Soundness, completeness, aesthetics

[Update to linked file: 27 Sept]

There’s one big change in the latest version of IFL2. I’ve taken up a good suggestion (in so doing, once more appreciating the kindness of strangers), and I have re-arranged the material on soundness and completeness.

The chapters on PL and QL metatheory in the main text now just explain what those metatheorems say and why they matter. Outline proofs are now in an Appendix. This way, the main text isn’t interrupted by sections signalled as skippable in a first course; while the proofs get a more expansive treatment than they did before so those readers who are interested have a better chance of following the arguments. This seems to me to work much better.

The Appendix is almost stand-alone. To understand it, you need to know that the Fitch-style system I’m talking about has dummy names (parameters) but no free variables, and terms are just proper names or dummy names. A q-valuation is, as you would expect, an assignment of domain, references to names, extensions to predicates. An expanded q-valuation for a language adds assignments of references to one or more dummy names as needed. And set/collection talk can be taken as talk of virtual classes, interchangeable with plural talk, with choice of idiom dependent on local convenience. With that by way of preamble here is the new Appendix. I hope it is clear the sort of level of understanding I am aiming to convey. I’ll no doubt revise this again for minor glitches. But at this stage all comments still most welcome of course.

In the latest issue of the London Review of Books, the novelist Sarah Perry reviews a book about depictions of malaria in nineteenth-century and postcolonial fiction. Which was actually sounding surprisingly interesting — for Sarah Perry herself just can’t write badly! — until she tells us that this book “does not offer any particular aesthetic pleasures. Elegance and clarity of style is neither attempted nor achieved. This is an academic monograph …”

Oh dear. What is the point of writing such a book — after all, one dealing with literary themes and the human world they engage with — without trying to trying to give the reader at least some literary pleasure in well-turned phrases and elegant juxtapositions?

And introductory logic books too ought to aim for readability and lightness of touch, and offer some modest aesthetic pleasures. We can all think of well-known and often-used books which are worthy but, by this measure, fail spectacularly (no names, no pack drill). This is a rather daunting thought when you are about to launch your own effort into the world. I like to think that the new Appendix has it cute moments. But fond authors aren’t the best judges!


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