Formal logic text reccomendations

September 9, 2007 5:58 PM

Help me explore my new found interest in formal logic.

I'm interested in doing some reading on formal logic. I didn't have time in undergrad to take a logic class, and I'm regretting it now. What do you consider essential texts? Where is a good place to start if I am going to be (attempting to) teach myself?

posted by zennoshinjou to education (21 comments total)

Causey's Logic, Sets & Recursion is a very good book. It contains a lot of exercises that are suitable for self-study.
posted by jayder at 6:12 PM on September 9, 2007

I used A Concise Introduction to Logic and The Game of Logic when I was studying for the LSAT.
posted by T.D. Strange at 6:26 PM on September 9, 2007

Wilfred Hodges' 'Logic' is a good standby. Make sure you get a recent edition (early ones had a lot of minor errors).
posted by fingerbang at 6:29 PM on September 9, 2007

My undergraduate introduction class used Logic and Philosophy by Tidman, Kahane, et al. It's really simple and straightforward, to get you used to the symbolism and proofs.
posted by Ms. Saint at 7:11 PM on September 9, 2007

What do you want to use it for? Are you mainly interested in philosophical applications, parsing English sentences and practical real-life reasoning situations, or the math/computer science angle?
posted by LobsterMitten at 7:16 PM on September 9, 2007

And, do you like a chatty approach that gives a lot of English exposition relative to the amount of symbolic stuff, or do you like a down-to-business, I'm-not-afraid-of-symbols, approach?
posted by LobsterMitten at 7:18 PM on September 9, 2007

I've taken logic classes as an undergrad, a grad student, and I've TA'd a couple.

The most basic course in the series used Salmon's Into to Logic & Crit Thinking. It's focus is on logic and critical thinking. It doesn't do much with symbolic logic and is split pretty evenly between inductive and deductive logic.

I also TA'd the advanced version of that same course, and it focused a bit more on symbolic logic. We used Hurley's A Concise Introduction to Logic It's expensive, but it comes with a CD rom that has a ton of practice material with instant feedback.

The first symbolic logic book I used was Copi's Symbolic Logic. I don't remember it being $90, but I probably bought it used (it's available for $40 used on amazon). It's a little outdated, but for learning the basic of symbolic logic, it's pretty solid. Before starting grad school I wanted to review logic, so I went through and did most of the exercises in this book. It's been around long enough, I bet there's places you can check at least some of your answers. Some of the reviews say it's "outdated" but

I've also taken 2 advanced logic courses as a grad student. We used Metalogic: An Introduction to Metatheory of Standard First Order Logic in one of the courses (metalogic). I thought it was pretty easy to follow and it is commonly taught from. Not always because it's great in every area, but because it's one of the few books that really covers these topics.

In the other advanced logic course (advanced symbolic logic) we used the fourth edition of Computability and Logic, which apparently now has a 5th edition out. This book really is a classic, and it's a little more mathematical than the metalogic book. It focuses more on Turing Machines and Godel's theories. The first 3 editions were by Boolos and Jeffrey (at least the 3rd ed. was for sure, and I think the first two were as well). The fourth edition is actually quite different from the third, and I have both, and it might be worth it to get both if you can. The fourth added Burgess as an author and he added quite a bit and wrote more problems at the end of each chapter.

A book which I haven't used in class, but is considered by some to be the "Bible" of mathematical logic is From Frege to Godel: A Source Book in Mathematical Logic, 1873-1931. This isn't really a textbook, like the other books I have listed, but it contains a collection of primary source articles and gives a good history of logic. Godel's proofs were some of the most important in logic and a lot of 20th century logic is in response to them.

I also once asked one of my logic professors for any "can't miss" logic books. He recommended the Frege to Godel book and the Computability and Logic books mentioned above.

He also said in his Intro to Symbolic Logic class he uses Language, Proof and Logic which comes with some useful software. He called it "remarkable" and said he used it in his advanced logic course one year.

He also recommended A Mathematical Introduction to Logic which is expensive on amazon, but I'm pretty sure my mom got it cheap from somewhere (it was a Christmas present). It might have even come from England.

Also, if you can't tell, I'm a logic fan, and I like teaching (and could use the practice), feel free to email me if you have some questions once you start.
posted by chndrcks at 7:31 PM on September 9, 2007 [17 favorites has favorites]

Woops, in my paragraph on Copi's Symbolic Logic, I meant to say that "some of the reviews say it's 'outdated', but at least the chapters on the rules of inference, rules of substition, and quantifiers (most of what you'd learn in a 200 level symbolic logic course) are really quite timeless. "
posted by chndrcks at 7:40 PM on September 9, 2007

Language Proof and Logic comes with software that allows you to prove things about a little world of shapes (eg given certain facts, you will prove that the triangle is above the circle), very nice if you are a visual or more hands-on type since you can see the effects of different operations. The software (in the editions I've used) allows you to send in your problem sets over the internet to get "graded", as well. It's the most often used text for logic courses that I've been around for.

