This and that

Postcard from Monmouth

We have been staying in a cottage near Monmouth for a few days. The countryside here is indeed a particularly green and pleasant land; we can sit outside the cottage looking over many rolling miles towards the Black Mountains. The ruins of Tintern Abbey are close by, as is Raglan Castle (both so very well looked after by Cadw for the Welsh Government, and both sites surprising quiet). There is a lot of wonderful walking here, through local woodlands, and in the Usk valley and the Wye valley. The weather has been kind. So a delightful escape from Cambridge.

With brilliant timing, the day before coming away, when I should have been concentrating on things domestic, Logic Matters got hacked. Or rather — since “” then delivered a Chinese language advert, which hardly looked like a hack aimed at the typical reader here — I suspect some WordPress plugin had been hacked. (I’d been experimenting with different plugins while giving this site a fresh coat of paint). It took a while for me to find the source of the trouble; but then someone kindly recommended the Wordfence security plugin which quickly pinpointed where the evil code been added. Fingers crossed, but I hope the site is now more secure from such exploits. A long afternoon quite, quite wasted though. Not good for the blood pressure.

Calm was restored driving down to Monmouth and stopping at Kiftsgsate Court Gardens and then on to High Glanau, both gardens real works of art. We will visit Coton Manor Garden on the way home, which is even more stunning in its way (though perhaps I prefer the slightly wilder, less perfectly kempt style of Kiftsgate). I have said before, that gardens can be art-works of a kind that the English both do particularly well and particularly love. Is there, I wonder, anything attractively and insightfully written by modern philosophers on the aesthetics of gardens? (A genuine question!)

… and back again

Update on the Logic Matters website. You can get lost down the infinite rabbit hole of WordPress customizations. But I’ve managed to escape, fixed on a theme, suppressed most of its fancy options, aiming for simplicity verging on starkness, and have got to work … Lots still to be done (for a start, in making more tablet and phone friendly), but you’ll get the basic idea. Any helpful comments/suggestions will of course be welcome.

Update on the hardback of Gödel Without (Too Many) Tears. Hooray! — a copy (from UK Amazon) has arrived at last, and another copy (from Blackwell’s, one to send on to the British Library) arrives tomorrow. UK and US Amazon are both now promising very speedy delivery.

I must say that I am very pleased with the result, it is really decently produced. So that, together with the sales figures, encourages me to organize hardback library copies of IFL and IGT. More about that anon. But for the moment, do please remember to get your local friendly librarian to order the hardback GWT for the library! — details here.

Down the rabbit hole …

This Logic Matters site currently lives on Bluehost. But for various reasons, I’m in the middle of moving to a different hosting provider, Siteground: significantly more expensive (after the initial year’s discount) but by very many accounts also significantly better. Certainly, an experimental test version of the site runs there a lot faster, both on my iMac and even more so on an iPhone. As I’ve said before, the whole site could do with a good deal of tidying under the bonnet. So the needed update will keep me from fretting about the state of the world for a week or two.

I’ll need then to chose a modern WordPress theme that maintains the uncluttered look I like. I’ll ignore the pricey paid options. That only leaves about eight thousand free themes to choose from. So this is going to be dead easy. Down the rabbit hole I go …

Big Red Logic Books: half year report

Self-publishing seemed exactly appropriate for the Big Red Logic Books. They are aimed very particularly at students, so why not make them available as widely as can be? — free to download as PDFs, for those happy to work from their screens, and at the smallest possible cost for the significant number who prefer to work from a physical copy.

I’d certainly warmly encourage others to self-publish, if it is appropriate. However, as Bishop Butler didn’t quite say, every book is what it is and not another book. And every author’s situation is what it is. But if you want info about the whys and hows and wherefores of self-publishing do get in touch.

With minor hiccups, my experience with the Amazon KDP system has been very easy and straightforward. I started writing up some detailed techie notes to post here, but quickly realized they were likely to be of very little general interest! But some might be interested, and a few encouraged to follow my example, by the raw figures for the first half of 2021 (so this is the period after the initial flurries of downloads and sales last year, and without any particular advertising efforts).

