Smith on the Open Logic Text

Peter Smith has written two blog posts (one, two) about the Open Logic Text.  He makes some very good points and raises some issues.  Since the OLP is under continuous development and still in the “alpha” stage, of course it won’t yet be a perfect replacement for a commercially published textbook without at least some work on behalf of an instructor who wants to use it.  The PDFs we produce so far, in particular, are not suitable for self-study.  Stay tuned for the “beta” release, when we hope to produce self-contained PDFs that can be used out-of-the-box.

Here are some of the specific criticisms, with links to the GitHub issues I’ve created for them. Feel free to comment on those or other issues or add your own!  And in the spirit of open source: feel free to propose some of these additional motivations and explanations!

  • If you start with the part on “First-order Logic”, you will need to have previous experience with basic set theory for notation and mathematical background, and be familiar with proof methods such as induction.  The former is covered in the part on “Sets, Functions, and Relations”, the latter, a part on “Methods” is in the works (issue #60). The part on “First-order Logic” of course also needs an introduction (issue #69)!
  • The sequent calculus material is sparse; we need more explanation of what proof systems do in general, how the proof systems relate to others a student might be familiar with from an intro course.  We now do have an alternate chapter on natural deduction, but that also needs to be related to the Fitch-style variants commonly used in intro textbooks (issue #61).
  • We have a chapter on “Beyond First-order Logic”. As Smith says, it’s a “place-holder for later developments”, however, it can already serve the useful purpose of providing pointers to further topics in a course that can’t cover them in detail.  Of course, we do plan to cover them in detail eventually. I’ve added issues for modal, second-order, and intuitionistic logic as first priorities.  We already have some material for modal logic ready to be converted to OLP format.
  • Smith describes Aldo’s treatment of interpolation and Lindström’s theorem as “crisply and clearly done.” However, the coverage of elementary model theory is spotty and much too fast (issue #65).
  • The chapter on the lambda calculus has to be expanded to be useful (issue #66)
  • Smith suggests to add “quite a lot more arm-waving motivation” to the arithmetization chapter (issue #67).

I do want to repeat here a comment I made in response to Smith’s summary remarks,

A general reflection on OLT. Having got to the end, it is clear that the different segments by different hands presuppose quite significantly different levels of sophistication from the reader. This makes me wonder a bit about the wisdom of presenting this resource as one long document rather than as a suite of separate modules. From the point of view of the rather daunted student, splitting things up would make it a lot clearer that you can and should  pick and choose various parts, depending on your background and interests. But also dividing things into modules might encourage the potential contributor.

It is true, the PDFs we have on the download page “look” like complete books, but they aren’t (yet) — they’re just dumps of the material in the repository in its entirety. And that material is carved into modules. Every section is its own file. If someone likes part Y but prefers a different approach in parts X and Z, they can just make a PDF out of Y. Or they can write their own treatment of X and Z and combine it with Y (and, hopefully, gift their alternative version of X and Z back to the project). The download page contains a link to a PDF I used as the text for the course on Intermediate Logic I taught at McGill last term, and I wrote about how to make your own such text previously.  That said, if you just look at the “complete” PDF you will have Smith’s reaction and justifiably so.  I’ve added issue #68 to remind myself to add an “instrnote” environment to hold comments to the (potential) instructor about the state of parts and chapters, what they depend on, and hints on how to arrange and customize them.