# Teach Yourself Logic, #7. A bit of deviance

There’s a new version of the self-help Guide downloadable from the Teach Yourself Logic page (added: updated to Version 7.1, Nov. 26).

Heavens this is time consuming! — but having (as it now seems, foolishly) started, I guess I should do the best job on this that I can. Anyway, there are new sections on extensions of classical logic (second order, plural, free) and deviations from the classical paradigm (intuitionism, relevance logics). There also is a major structural change to the Guide. It is now going to be in two big chapters, one on the basics and one on more advanced stuff. Partly this is to make it all look less daunting (the idea is that any grad student working in logic-relevant areas ought to know the sort of stuff that is in Ch. 1, and then the enthusiasts for this or that area can pursue the relevant sections of Ch. 2). And partly this is to acknowledge the fact more advanced work in one area can often presuppose familiarity the basics in other areas.

All suggestions for improvement welcome as always. I’d welcome in particular any additional introductory suggestions on Second-Order Logic, and on Intuitionistic Logic. At the moment, on Second-Order Logic, I start by mentioning the article

• Herbert Enderton, ‘Second-order and Higher-order Logic’, Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/logic-higher-order/

And suggest following that up with

• John L. Bell, David DeVidi and Graham Solomon’s Logical Options: An Introduction to Classical and Alternative Logics (Broadview Press 2001), §3.3.

But now what? Stewart Shapiro, Foundations without Foundationalism: A Case for Second-Order Logic, Oxford Logic Guides 17 (Clarendon Press, 1991) is very accessible — but is there something less weighty to read beforehand?

And on Intuitionist Logic, I suggest starting with

• John L. Bell, David DeVidi and Graham Solomon’s Logical Options §§5.2, 5.3., which give an elementary explanation of the contructivist motivation for intuitionist logic, and then explains a tree-based proof system for both propositional and predicate logic.
• Graham Priest, An Introduction to Non-Classical Logic (CUP, much expanded 2nd edition 2008), Chs. 6, 20. These chapters of course flow on naturally from Priest’s treatment in that book of modal logics, first propositional and then pred icate.
• Then, up a notch in mathematical sophistication (but manageable if you have tackled earlier chapters in this book, so you are familiar with the style), there is Dirk van Dalen, Logic and Structure (Springer, 4th edition 2004), §§5.1–5.3.

We will return in Ch. 2 to some further explorations of intuitionism where we’ll mention e.g. Dummett’s book. But what about other more introductory level material?

### 11 thoughts on “Teach Yourself Logic, #7. A bit of deviance”

1. what I am missing is a good introduction into (evil) axiomatic logic, I my self was thinking about Zemans ” modal logic” (also free online http://www.clas.ufl.edu/users/jzeman/modallogic/ ) but that is in the (maybe even more evil) Polish Notation.

But still what would you advice students who want to learn axiomatic logic and polish notation/ condenced detachment?

1. I say early on that one ought to know about natural deduction and tableaux; but yes, one should also get at least a slight acquaintance with axiomatic systems (and indeed at some point there’s sequent calculi to cover too). In fact, one feature of Bostock’s book (recommended in the starting-first-order-logic section) is that it covers different proof-systems

Perhaps Bell DeVidi and Solomon would also help here. I’ll check this (and look out my old teaching notes related to this too).

And yes, I suppose I ought to refer to Polish notation somewhere …!

1. You can always refer students to the WFF ‘N PROOF game. A quick googling tells me that it has been reissued, but not, it seems, in the wonderful dusty blue box of my youth.

1. I tried to buy the game somewhere in the UK,
but sadly failed. (buying it in the US is just prohibitive :( )
No I only have the instruction book second hand from amazon

2. Part 1 of Fitting’s Intuitionistic Logic, Model Theory, and Forcing provides a good introduction to intuitionistic logic. It covers proof theory and model theory of both propositional and first-order intuitionistic logic. It gives kripke and Beth semantics and provides some basic meta-theoretical results, such as completeness. The proof theory focuses on tableaux proofs, but it connects it to an axiomatic presentation as well. The first part of the book is independent of the second part.

3. There’s A Short Introduction to Intuitionistic Logic by Grigori Mints.

It’s been ages since I last looked at it, though, so I can’t comment on how suitable it might be. However, I noticed a curious comment in one of the Amazon US reviews:

… an excellent introduction to intuitionistic logic can be found in a nominally unlikely book “Lectures On The Curry-Howard Isomorphism” by Sorensen and Urzyczyn. This is a great book on logic, beautifully written.

1. Oops, smites forehead again, as I had known about Mints book (have a copy somewhere) but clean forgotten it. I’ll check it out again.

I didn’t know of Sorensen and Urzyczyn, and have got a copy out to look at. It indeed immediately looks v. interesting, so thanks a lot for this pointer.

4. I was impressed by The Blackwell Guide to Philosophical Logic the last time I looked at it.

It has an article by Dirk van Dalen on “Intuitionistic Logic”, as well as Wilfrid Hodges on “First-Order Logic”, Stewart Shapiro on “Higher-order Logic”, John Burgess on “Set Theory”, Smullyan on “Godel’s Incompleteness Theorems”, Cresswell on “Modal Logic”, Karell Lambert on “Free Logics”, and so on.

It is a collection of articles, and I’m not sure how many of them are good, but when it comes to “deviance”, it seems to be largely a choice between books like this and ones that offer a broad survey by one to three authors; so I think it’s worth a look.

5. Do you have any thoughts on Logic for Philosophy by Sider? It seems like its goal is something along the lines of this TYL project? Is it successful? Or is there simply not a way to become comfortable without spending a nice amount of time with several books?

1. Thanks very much for the reminder about Sider’s book (I glanced at it a while back, but didn’t get a copy). My impression was that the title was rather misleading, suggesting a wide ranging book, but it in fact very much focuses on modal logics. Also it doesn’t even get as far as a completeness proof for predicate logic. So I’d think of it as suitable for undergraduates but falling short of what you’d want serious graduate students to be coping with. However, I recall Sider’s book as looking quite well done at a first glance, so I’ll take another look and maybe add some references to the book in TYL at appropriate points. So thanks again.

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