There’s an even bigger, even better, shiny new Version 10.0 of the TYL Study Guide now available at the usual URL https://logicmatters.net/tyl/ Form an orderly queue …

The structure of the Guide has significantly changed again (hence the jump in version number). The key section on basic first-order logic at the beginning of the mathematical logic chapter was getting more and more sprawling: it has now been hived off into a separate chapter, divided into sections, and further expanded. My sense is that quite a few readers are particularly interested in getting advice on this first step after baby logic, so nearly all the effort in this particular revision of the Guide has been concentrated on making improvements here. So, inter alia, there are new comments on four outstanding relatively elementary books: Derek Goldrei’s *Propositional and Predicate Calculus*, Melvin Fitting’s *First-Order Logic and Automated Theorem Proving*, Raymond Smullyan’s *Logical Labyrinths*, and (not least) Jan von Plato’s very recent *Elements of Logical Reasoning*.

I still intend sometime to return to say more about the last of these when I’ve had a chance to re-read it: it is in many ways a very welcome addition to the literature. For the moment, I just remark that this book is based on the author’s introductory lectures. I rather suspect that without his lectures and classroom work to round things out, the fairly bare bones presented here in a relatively short compass would be quite tough as a first introduction, as von Plato talks about a number of variant natural deduction and sequent calculi. But suppose you have already met one system of natural deduction, and (still a beginner) want to know rather more about ‘proof-theoretic’ aspects of this and related systems. Suppose, for example, that you want to know about variant ways of setting up ND systems, about proof-search, about the relation with so-called sequent calculi, etc. Then this is a very clear, very approachable and interesting book. Experts will see that there are some novel twists, with deductive systems tweaked to have some very nice features: beginners will be put on the road towards understanding some of the initial concerns and issues in proof theory.

Christian RemlingPeter, great resource, thanks for putting this together and keeping it up to date!

Just one minor comment, for what it’s worth: I think you’re too harsh on Hodel. While (you argue) he may not use the pedagogically best setup and basis definitions, the writing is crystal clear and extremely careful, almost frighteningly so; one of the best math books I’ve come across (and I’ve read a few, at all levels).

RohanGreat Guide! Just a few comments:

1. Have you thought of including the mathematician Marcus Kracht’s text http://wwwhomes.uni-bielefeld.de/mkracht/html/tools/book.pdf in your section on modal logic, whose second part looks at duality theory, correspondence theory, transfer theory and lattice theory?

2. Lots of the logic useful to Philosophers these days relates to natural language semantics, of the sort pioneered by Montague. Your guide does not really help for someone who wants to understand the formidable complexity of Montague’s papers, or the way the type theoretic approach has been developed by people like Johan Van Bentham and Groenendijk and Stokhov. There is little, either, on situation semantics, which is a growth area, nor of Generalised Quantifier Theory (GQT), which occupies an interesting position vis-à-vis the relationship between FOL and SOL. GQT is of interest to Mathematicians, Linguists and Philosophers, as the wonderful book by Stanley Peters and Dag Westerståhl, “Quantifiers in Language and Logic” illustrates (of particular interest to readers of this blog is the outstanding discussion of recent work and techniques concerning quantifier definability over finite domains and finite model theory). A final area that is not discussed is the interesting work done in Formal Language theory: Bûchi’s theorem (a stringset is a regular stringset iff it corresponds to a class of stringlike structures that is finitely axiomatizable in weak monadic second-order logic (this theorem is essential to descriptive complexity theory in Computer Science), Parikh’s theorem (that a stringset over the natural numbers is semilinear iff it is letter-equivalent to a regular set) and the Ginsburg-Spanier theorem (that a stringset over the natural numbers is semilinear iff it is definable in Presburger arithmetic). These are all things that many Philosophers should know about, and an excellent guide to this area is Kracht’s “The Mathematics of Language” http://pub.uni-bielefeld.de/luur/download?func=downloadFile&recordOId=2594509&fileOId=2610875 . Is there any good reason why you have not included discussion of these topics, given that, increasingly in Philosophical Logic and Philosophy of Language a technical knowledge of these subjects is absolutely necessary?

Peter SmithMany thanks for this. I’ll certainly take a look at Marcus Kract’s book. And yes, I agree that I should cover more relevant to natural language semantics. So thanks again!

Daniel NagaseI noticed that you added a section on Monk’s book, but haven’t commented on it yet. Could you give me at least a summary of your opinion about it? I ask this because it has been seating on my desk for a while (a library loan), but I haven’t had the courage to actually read it. I did browse it, though, and his introduction of computability first does seem to make for a different approach to some matters (if I’m not mistaken, he uses Gödel numbering right from the beginning, even using it to prove things like unique readability), but it also appeared to me very tough, perhaps on the same level (or slightly below) Schoenfield. What do you think?

Peter SmithOoops, I’d forgotten I’d optimistically added the heading, and have now deleted it for the moment … I think you are probably right that the book is quite tough (though more than one person has recommended it to me).