IFL2, back to the drawing board …
Help!
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 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 bit under 350 text pages between the prelims and the end matter. Of those, about 270 pages cover “core” material that will survive in rewritten 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). The other 80 pages cover propositional and quantificational trees.
So the only proof system in IFL1 is a tree system. Tree systems are elegant and students find them easy to play with; but many/most teachers think that beginners ought to know something about natural deduction. Indeed I think that too! — but IFL1 was basically 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 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.
Well, …
It doesn’t seem to be panning out quite like that ….!
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 half 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 no way that CUP will wear that. Moreover, the sheer length of the book will look rather off-putting, another reason for keeping to length.
I seem to have three options
Find and apply Alice’s magical “Shrink me” potion, and try to cram everything in.
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.)
I really, really, don’t think that (1) will fly, or I wouldn’t be (this far into the work on the second edition) facing the issues that I am.
Keeping to (2) 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 (3) is therefore tempting, as I think I can present an intuitively-attractive Fitch-style system in a very user-friendly way.
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.
So which way should I jump? Choices, choices …!
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