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In my discrete math course we went over the basics of propositional logic and predicate logic. We covered things like truth tables, connectives, and quantifiers. I am interested in studying more mathematical logic, but I don’t know which book to choose. I’ve looked at Peter Smith’s Guide but I’m still having a hard time knowing which book to choose. It seems like things are done differently from book to book. I’ve looked at reviews for a lot of logic books reviewed on Peter Smiths blog and Amazon but I can’t really pinpoint a book because usually there is something each book doesn’t do great. For example in a lot of the reviews the reviewer usually mentions that a book uses a deduction system that they don’t like. I’m looking for a book that can teach me more about propositional and first order logic but also go a little further. For example, a book that could teach me what a deduction system is. I want something that can teach me more formal logic at a good level for a person self-studying the subject. Is there some sort of standard text that is used to begin learning formal mathematical logic? Thank you!

Dr. J
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    Goldrei, Propositional and Predicate Calculus: A Model of Argument is a wonderful book for beginners. I used it for self study. It doesn't cover natural deduction though, which I recommend you learn. – Porky Jun 29 '24 at 08:02
  • I agree with @Porky's choice of Goldrei's book. Possibly useful is my own path in logic as described in this MSE answer (which I haven't yet gotten around to continuing since then). – Dave L. Renfro Jun 29 '24 at 11:06
  • I can't recommend any particular book, but I think you should get one with accompanying proof checking software to get immediate feedback on each line of proof as you enter it. – Dan Christensen Jun 29 '24 at 18:20
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    Aren't ALL book recommendations and reference requests "opinion based?" – Dan Christensen Jun 30 '24 at 04:55
  • Yeah lol. Idk who closed the question – Dr. J Jun 30 '24 at 05:13

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"I’ve looked at Peter Smith’s Guide but I’m still having a hard time knowing which book to choose. It seems like things are done differently from book to book." Yes, things are done differently in different books -- at different levels, in different presentational styles, prioritising different proof systems, etc. That is exactly why I put together the Guide to help people orientate themselves.

And judging from the vagueness of your question, I suspect that you aren't really clear quite what you are looking for. Which is absolutely just fine if you are just starting out! So probably the thing to do is to dip into a few of the alternatives recommended in the Guide (like Goldrei's book which others have recommended in comments but equally which some readers will find too slow/pedestrian) and see what works best for you. We can't predict that!

All the recommended books in the Guide would, I think, be widely regarded as very respectable, with their own strengths (though of course different people would rank-order them differently), so whatever you choose (and ideally, look at more than one on a particular topic-area) -- if they seem attractive to you -- should repay study.

Peter Smith
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  • I found that learning logic helped me understand proofs better and helped me with writing them. I want to learn more about quantifiers, how to translate complicated English statements about math into symbolic form. I also want to learn more formal mathematical logic like natural deduction, Godels Incompleteness theorems, etc. I am willing to build up to it, I’m just having trouble finding the best book to start with to build up to the more advanced books. – Dr. J Jun 29 '24 at 19:22
  • In my case as an absolute beginner would it be best just to choose a book and read it, without worrying about the technicalities in the reviews such as the deduction system used? – Dr. J Jun 29 '24 at 19:22
  • @Dr.J Just choose a book whose style/level you like and work through it seems a good plan! – Peter Smith Jun 29 '24 at 19:35