**Quick links**

**Teach Yourself Logic 2017: A Study Guide**(find it on academia.edu by preference, or here)**Appendix: Some Big Books on Mathematical Logic**(pdf)**Book Notes**(links to 35 book-by-book webpages, the content overlapping with the Appendix)

**In more detail, on TYL**

Most philosophy departments, and many maths departments too, teach little or no serious logic, despite the centrality of the subject. Many students will therefore need to teach themselves, either solo or by organizing study groups. But what to read? Students need annotated reading lists for self-study, giving advice about the available texts. The *Teach Yourself Logic *Study Guide* *aims to provide the needed advice by suggesting some stand-out books on various areas of mathematical logic. NB: *mathematical* logic — so we are working a step up from the kind of ‘baby logic’ that philosophers may encounter in their first year courses. You can also find here some supplements and further *Book Notes* of various kinds.

The main Guide and its Appendix are in PDF form, designed for on-screen reading. Learning mathematical logic involves a serious time commitment, and different people have different backgrounds/requirements, so you’ll want detailed advice from which you can work out which books might be suitable for you. That’s why the full Guide *is* rather long. But it is (I hope) approachable written and informative. Try it out here:

**Teach Yourself Logic 2017: A Study Guide**Last updated 1 Jan 2017. (Find it on academia.edu by preference, or here).

If the Guide’s length makes it sound daunting, there are also some supplementary webpages which might help ease your way in:

**About the Guide**Is the Guide for you? A short excerpt on the general aim of the Guide and what it covers.**The Very Short Teach Yourself Logic Guide**A summary of the headline recommendations on the core mathematical logic curriculum.

**In more detail, on other book notes**

**Appendix: Some Big Books on Mathematical Logic**(PDF, 40pp.) And appendix to TYL, with comments on a number of the more general, multi-area, textbooks on mathematical logic. Last updated 14 December 2015.**Book Notes**Links to 35 separate webpages on the books covered in the Appendix and also to various other books on logic and the philosophy of mathematics. Latest new page added 10 March 2016.

It goes without saying, of course, that all constructive comments and suggestions continue to be most warmly welcomed. Many thanks, in particular, to those who have earlier sent comments which are now deleted because I’ve taken up (or plan to take up) the suggestions in newer versions of the Guide.

Dear Prof. Smith,

firstly, thank you for assembling all this information about Logic and writing the Guide. I not only bought your books (willing to have the proper time to finally get through IGT) but also rely on your inputs – for instance: it was a very refreshing and rewarding experience reading the first 4 or 5 chapters of Chiswell&Hodges after I had Van Dalen as a course book on introductory logic (ouch!), so your comments on the Guide were surely very useful.

I’d like to ask then if you have any thoughts about Haskell Curry’s Foundations of Mathematical Logic, I didn’t find nothing about it here. I got this book and I wonder if there is something interesting about it.

Best Regards,

Rodrigo de Almeida

I would like to know what you think of Katalin Bimbó’s new book “Proof Theory: Sequent Calculi and Related Formalisms” (2014, Taylor and Francis). It’s a textbook aimed at advanced undergraduates focusing ‘on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic.’

Do you think it would be suitable for learning more about sequent calculi in general, and proof theory in specific?

Thanks for alerting me to this book, which I didn’t know of before. I can’t give you a view, then, though preview pages look pretty encouraging.

I’ve noticed a new category theory book that takes a different sort of approach:

Category Theory for the Sciencesby David I. Spivak (MIT Press). It’s not quite out in the UK but is available from US Amazon. It focuses on ideas and examples, rather than proofs for theorems, and it looks like it aims to show how category theory can be useful outside mathematics.There is a version online at the author’s website, here: http://math.mit.edu/~dspivak/teaching/sp13/CT4S–static.pdf

I’ll take a look, and thanks for the info!

I’d be interested in hearing what you think of Johan van Benthem’s “Modal logic for open minds”. I just got it in the mail today and I like what I see on a quick flip-trough. Of the other books I’ve used (Hughes & Cresswell, Sider, Girle…) this seems by far most similar to Girle’s book—not just in content but also in being written in a readable and engaging style. However, it’s more than 100 pages bigger than Girle’s, and I believe a bit wider in scope.

