surely the first answer is special and congratulation until now you have 100 pages of answers!!+1 –  Sami Ben Romdhane Dec 22 '13 at 16:08
    
Thanks, @Sami ! –  amWhy Dec 22 '13 at 16:10
    
What are you talking about, @Bill? My comment applies, and I seem to remember that trivial edits are a pet peeve of yours! –  amWhy Jun 26 at 16:28
    
Feel free to contact the team, @Bill. I honestly don't know what you're referring to. Prior to my recently posted comment below your post, my last interaction with you was on meta, re: congratulations to DonAntonio, weeks ago. I was, half in jest, referencing that comment in my earlier comment. I will certainly remove my earlier comment if it's ruffled your feathers. –  amWhy Jun 26 at 16:33

My first suggestion would be the following article:

Samuel R. Buss, Alexander S. Kechris, Anand Pillay & Richard A. Shore, The Prospects for Mathematical Logic in the Twenty-First Century, 2001, Bulletin of Symbolic Logic 7 (2):169-196.

As a second suggestion, I would suggest reading the articles on Stanford Encyclopedia of Philosophy, the quality is wonderful. Each article is written by an expert on the topic. If you want to know more about a topic, check the list of references at the button of the article.

ps: Berkley and CMU also have quite good programs at the intersection of logic and philosophy, and you can find similar programs by Googling.

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So this isn't the logic reference you asked for, but if you are interested in Philosophy and Computer Science, you might want to check out this website for an MIT course run by Scott Aaronson called "Philosophy and Theoretical Computer Science"

https://stellar.mit.edu/S/course/6/fa11/6.893/index.html

It is a good collection of papers and other references, including a paper of Scott's called "Why Philosophers Should Care About Computational Complexity" that is pretty interesting.

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