The *Teach Yourself Logic 2016 Study Guide* is linked here at Logic Matters but also at my (decidedly sparse) academia.edu page. Rather startlingly, the latter link has now been followed up over 50K times. Who knows how much impact the *Guide* really has. Still, I occasionally get appreciative emails (and equally cheeringly, I don’t get protests from colleagues complaining bitterly that I am leading the youth astray). So, hopefully, *TYL 2016 *is doing some good in spreading the logical word.

That’s the plus side. The downside is that, given it indeed seems to be used quite a bit, I suppose I should keep on updating the *Guide*. The year is already rattling by, and I guess I should soon start turning my mind to the time-consuming business of (re)reading around logic books old and new, familiar and less familiar, as background homework for producing *TYL 2017*. So if you do have suggestions for improvement, and in particular suggestions of recent books I should really take a look at over the next few months, do let me know sooner rather than later.

So many logic books, so little time …

One book that I don’t remember seeing mentioned is Craig Smoryński’s

Logical Number Theory I(unfortunately, I don’t think volume II will see the light of day). Although the books is more advanced (and the beginning does involve a bit more math than your typical logic book), it is a must read for anyone who wants to dive a bit deeper into the interrelations between logic and arithmetic. In particular, the book has a really in-depth treatment of both Presburger arithmetic and Skolem arithmetic (the theory of multiplication), with lots of good pointers about where to look for further information. Also, I really like Smoryńki’s more conversational style and he often offers many interesting digressions and philosophical or historical asides.Perhaps you could add a new section on Teaching Yourself Philosophical Issues in Logic, listing relevant research papers (as opposed to just textbooks). After all the technical work, it’d be good to see what philosophers have said on it. Specifically, I’m thinking of things like:

– An addendum to the modal logic section: What is modal logic good for? What is the nature of possible worlds? What else can we model with modal logic, apart from necessity and possibility? This section could include debates between Quine and Barcan Marcus, the nature of possible worlds (a bit iffy, but it comes up in philosophical talk), modal logic and belief revision, and modal logic and information.

– Philosophical applications of the Incompleteness theorem: What import do the theorems have? This could cover Hilbert’s Program, and the Lucas-Penrose argument. (This is already well-covered by Torkel Franzén’s book, so perhaps this section isn’t so necessary.)

– Work on logic and truth: What does logic have to do with the Liar Paradox, Curry’s Paradox, and other paradoxes? An initial read could be Roy Cook’s book on Paradoxes (Polity, 2013), supplemented by relevant research papers.

– The relationship between logic, reasoning and language: Harman’s criticisms of logic as providing the norms for thought, and inferentialist approaches to logic – and how they affect the proof theory.

– We have probability-based representations of belief, and logic-based representations of belief: how are the two related? Ton Sales has an initial article in the Handbook of Philosophical Logic, and I’m sure there’s much more out there.

A guide to the philosophical applications of logic would be very welcome, especially to those who have done formal work and are wondering about the philosophical issues around it.

I hesitate to expand TYL very far in this direction. It would add very significantly to what is already a time-consuming project. But also the Stanford Encyclopaedia articles on topics in philosophical logic are usually very good (often really excellent), with extensive further pointers to the literature, so we already have a terrific resource of “guide[s] to the philosophical applications of logic”.

On some topics, TYL does indeed refer to the relevant SEP article. But yes, I will check. Maybe I do need to be a bit more consistent topic by topic in giving pointers to review articles on the philosophical literature.