There was a brief comment in version 10 of the Teach Yourself Logic Guide. It said:

Some would say that Johan van Benthem’s Modal Logic for Open Minds (CSLI 2010) belongs much earlier in this Guide. But, though developed from a course intended to give ‘a modern introduction to modal logic’, it is not really routine enough in coverage and approach to serve at an elementary level. It takes up some themes relevant to computer science: worth having a look at to get an idea of how modal logic fares in the wider world.

I would like to know what you think of Paul Tomassi’s ‘Logic’? One difficulty I found with this book, is that there are no solutions therein, and the webpage for access to the solutions has, since Paul Tomassi’s passing, taken them offline.

Tomassi’s book is OK — but I’d say counts as baby logic, which isn’t really the topic of the Guide, and there are better books at that level.

Yeah, after I reread the introduction to your book, I realized that you might not include it for that reason. Thanks for the great resource, I am especcially pleased that you introduced the books that deal,with mathematical topics that might be missing from an introductory Logic course like More Precisley by Steinhart, very useful.

As the guide is made towards people studying logics for the purposes of both mathematics and philosophy, why not suggest Susan Haack’s Philosophy of Logics? I am a mathematics student with interest in logics and lately bought this book. It’s an amazing read, and it talks a lot about why we need logic and how to build a logic.

Well, I’m remember Haack’s old book as indeed being good of its kind, and I’m glad that you found it helpful. I’ll have to take another look at it and consider whether this (and some similar books) might be mentioned in what is, basically, a guide to mathematical logic.

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I used J L Bell & M Machover’s ‘A Course in Mathematical Logic” (1977) when it first appeared as a friendlier alternative to Schoenfield. At the time this was in conjunction with Bell & Slomson’s “Models and Ultraproducts”. Bell & Machover’s book is still in print and not particularly expensive.

Bell and Machover is indeed pretty good — it’s on my list of books to comment on one day!

First off, thank you for providing this great resource. Having a guide is great for allowing more time to admire the scenery, rather than focusing wholly on not falling over cliffs, so to speak. Second, what are your thoughts on “The development of Logic”, by W. & M. Kneale?

I think the Kneale’s book was a remarkable achievement in its time, and it does stand up remarkably well 50 years on. But obviously a lot more, some very good indeed, has been written on the history of logic since then!

Thank you for your work in laying out a path to follow for self-study.

I am a little sad there isn’t more in the way of free books as the price can be very much like a closed door to so many of us who do not have access to large universities, and getting worse these days with the crunch in fund to public libraries. All the same, it look like you have done a very good service to people – I hope to prove that in coming days!!

I very much appreciate the point about the expense of logic books (even libraries in not-so-rich universities have problems keeping up). I do mark in the Guide some particularly good-value books and even a few freely available resources: but I realise that isn’t enough for those who have no access to major libraries (though you might find that such public libraries which you do have access to have an interlibrary load system.

Obviously, I can’t link to the well-known PDF repositories which break copyright (even when the copied books are old ones and even out-of-print).

I do think there are various good reasons for maintaining traditional book publishing (though I’m open to persuasion on the point). But I do think that it should be default that academic publishers — especially those that are university presses — put a significant amount of their back catalogue into the public domain e.g. a decade after publication. By that point sales will usually be low, so neither press nor author will lose much, but the book can gain a new lease of life.

Thank you very much for your guide. I have found it very useful in preparing for graduate school. I was wondering what you thought about “Introduction to Mathematical Logic” by Alonzo Church.

Church’s book was, in its time, a wonderful achievement and an immensely influential classic. It is, however, ages since I have looked at it. I ought to do so again one day!

What do you think about Schaum’s Outline of Logic, Second Edition of Nolt, Rohatyn and Varzi. I think it is the best for ‘baby logic’.

I don’t know the book, so can’t comment, sorry!

Thank you for putting this together. I stopped the guide where it says its not for elementary logic. I don’t have any experience with logic. Are there any free resources you recommend to learn elementary logic?

