And it is now exactly a year since the self-published version of the second edition of An Introduction to Formal Logic was published as a paperback. This sells about 75 copies a month, very steadily. Again, the figure strikes me as surprisingly high, given that the PDF has also been freely available all along — and that’s downloaded about 850 times a month. Some of the online support materials, like the answers to exercises, are quite well used too. All in all, pretty pleasing.
I occasionally get friendly feedback about the book: and it will be interesting to see if sales/downloads jump at the beginning of the new term/semester as one or two more lecturers adopt the book as a main text. I do hope so (if only because students shouldn’t be being asked to fork out $100 for second-rate course-texts!).
Still, there’s a lot about this book that could be better, so I really do want to have a third bash at an introductory logic text, and sooner rather than later. But I haven’t yet decided quite how to handle this. Something that is recognisably a third edition of the present book? Or, leaving this version out there as it is (apart from any needed corrections), a rather different, brisker book, requiring just a bit more of the reader? Choices, choices …
3 thoughts on “Big Red Logic Book, no. 2 — a year on”
A “rather different, brisker book, requiring just a bit more of the reader” sounds more interesting to me. Would it also be a more interesting project from your POV? Is there so much about IFL2 that ‘could be better’ that it already needs a 3rd edition?
I think a different book might let you work with your ideas about better ways to present logic, without feeling an undertow (so to speak) towards an existing text, in the way a revision might; and that exploration could then feed into an IFL revision if one still seems desirable.
(Anyway, such thoughts reminded a bit of what happened with Hughes and Cresswell’s An Introduction to Modal Logic which was followed by A Companion to Modal Logic, and finally by A New Introduction to Modal Logic.)
I truly believe this is the best introduction to this level of logic that exists so I am not surprised that it has been downloaded so many times (I also purchased a hard copy just to have handy). My only suggestion for a new edition of the book is to do something you have mentioned before, work in both natural deduction and tableaux. I agree with your sentiments that students (and others!) find trees to just be very fun to use, and it is a good idea to early on show both refutation and non-refutation systems. It both provides a clear example of “there is more than one way to carry out the mechanics of this subject” and it helps point towards applications of logic, tableaux being used in subjects like computer science and natural deduction more reflective of what a mathematician might do in practice.
I could see, at first glace, three approaches to this. First would be to write a cohesive book first using one system and then building off of that exposition to introduce the other. However, this lends difficulties to a teacher who might want to use the second system in their course instead of the first. So another option would be to introduce one and the other in modular and independent places in the book, so that anyone would be at liberty to pick and choose which system they want when teaching or learning. The issue here of course is that there would necessarily be repetition in the exposition and would probably unduly increase the length of the book. The third option I see would be to rework the extra notes you have online now for trees into an appendix. I feel like this is a little bit inelegant of a solution, but probably not the worst idea in the world. Personally, I like the first idea the best, but I can agree with the anticipated criticism that this approach would make it difficult to use the text in a class just using the secondly introduced system. Hence, though, another reason why it would be good for the teacher to introduce both types of systems! Surely any of these, or of course other, options would qualify as a genuine third edition as opposed to just a revision and I think it would serve to fill an important place in the literature.
As an anecdote, there is a twitter bot which tweets out propositional tautologies every few hours, https://twitter.com/mathslogicbot, and every time I see one I work out a natural deduction and a tree proof that it’s a tautology, sort of like a relatively easy daily chess puzzle. There are also bots others have made who reply to the tweet with worked out solutions in both systems and one which tells whether or not the proposition is intuitionistically valid, so you can easily check your answer. Sometimes, though, I forget exactly what the rule for e.g. a negated biconditional is so I check your notes on trees to quickly look up the rule instead of just enlarging the tree by expanding it out as a negated conjunction of converse implications. The notes are very good, and I think it would be great to reincorporate them into the book in some way.
I believe that this version is perfect. No matter what, you always think what if I wrote that part differently. However, it would be more useful to write a sequel, a next level text in logic, maybe an introduction to metalogic.