Of making many intro logic books there is no end

There was an interesting post on Daily Nous by Curtis Franks a few days ago. He starts with some comments on the much used book and software package Language, Proof and Logic (LPL) by Jon Barwise, John Etchemendy, and Dave Barker-Plummer. I do agree, by the way, with the criticisms. Franks’s discussion then opens out to look at some other intro logic texts, with and without associated courseware.

There are a number of books mentioned that are not familiar to me, but then I haven’t been keeping up with what’s out there. I’ll have to dip into those that are available online sometime. Curtis Franks doesn’t mention Nick Smith’s excellent text at all (rather a surprise), so I’m in good company, as he doesn’t list my IFL either. One commentator mentions using IFL but his students finding it too challenging as soon as it moves beyond the initial very introductory chapters (that soon?)

It is sheer madness I know, but despite the multitude of intro logic texts, I confess I am still inclined to have another bash at an entry-level book, Another Introduction to Formal Logic. But freed from the IFL1 constraints of fitting round the then first-year Cambridge syllabus, or the IFL2 constraints of length and level for the CUP Introductions to Philosophy series, I’d structure it rather differently and make it slightly more sophisticated, and indulge myself …  There is no point in trying, impossibly, to please everyone!

7 thoughts on “Of making many intro logic books there is no end”

  1. It appears that the material on deductive machinery and basic metatheory, at the end (included there to show that despite the piles of insults found in the earlier chapters and the framing of the project (e.g., “the usual emphasis on formal proof somehow suggests that mathematical activities are the highest point of logical intellectual skills, a claim as debatable as thinking that the best test of someone’s moral fiber is her behavior in church.”), the authors “have no quarrel with standard curricula”), is still in progress.

    Is there a danger that a person who is comfortable with sentences like that might have a blind spot when it comes to judging introductory textbooks?

  2. Daniel M Gessel

    I have been enjoying working through the programming assignments in “Mathematical Logic through Python”. The provided framework leaves a well selected set of tasks to the reader and working through implementation details is ideal for some learners (myself, at least). While not everybody loves Python (it’s not terribly efficient), the level of abstraction (most especially container comprehensions) supports simple and elegant solutions.

    1. Why don’t you write a sequel? Your book is great and you don’t need to change it. Maybe a book on metalogical results for propositional and FOL?

  3. Franks is an Associate Professor of Philosophy, and it has often struck me in the past that it’s primarily philosophers who seem interested in introductions to formal logic.

    When I was a maths student (quite a way back by now), the intro logic course was offered by the Philosophy Department, not Maths. It used one of the Copi books as a text and some early software that students used to construct proofs in propositional logic and FOL. The closest Maths came to intro logic was a course in Mathematical Logic that used Enderton’s book as a text. It was considered difficult and spent almost no time on actually constructing formal proofs. (There might have been a few exercises, nothing more.) Prove things about formal proofs, yes; prove things formally, no.

  4. I wish you wrote your own version of “Computability and Logic”. There are hundreds of decent intro to logic texts out there.

  5. I’m currently working through GWT 2nd Ed – I’m using it as a preliminary to get up to speed on the relevant content so I can work on axiomatic theories of truth. I’m the paradigmatic case of a philosopher who started out symbolphobic and maths-loathing and slowly got absorbed into the world of mathematical logic bit by bit. This has meant having to use (and be frustrated by) many intro-to-logic textbooks. A year ago I was fulminating vengeful plans to write my own and show ’em how it’s done once and for all, and hopefully maybe one day I will, but I see now that the pursuit of “the last logic textbook anyone will ever need” is a moving target if anything is. That said, I think I have found a prescription for logic textbooks that is objectively correct:

    If definitions/theorems/proofs are to be compared, present them side by side on the same page.

    Say you’ve stated and proved theorem 74. It has some interesting schematic similarity with theorem 67 which the reader encountered two chapters ago. A reference to the page, or a link in the PDF, is nice. But honestly, just write theorem 67 down on the page next to theorem 74. Let the comparison be visually immediate.

    I think this prescription generalises further to the tune of: restate things, mercilessly. Just….say it again. Restate the definition wholesale. Copy/paste the three lines of the theorem rather than merely invoking it by its numerical label and leaving the reader to flip back to the page that it was on. Repeat stuff. Just label it and repeat it.

    (I think Peter’s books do this a lot more than most other logic texts, and are so much more readable for it. But Peter could go further still!)

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