Well, in the Guide I do recommend Paul Teller’s introductory book which is freely available online.

Hey Dr. Smith! I’m a baby logic student reading your introductory text and the TYL Guide and I thought you might want to know that there’s a typo on page twenty-seven of the TYL Guide: “Now, I recommended A Friendly Introduction as a follow-up to C&H: but Leary’s book might not in every library”. I think the word ‘be’ was intended to be in there?

Also, I’m wondering what you think of Smullyan’s A Beginner’s Guide to Mathematical Logic. It might help me gauge what I’ll think of other texts.

I found your Guide really helpful for up-skilling in logic, sufficient to TA a class in Intermediate Logic—thank you.

I’m wondering if you’re aware of anything comparable in other areas of mathematics, particularly probability and statistics?

Thanks for the nice words about the Guide. But no, I don’t know of anything comparable in the probability area — I’d be reduced to googling, like you!

This looks very interesting and I want to start but I didn’t study philosophy at an undergraduate level at all. Could you recommend me any texts I could read to familiarise myself with Baby Logic?

Oooh sorry, I saw your answer to Shealton George. Will try Paul Teller’s book. Would be grateful for any other suggestions you can throw out.

Thank you so much for putting this guide together. It looks like a very helpful map!

I think that in the latest version of Appendix there are references to other sections which has been removed (see page 6,8, 33 and 36). Please take a look at them.

I love this guide! It’s very helpful.

I was wondering if you’ve read John Burgess’ “Philosophical Logic”. If so, what are your thoughts on it?

I am not a philosopher with no academic prospects whatsoever but I am interested in formal logic and this exactly what I have been looking for! There’s always a mountain of books to choose from when looking into any academic field and it is positively dizzying to choose among them, for a neophyte it often feels like being beset by a swarm of locusts. As soon as the uni opens up I’m heading to the library and scouting out your beginners recommendations! Thank you again :)

Hi,

Thank you so much for putting this online! I have spent some time reading your guide, and have concluded that my knowledge of mathematical logic is restricted to some baby logic: I have finished reading (and doing all the exercises of) Patrick Suppes’ and Shirley Hill’s ‘First course in Mathematical Logic’ and have started reading G.T. Kneebones’ ‘Mathematical Logic and the Foundations of Mathematics’ (with S.T. Kleene’s Mathematical Logic waiting to be read – I know it’s in your recommendations). I’m still a bit confused at what the next step should be: reading Modern Formal Logic Primer by Paul Teller, or can I start with a book on FOL? Or is this too early too? My budget is limited, so I’m restricted to (legally) free online resources or the Dover publications. Thanks in advance.

Pierre

Hello, do you have any references about these 2 books?

1- Introduction to Logic by Harry J. Gensler

2- Introduction to Logic by Irving M. Copi.

Thank you very much.

I don’t know Gentler. But Copi is at a more elementary level than the Guide is dealing with.

I have found many books recommended in your guide encouraging so far as I could preview them online. But, equally, many become quite unencouraging to a poor student trying to teach himself logic from scratch when he sees their price.

P. D. Magnus’s text «forall x» is freely available online, and, I believe, is currently used for the Part IA logic paper. What is your opinion of this text?

The other more affordable books I have found are

Volker Halbach’s «The logic manual»,

Raymond Smullyan’s «A beginner’s guide to mathematical logic»,

Joel W. Robbins’ «Mathematical logic: a first course»,

Patrick Suppes’ «Introduction to logic»,

Suppes and Shirley Hill’s «First course in mathematical logic»,

Wilfrid Hodges’ «Logic», and

Alice Ambrose and Morris Lazerowitz’s «Logic: the theory of formal inference».

I would appreciate your comments on as many of these books as you have encountered.

I’ll hope to comment on a few of these in the next edition of TYL

There’s a brief (1-paragraph) comment on Smullyan’s

A Beginner’s Guide to Mathematical Logicin the current version of TYL and a proper discussion of Robbins,Mathematical Logic: A First Course, in the TYL book notes, here:http://www.logicmatters.net/tyl/booknotes/robbin/

Are you familiar with Gamut’s Logic, Language, and Meaning, Volume 1: Introduction to Logic as an intro?

