Thinking about writing a book

I've managed to arrange my teaching for 2016-17 to be basically perfect: I'm doing the first-year introduction to logic course (mandatory for certain degree programmes involving philosophy) and a repeat, though with variation, of this year's third-year logic seminar (completely elective, and advertised also to math and computer science majors). So I've been thinking a lot lately about textbooks.

This year, for the seminar, we did the first seven chapters of Hughes and Cresswell's New Introduction to Modal Logic, and chapter four of Goldstern & Judah's The Incompleteness Phenomenon. Before teaching, I was familiar with H&C since that's the book I learned my modal logic from initially, but G&J was new to me. It, however, fit the bill of being relatively self-contained and something that could allow us to cover the first incompleteness theorem in half a year. We just had our final meeting yesterday, and while the book certainly wasn't awful, we all came away with a distinct feeling that it could've been better -- more explanation, fewer typos, that sort of thing. We collected two pages of errata from that one chapter alone, and in the end I decided their coverage of recursive functions in the final section just didn't do what I wanted it to do, so I scrapped it entirely and wrote my own material for them.

Next year will be my first time doing the intro logic course at Durham, which has previously been taught using tableaux. I am unconvinced of the utility of teaching tableaux in a first year course: Yes, they are easy; yes, students figure them out pretty quickly; yes, they are easy to grade. But, no, they don't really help students understand what it is that logic is. They blur syntax and semantics in a way that can make what logic is and what logicians do utterly opaque -- as I discovered last year when I had a second-year logic class inherited from that first-year one, and I found they didn't understand the difference between syntax and semantics, and thus didn't have a good grasp on concepts like soundness and completeness. My preferred proof-method is natural deduction (again, it's what I first learned, so there is some bias towards it in that respect), because it is somewhat mechanical but also somewhat requiring of imagination, and it makes it easy to do non-trivial soundness and completeness proofs. Now, over the years, I've collected quite a few intro logic books, and I also asked on twitter for suggestions:

#Logicians: What is your favorite textbook for 1st year intro logic that uses natural deduction/Fitch-style proofs?

— Sara L. Uckelman (@SaraLUckelman) April 11, 2016

I got a wide range of responses, including Tim Button's forallx, which looks really interesting. Still, nothing has quite fit the bill, for either the intro class or the revised version of the seminar, despite the plethora of options. In fact, I think there is a connection here: There is a plethora of options because teaching logic is such a personal thing, every person who does it has specific ideas about how to do it, and eventually they reach the point where they are frustrated enough with the teaching materials out there that they decide to write their own.

I think I'm nearing that stage, especially because I've got not one but two courses neither of which have perfectly suitable material already out there. I've already got lecture notes from a second year class on modal logic (mostly applied, little theory); lecture notes from a master's level temporal logic class; and lecture notes from parts of this year's seminar on modal logic and incompleteness. Wouldn't it be nice if I could kill two birds with one stone, and develop a book that would work for both the intro class and the upper level class? (They'd be using different parts of it, of course). But it would give intro students a view towards where they could be going, and it would give advanced students a handy place to refresh their memories -- especially since the math students coming into the third-year seminar probably haven't had any logic before.

Yesterday I took those disparate notes and combined them into a single document. It's got the following table of contents:

• What is logic?
1. Formal argumentation
• Classical Buddhist dialectics
• Aristotelian dialectics
• Medieval dialectics
2. Classical logics
• Term logic
• Propositional logic
• Predicate logic
3. Extensions of classical logic
• Peano Arithmetic
• Modal logic
• Temporal logic
• Dynamic logic
4. Non-classical logics
• Intuitionistic and constructive logics
• Paraconsistent logics
5. Exercises, Glossary, and Bibliography

I'm trying to figure out what to call it. I'm very attracted to the Summa Logicae titles of medieval logic texts, because I do want this to be a sum(mary) of logic. I've thought about Summa Totius Logicae Modernae, except people might think this is "the sum of the whole of modern logic" when I really want it to be "the sum of the whole of logic available modernly". Also, I probably can't get away with titling a textbook in Latin.

So, dear readers, what should I call this book, that demonstrates that this isn't just an introduction to logic, it isn't just an advanced logic text, it isn't merely symbolic logic, it has history and depth and breadth and everything?