Another often used introductory book is The Logic Book by Merrie Bergmann et al.

One that I love for its chatty approach and lots of goofy little side excursions is Sweet Reason by Jim Henle and Tom Tymoczko. The examples are pretty dated (eg lots of stuff about Madonna and George Bush Sr.), and if you're a down-to-business type don't get this one -- it will drive you crazy with its chattiness.
posted by LobsterMitten at 7:40 PM on September 9, 2007

And for books once you've got the tools down and want to move on into work real philosophers use, I've always heard Boolos's Logic Logic and Logic described as the book to read. (Though I haven't.)
posted by LobsterMitten at 7:46 PM on September 9, 2007

Sweet Reason - chatty, organized very idiosyncratically, but lovable.
The Logic Book - dry but very often used for its exhaustive coverage
posted by LobsterMitten at 7:51 PM on September 9, 2007

He also recommended A Mathematical Introduction to Logic which is expensive on amazon, but I'm pretty sure my mom got it cheap from somewhere (it was a Christmas present). It might have even come from England.

Oh, Jesus, no, not Enderton. That book is impenetrable. I think it is impossible to get anywhere with Enderton on your own; you have to be in a good class.
posted by jayder at 7:51 PM on September 9, 2007

Enderton's Mathematical Introduction to Logic is actualy a classic textbook, and I would recommend it if you have a strong mathematical background. I think it's actually very clearly written for a mathematics textbook. You can find a slightly more modern approach to the same material in Ebbinghaus, Flum, and Thomas's Mathematical Logic (which also appears to be less expensive). But both of these are at the level of advanced undergraduate mathematics textbooks, so if that's not what you're after, you may want to look elsewhere...
posted by klausness at 3:40 AM on September 10, 2007

Thanks for all the recommendations- this is a great set of information to draw from.

LobsterMitten- I'm primarily interested in it I guess as a check on myself and a way to refine whatever nascent logic might already be present in my head. I like thinking in a well reasoned manner and find systems for doing things appealing as another tool to approach that.
posted by zennoshinjou at 4:02 AM on September 10, 2007

There's also hughes and cresswell, a standard textbook for modal logic.
posted by advil at 5:16 AM on September 10, 2007

Godel, Escher & Bach, an Eternal Golden Braid.
posted by polyglot at 7:02 AM on September 10, 2007

In a class I'm taking right now we're using A Modern Fromal Logic Primer by Paul Teller. As a bonus, it's all available online for free.
posted by MsMolly at 8:59 AM on September 10, 2007

A great introductory logic book, particularly good at talking about how hard it is to change basic english into logical symbols, is Quine's

Elementary Logic, Revised Edition

It's short too. (I wish I had not gotten rid of my copy a few years ago.)

(yay -- i finally posted a link successfully)
posted by wittgenstein at 12:09 PM on September 10, 2007

I was a TA for a couple of logic classes, and we too used The Logic Book. I've since had the chance to examine a number of other logic books since then, and I still consider it to be pretty good. I might even be able to dig up one of my older copies to pass on if you're interested - drop me an email if you'd like me to look around for one.
posted by emmastory at 12:43 PM on September 10, 2007

zennoshinjou: Given that seem to want logic as a general check on your thinking (rather than as, for example, a background for math) here is my advice. Unless you are *very* comfortable with symbol manipulation and math, I would say that you want to use one of the intro-level books described here. Don't mistakenly think that you can start with an advanced book just because you are generally smart. Some more advanced logic books are almost entirely proofs with symbols, which can be very hard to read if you're not comfortable with the notation. (It can be like reading a book written in a foreign language, rather than a book in your own language that teaches you how to speak the foreign language -- discouraging!) Even if you are very comfortable with symbolic stuff, you'll still need the groundwork of basic first order logic before going on to the next levels.
posted by LobsterMitten at 1:43 PM on September 11, 2007

LobsterMitten's definitely right that formal logic isn't something you can just jump into the deep end of. However, I think that someone who was comfortable around math in college would be able to understand most of Nagel and Newman's Gödel's Proof. It's about very abstract logical concepts and you need some interest in the foundations of mathematics, but it's really clear and readable.
posted by ontic at 11:12 PM on September 11, 2007