I’m hearing about this quite a bit.

Do you have any opinion on his?

In the past, I did take a quick look at this, but obviously wasn’t enthused enough to recommend it in TYL. But I have had other recommendations, so perhaps I should take another look!

Some 50 years ago I learned a lot of (the Dutch translation of) J.E. Lemmon’s “Beginning Logic”: https://www.goodreads.com/book/show/606295.Beginning_Logic

There seem to be a small mistake in the TYL, in section 4.4.1.: Leila Haaparanta’s book is called ‘The Development of Modern Logic’ instead of ‘The History of Modern Logic’.

Mr Smith,

Thank you so much for writing and posting this guide! I study philosophy in a continental philosophy-oriented college and, desperate as I was for advanced courses in logic, I almost cried when I found this jewel on the web (ok, maybe not, but I was very happy). Keep up the good work, you’re actually helping people out there!

Always good to hear the Guide is helping someone!

hey i was wondering your thoughts on one of the other books in the second oxford texts in logic series: proof and disproof by bornat.

i realize that it is much more germane to computer science, but all the same, if youre familiar with it im curious to know where it might be placed in the guide in terms of difficulty and coverage and if you might know a better way of familiarizing oneself with the concepts covered: constructive proof, disproof, hoare triples, etc.

in any case,

thank you for the guide it has helped immensely!

Maybe in the next edition! But at the moment I don’t know the book well enough to say anything helpful about it.

I’m actually new to philosophy and wanting to delve into philosophy of logic. Is this guide recommended for a complete amateur? And is the book: A Concise Introduction to Logic by Patrick J. Hurley a good elementary book?

The Guide isn’t really for beginners. Hurley’s book is ok as an elementary text; but I would rather recommend Nick Smith’s Logic, The Laws of Truth.

Hi!

I am just interested in your thoughts on Daniel Cunninghams “Set Theory: A First Course” (Cambridge Mathematical Textbooks).

Thanks for this wonderful resource!

I did take a look at Cunningham’s book when it came out, but wasn’t immediately excited. It is at quite an elementary level, and I’m not sure why one would choose it over other classic elementary texts. But I’d need to spend more time on the book to make a fair comparison.

Dear Prof. Smith,

thank you for your helpful guide!

I wonder what is your opinion on one of the newer set theory textbooks, namely, the one by Abhijit Dasgupta, please see the link:

https://www.amazon.com/Set-Theory-Introduction-Real-Point/dp/1461488532/

Should one prefer it to Goldrei/Enderton as a first course?

Thank you very much!

Yours sincerely,

Karl.

Thanks for bringing Dasgupta’s book to my attention — I hadn’t come across it before. Looking at the detailed table of contents, it looks rather different in style and approach to Goldrei/Enderton. The latter two both introduce axioms early and don’t develop a lot of what you might call the ordinary mathematics of sets; in Dasgupta you get much more set-theory-for-mathematicians and the axiomatic approach comes much later. Which approach is appropriate to a first course would depend very much on the aims and objectives of the course.

Dear Prof. Smith,

thank you very much for precisely pointing the difference between the books. It is interesting to note that recently there appeared another book on the set theory that seems to belong to the opposite pole in the sense that the strong accent is put on the axioms from the very beginning. This is the book of Daniel Cunningham,

https://www.amazon.com/Set-Theory-Cambridge-Mathematical-Textbooks/dp/1107120322

They might complement each other well.

It is important to choose the right textbook from the start, that is why I am so captious as to finding the most appropriate one for me. I was heavily traumatized in my school years by the Gindikin’s book on the algebraic logic, which I was trying to learn the logic from. I would avoid repeating the experience.

Hi Peter.

Will the TYL study guide be updated for 2018? When in that case? I plan to start reading it soon.

Yes … eventually. But mostly in minor, presentational ways. I’m not planning a major overhaul of the recommendations this time around. Though it is worth highlighting that The Friendly Introduction to Mathematical Logic which I warmly recommend anyway is now freely downloadable.