Year: 2019

Truth trees for propositional and predicate logic

With IFL2 (the book itself) temporarily put aside, I’m turning to the task of putting together its associated webpages.

The initial effort will go into supplying  answers to the end-of-chapter exercises. This might take a little while! (Even when there is a significant overlap with the exercises for IFL1, I’ll have to LaTeX all the solutions for the first time.)

One task, though, is already done. Regular readers here will know — heavens, I’ve bored on about it often enough! — that while IFL1 did logic by truth trees, IFL2 instead uses a Fitch-style natural deduction system. However, if you are fan of trees, all is not lost. I’m making material on trees available as online supplements. These are now available.

So you will  find linked here two PDFs. The first, already pre-circulated here,  is heavily rewritten from the propositional truth-tree material in IFL1. The second contains three chapters on quantification trees, a pre-revision version soon to be replaced with an improved one! Both PDFs should be of some use  to students who want to know about trees (or would like supplementary reading for a tree-based course) even if they aren’t using IFL2. So long as you know something of the basics of propositional logic and truth-tables, and then know the language of quantificational logic, both documents should be quite accessible.

Sound the trumpet!

A full PDF of IFL2 is off to CUP! Again. And not for the last time, because there’s the whole process of sending it out a proof-reader still to be gone through. But it’s a major step on the road. The book is at last in a stable state, and it is — let’s hope — very minor tinkering from here on in.

Heavens, this all seems to have been a great deal of work. Remind me again why I agreed to do a second edition?

The small matter of a cover picture … and one that got away

Paul Klee, Castle and Sun 1928

The Cambridge Introductions to Philosophy series has a standard cover layout — for example, here’s the cover of my Gödel book in the series, with a rather anonymous bit of abstract artwork (not chosen by me). Some other books use more interesting illustrations — for example, here’s the cover Martin Peterson’s book on Decision Theory (this is part of The Cheat with the Ace of Clubs (c. 1630) by Georges de la Tour).

Well, I’d wanted to use the Paul Klee’s Castle and Sun for the second edition of IFL which will appear in the same series. But sadly, CUP’s arrangement with Getty Images has changed, and that’s no longer an option. So I wondered about a Cézanne still life from Chicago. I had a print of another of his still lifes with apples on my wall as a logic student all those years ago, and rather liked the idea of — as it were — going full circle with another one. But my editor thinks it isn’t sufficiently “logical/technological”, and I can see the point.

But that leaves me at a bit of a loss where to go next. So suggestions of suitable cover art for an introductory logic text will be most welcome! It needs to be reasonably vibrant in colour to fit into the overall series design, of the same general shape as the two illustrated examples. and, ideally, freely available under a creative commons licence or similar. Any thoughts?

[By the way, I’ve only just discovered the website of the Chicago Art Institute: well worth a visit!]

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!

 

J. Donald Monk, Mathematical Logic and Lectures on Set Theory

I have only just noticed that J. Donald Monk has made his admirable Mathematical Logic (Springer, 1976) freely available for download, which could well be of interest to some readers here.

A smaller number of discerning readers might also be interested his book-length Lectures on Set Theory (work in progress, it seems, last updated a few months ago). Unlike that earlier more discursive book, these are rather terser notes. But they consequently cover a great deal, including — on a quick look — a significant amount of relatively recent material. The main parts of the Lectures are

    1. Logic
    2. Elementary Set Theory
    3. Generic sets and forcing, I
    4. Infinite combinatorics
    5. Generic sets and forcing, II
    6. PCF
    7. Continuum cardinals

This seems as if it could be a useful resource.

 

Modernizing

There have been two big distractions from blogging over the last month. Well, there have been three if you count the political chaos here in the UK, and the unnerving sense that things really are falling apart in a dangerously nasty way. But I have nothing to add on that, except perhaps a recommendation of Chris Grey’s long-running Brexit blog, in the unlikely event that you are interested in finding informed writing on the ongoing shitshow here yet haven’t come across this truly admirable weekly commentary.

But back to local distractions. One is having major building work done, a loft extension, and some other modernizing of the house. And I have no horror stories to report. All is going very well, it seems; our builders have been/are continuing to be terrific, and everything looks as if it is going to turn out even better than we hoped. But still, despite that … Three months of fairly continuous disturbance, albeit mostly at quite a low level, have been strangely unsettling — considerably more so than is rational, no doubt for deep reasons of having your space invaded. Weekends have been cherished oases of peace. However, after two solid weeks, the plasterers finished on Friday. So from here on, there won’t be the same levels of dirt and dust to contend with. There’s still a lot of upheaval in the house but I’ve ceremoniously taken down the dustsheets from all over the books in my miniature study, and a more cheering semi-normality returns  … Only another two months, on and off, to go …

The other distraction has been the dratted IFL2. Yes, I did get a full version in to CUP by the beginning of August. But — long story — the Press have decided that they don’t like the layout I thought we’d agreed, so I’ve been recasting the logic book into the same format as my Gödel book which they also published, Computer Modernizing the text. But of course, it isn’t as simple as changing the LaTeX font command in the preamble. Oh no! For a start, lots of proofs that can’t be split over pages now need to be relocated, nudged up and down by rewriting surrounding text. And other text needs to be rewritten to stop chapters now ending a few lines onto a new page. And so on. And so forth. You really don’t want to know the ins and outs. Partly I’ve been grinding my teeth in frustration. But partly I’ve been forced to do some close re-re-reading, and this has led to some significant improvements in clarity and even a late rearrangement of some material. So it’s not at all been wasted time. But I’ll be pleased when this is all done. And oh my days, how boring is indexing?

So Brexit, building and book has for a while meant no blogging energy. But I’m now going to try to pick up the threads … Onwards!

Rachel Podger in conversation

I didn’t mention here a recent concert at Wigmore Hall with Rachel Podger and her small band of friends, Brecon Baroque, playing Vivaldi with such enormous verve and love for the music. A wonderful experience, which left the audience cheering for more!

So I’ve just listened with particular enjoyment to this Wigmore Hall podcast where Rachel Podger talks delightfully about playing baroque violin, about her band Brecon Baroque, and about Bach and Vivaldi. Worth the listen!

A LaTeX indexing trick

Oh, the joys of indexing … Though using the LaTeX indexing tools reduces the pain a bit. Encountered one problem, however:

Suppose you mention Aristotle (as you do) at the top of p. 40. And then you discuss a quite different point from Aristotle e.g. from the bottom of p. 41 over to page 43. Then you surely want the index entry to read

Aristotle, 40, 41–43

So you put \index{Aristotle} in your text around the top p. 40, and then mark the start of the page range with \index{Aristotle|(} near the bottom of p. 41 and finish the range with \index{Aristotle|)}. Only to find to your annoyance that Makeindex produces

Aristotle, 40–43

Drat! What to do?

As I discovered from tex.stackexchange, the thing to do is to use the imakeidx package, and so your preamble has

\usepackage{imakeidx}
\makeindex[options=-r]

The option suppresses adjacent page numbers for an index heading being crunched into a page range, so that page ranges are given only in response to explicit codings for ranges using \index{headword|(} and \index{headword|)}.

Maybe everyone except me knew that! — but I will add a note for posterity to LaTeX for Logicians.

Scroll to Top