Books are never really finished.
But the pressure to publish, to have something to show for your time, becomes too great. Or your friendly publisher goes from merely nagging to threatening to take back even your meagre advance if you delay delivery any more. Or you simply can’t, for the time being, face another rewrite. Or all three, in the case of the first edition of An Introduction to Formal Logic.
As I work through that book again — and fingers crossed that the Syndics of the Press formally agree to a second edition, as I’m now about 100 pages into a rewrite — I’m struck what a really mixed bag that edition is. There are some quite nice episodes, which I still like and which need little reworking; other episodes where things need to be smoothed but which are basically on the right lines; but also far too many places where I need to do a lot better.
And in some of those cases it isn’t just presentational changes that are needed. There are thoughtless foul-ups that require sorting out. There I am, in the old Chapter 10, giving a sermon on minding our ‘$latex \textsf{P}$’s and ‘$latex \textsf{Q}$’s (propositional letters in a formal language) and distinguishing them from ‘A’s and ‘B’s (schematic variables helpfully added to logicians’ English to help us, inter alia, generalize about wffs in our formal language). And then, dammit, in Chapter 11, when talking about the expressive adequacy of a language with conjunction, disjunction and negation as the built-in connectives, I find that they are places where I do things in terms of ‘$latex \textsf{P}$’s and ‘$latex \textsf{Q}$’s where really I needed, for the intended generality, ‘A’s and ‘B’s. Hell’s bells. How on earth did I not notice that before, when it should have been glaringly obvious all these years? After all, this is baby logic…
One of those occasions, then, for those uncomfortably mixed feelings known to authors lucky enough to get a second shot at a book (I remember the sensation well, from when I was revising my Gödel book). There is horror at the earlier foul-up, relief that you have spotted it and can make it good, and sheer panic at the thought that if you managed to make that egregious mistake without noticing it for years, there could well be other things, equally bad, that are still passing you by.
Oh, the joys of logical authorship. Wouldn’t be without them for the world, of course.
At that point in my baby logic class I get pretty expansive and detailed about use/mention and generality. And, since I’m writing either on a whiteboard or a document projector, I use α and β, since fon-stylings are hard to write and the switch to Greek emphasizes the distinction. (I also opt for the “we don’t know what the symbols actually look like, these are their names” view and, for a few sophisticates, something about juxtaposition indicating concatenation. But mostly, it’s to avoid writing quote marks when they’re not really needed.
… The name of the song is called “Haddocks’ Eyes”.’
‘Oh, that’s the name of the song, is it?’ Alice said, trying to feel interested.
‘No, you don’t understand,’ the Knight said, looking a little vexed. ‘That’s what the name is called. The name really is “The Aged Aged Man”.’
‘Then I ought to have said “That’s what the song is called”?’ Alice corrected herself.
‘No, you oughtn’t: that’s quite another thing! The song is called “Ways and Means”: but that’s only what it’s called, you know!’
‘Well, what is the song, then?’ said Alice, who was by this time completely bewildered.
‘I was coming to that,’ the Knight said. ‘The song really is “A-sitting On a Gate”: and the tune’s my own invention.’