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Can anyone recommend a good comprehensive introduction to formal logic? I realise the field is enormous. I am particularly interested in books that a) provide historical context, b) cover both first and higher order logic, and c) preferably includes a discussion of model theory.

Martin C.
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  • "Introduction to mathematical logic" by Elliott Mendelson. – YCB Jan 04 '18 at 20:56
  • @Gödel thanks, I’ll check it out. – Martin C. Jan 05 '18 at 08:31
  • @user21820 I think so - you are welcome to close this question, if that's what you're after. – Martin C. Apr 08 '24 at 13:32
  • @MartinC.: I've voted to close as duplicate, but 4 other users need to review and agree, or you (the asker) needs to agree. This doesn't imply that your question is bad, but simply links it to the other question. It also doesn't mean that the other question totally answers your question. In particular, Rautenberg doesn't cover higher-order logic, but it does cover model theory and proof theory and does provide a solid foundation for a rigorous study of logic, so you can easily learn higher-order logic on your own later. The comment above was auto-generated by SE when I voted to close. – user21820 Apr 10 '24 at 03:27

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forall $x$ is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. You can get it for free in PDF in its website, linked above.

I've been recommended Teach Yourself Logic 2017: A Study Guide, which you can also get for free.

Xander Henderson
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I personally like Bell & Machover's A Course in Mathematical Logic. It's not always the easiest text (some chapters are more brisk than is perhaps ideal), but it's pleasantly comprehensive. It's got propositional and first order proof theoretic basics, a pretty good introduction to model theory, two chapters on recursion theory, a chapter on intuitionistic logic, and closes with a surprisingly thorough introduction to set theory.

The box it does not check is higher order logics, but one is unlikely to find these in introductory logic texts (just like you're unlikely to find infinitary logics in an introductory text). Such logics are a somewhat less straightforward, more specialized topic, and you'll likely need a separate text to cover the topic in any detail.

Malice Vidrine
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