Well, it’s not back to square one, but it is time to radically re-think plans for the shape of the book (and what will go into it, and what will survive as online supplements). Let me explain the practical problem — as all thoughts and comments will be gratefully received. Being retired has all kinds of upsides, but I can no longer buttonhole colleagues or long-suffering grad students over coffee. So, dear readers, it is your help and advice I seek!
Background info. The first edition of my Intro to Formal Logic has a little under 350 text pages between the prelims and the end matter. Of those, about 270 pages gently cover “core” material that will survive in rewritten/improved form into the second edition (introductory chapters on the very idea of validity; PL languages and truth-table testing for tautological validity; extending this to deal with the conditional; explaining how QL languages work; defining validity for quantificational arguments; adding the identity predicate and functions to formal languages; a bit of philosophical commentary along the way). The other 80 pages cover propositional and quantificational trees.
So the only proof system in IFL1 is a tree system. Tree systems are very elegant and students find them easy to play with. And ease of use is not to be scoffed at (after all, exploring strategies for completing natural deduction proofs might be fun for the mathematically minded teacher, not so much for the more symbol-phobic beginning philosophy student!). Still, many/most teachers think that beginners ought to know something about natural deduction. Indeed I think that too! — but IFL1 started life as my handouts for a first year course given to students who were also going to do a compulsory second year logic course where they would hear about natural deduction, so I then just didn’t need to cover ND in my notes. Still, for a more standalone text, of wider use, very arguably I should cover ND. People certainly complained about the omission from IFL1, and said that that was why they weren’t adopting it as a course text.
Now, I initially believed that in revising IFL I could cut down various parts of the core material, speed up the treatment of trees (in part by repurposing some material as online Appendices) and “buy” myself some thirty pages that way. CUP said they would also allow me an extra 30 pages (maximum, to keep the overall length of the book under 400 pages). So I thought that would give me 60 pages for chapters on natural deduction.
It doesn’t seem to be panning out quite like that ….! In various ways, I hadn’t thought things through properly.
(A) For a start, in reworking the “core” material in the first part of the book — up to the introduction of quantifiers — I seem to have added to the page length here. Yes, the result is clearer, more readable, more accurate … but not shorter. OK, I have been able to speed up the treatment of propositional trees while improving that too. But it balances out, and the first part of the book is more or less just as long as it was. So I’m not hopeful now of being able to save too many core pages and/or cut down the treatment of trees by much. On the other hand, the material on natural deduction for propositional and predicate logic looks as if it will run to about 80 pages, if I aim for a comparable level of clarity, accessibility and user-friendliness.
So instead of adding 30 pages, I’m in danger of adding something like 70 pages to the book, if I cover both trees and natural deduction — and there is probably no way that CUP will wear that.
(B) But in any case, I’m beginning to think that a full-scale treatment of both trees and ND — length apart — is just too weighty for an avowedly introductory book, too daunting. A beginning student shouldn’t come away from a first logic text feeling overwhelmed! Better to have mastered one way of doing things, while having been told that isn’t the end of the story.
So even if I could find and apply Alice’s magical “Shrink me” potion, and could cram everything in, I now not sure that would be a wise way to go. Which leaves me with two options:
- Keep the text as a tree-based text, of much the same size as present, while adding ND chapters as an optional extra available online. (Perhaps using just some of those permitted extra printed pages as an arm-waving introduction to what is spelt out in the online chapters.)
- Make the text a ND-based one, of much the same size as present, while offering tree-based chapters as an optional extra available online. (Perhaps using just some of those permitted extra pages as an arm-waving introduction to what is spelt out in the online chapters.)
Keeping to (1) would, yes, give the world an improved version of IFL, but one still subject to the shortcomings that many perceived, namely that the book wouldn’t have a “real” proof-system.
Moving to (2) is therefore tempting, as I think I can present an intuitively-attractive Fitch-style system in a very user-friendly way.
But yes, I do still think that trees make for a very student-friendly way into a first formal system. But then, I do think natural deduction is more, well, natural — regimenting modes of reasoning we use all the time, so surely something beginners should know about early in their logical studies. And arguably (as now some commenters note below) a grasp of ND is something that students need to be able to carry forward into later studies.
So which way should I jump? Choices, choices …! I’m still mulling this over, and all thought-provoking comments that might help me decide will be most gratefully received.
[As well as comments below, there is a thought-provoking Twitter thread from Greg Restall, @consequently, with others responding.]