As I go through chapters of my Introduction to Formal Logic, heavily rewriting them for the second edition (only scattered paragraphs are surviving unaltered from the first edition, and I’m adding wholy new chapters too), I’m occasionally pulling other introductory books from my shelves, to check their coverage, to see how they handle particular points and whether they have nice expository ideas I could
steal gratefully emulate.
One excellent book which I seem not to have mentioned here before — and parts of which really should get warm recommendations in the Teach Yourself Logic Study Guide — is David Makinson’s Sets, Logic and Maths for Computing (Springer, 2nd ed. 2012). It deserves a full-scale review here: but for the moment, this post is a place-holder, to flag up the existence of this text.
As the title suggests, the book is primarily aimed at computer science students. But the assumed level of mathematical competence is pretty low, and many philosopher students could find this very useful, perhaps as a supplement to more conventionally arranged texts for students one step up from raw beginners at logic. Here, Makinson starts by looking at the kind of mathematical notions which any philosophy student leaning in a logical direction ought to know about — sets, relations, functions; ideas of induction and recursion (and there’s some more, e.g. about trees in the abstract). As he goes along, he introduces logical notions briefly “as they arise in the discussion of more ‘concrete’ material. This is done in ‘logic boxes’. Each box introduces just enough to get on with the task in hand. Much later, in the last three chapters, all this is brought together and extended. By then, the student should have little trouble appreciating what the subject is all about and how natural it all is, and will be ready to use other basic mathematical tools when studying it.”
A great deal of pedagogic thought has evidently gone into the book, and it is very admirably clear, and good at getting across Big Ideas and their motivations without getting bogged down by over-abstraction or unnecessary pernickety detail. So: well worth taking a look at if you don’t know the book (as indeed I didn’t until quite recently).