(For new readers: in our math logic reading group, we are working through Maria Manzano’s Model Theory, as a warm-up exercise to tackling Hodges’s Shorter Model Theory.)
Writing logic books involves all kinds of comprises and trade-offs between approachability and absolute precision, between breadth and depth; and all kinds of decisions have to be made about coverage, the amount of more philosophical commentary that you give, and so on and so forth. It is, as I found writing my two logic books, a horribly difficult business making sensible decisions — which is not to say that there is just one way of getting them right. So I’m now pretty reluctant to get too critical (am I mellowing with age?). Still, I have to say that I’ve come to think that Manzano’s book really isn’t terribly good. I certainly wouldn’t recommend anyone following our example, and using the book. True, Manzano is not at all well served by her translator, but that’s only a small part of it: key ideas are far too often just not sufficiently well-motivated and clearly explained. Which is a pity because there are certainly some nice sections. But it is all too uneven in execution to be the helpful introductory guide we were looking for. Though it is certainly not obvious who, at this sort of level, we should have been reading instead.
I hereby bag the title Model Theory without Tears: A Philosophical Introduction for the book which my counterpart in some more or less close possible world is beginning to wonder about writing before the equally not-yet-started Ordinals, Cuts and Consistency. Choices, choices.
2 thoughts on “So, not Manzano … but who?”
I have asking around about a good book on this subject for some time. The problem I have with standard textbooks is that they introduce the fundamental ideas very quickly. Some of them do this in a circular way. For example, one book defined the important concept of truth in terms of ‘satisfaction’. If you then searched for a definition of ‘satisfaction’, it was defined in terms of truth.
I pointed this out to a professional mathematician (not the author of the book) who agreed that it was circular, but said that in order to understand it, one would have to read on and do some examples and work through and so on, and eventually one would understand.
As you can imagine, this reply was guaranteed to throw someone with a philosophical training into an apoplectic fit.
Thus, unless you can recommend me a good book that covers the basics in a clear and coherent way, I recommend you write one. I for one would buy it. There would be less interest from the gentlemen’s book club, though.
A terrific idea. Do write it. And soon!
It will also help you get all that Gödel out of your system.