PDF downloads Paperback sales
Intro Formal Logic 5247 453
Intro Gödel’s Theorems 3730 352
Gödel Without Tears 995 432

I’m rather surprised by the very different ratio of downloads to sales for GWT. Overall,  I am more than happy with these figures. And no, I’m not making a fortune! — the royalties are set at pennies per book. The hope was just to cover set-up costs, and to defray some of the hosting costs for Logic Matters.  I’ll re-do the sums from time to time and lower the prices further if I can.

As I’ve noted before, there is now a hardback for libraries of GWT which has, to my surprise, sold 62 copies in the first two weeks. Or so say Ingramspark who provide the hardbacks. Though whether anyone has yet seen a copy out there in the wild, I have yet to hear! I’m still myself waiting for a copy from Amazon and a copy from Blackwell’s (two copies, so I can send one off to the British Library for posterity …).

More forthcoming logical treats

Two more books forthcoming from OUP that I am also really looking forward to seeing. First, there is Salvatore Florio and Øystein Linnebo’s The One and The Many: A Philosophical Study of Plural Logic. Since the ground-breaking work of my one-time colleagues Alex Oliver and Timothy Smiley, starting over twenty years ago, I’ve found this an intriguing topic. And I’m fully persuaded, for example, that low-level plural talk can do much of the work we conventionally use low-level set talk for, in an ontologically innocent way. But Alex and Timothy in the end push things a great deal further (both with e.g. what strike me as inelegant formal complications, and with over-ambitious claims about how far we can replace set theory with a theory of plurals). I’ll be very interested to see what Florio and Linnebo have to say in assessing the state-of-play in work on plural logic, and in their own philosophical discussions. Credit to OUP again: this book will be published as a pricey hardback but also as free open-access online.

Back in the day, I was for a while interested in the vexed topic of the sorites paradox and formal theories of vagueness. One of the most thought-provoking writers on vagueness at that time was Crispin Wright, and he has continued to revisit the topic repeatedly over the years. He is now collecting together fourteen papers written over nearly fifty years, with a long expository introduction by Richard Heck, as The Riddle of Vagueness (again OUP). I confess I never reached a settled view of what would count as a satisfying answer to the puzzlement about vagueness that I had, and in particular I was (and am) unclear exactly what a formal theory (supervaluationist, intuitionist, degree theory, whatever) is supposed to buy us. Having not thought about all this for a good while, I’m looking forward to revisiting Wright’s earlier papers and reading some of his later work on the topic.

A hardback version of Gödel Without (Too Many) Tears became available a couple of weeks ago (to add to the freely-downloadable PDF and the very cheap paperback). Aimed very much at libraries — because librarians turn up their noses as Am*z*n-only self-published paperbacks  — I hadn’t the foggiest idea how many copies a hardback would sell, or whether I’d recoup the modest set-up costs (including e.g. buying “proper” ISBN numbers attributed to Logic Matters as an official imprint).

Well, Ingramspark (who do the distribution of print-on-demand hardback copies to booksellers) report almost 60 sales. So I won’t end up out of pocket. I haven’t yet had my own ordered copy; so my fingers are still crossed that the hardback looks as good as the paperback. But assuming I’m happy with the copy when it arrives, that encourages me to similarly arrange for hardback library versions of An Introduction to Formal Logic and of An Introduction to Gödel’s Theorems. Watch for an announcement.

As I said a couple of posts back, I badly need to update this website. But it is becoming clear, looking at the under-the-bonnet tangle, that I really need to rebuild the site from the ground up, starting with a blank canvas and transferring across what’s worth keeping, editing as I go. That will appeal to my nerdy side, but will no doubt take quite a while. In the meantime, then, my apologies that pages on this old site are often loading very slowly. Though a couple of minor tweaks yesterday should have improved things slightly.

Forthcoming book: An Introduction to Proof Theory

The next chapter of my Beginning Mathematical Logic: A Study Guide is announced as covering proof theory. I’ve been quietly bemoaning the fact that there hasn’t been a good, well-written, up-to-date introduction that can readily be recommended as a teach-yourself book at the right sort of level. So I thought I was going to have to put together a rather complicated set of suggestions (“read this chapter from this book, then look at those excerpts from that book, and follow this up with some of that other book”), and that would require a lot of homework — especially as I was finding that my memories of what is covered where are pretty fallible.

So I’m just delighted to discover by accident that there is book forthcoming from OUP next month by Paolo Mancosu, Sergio Galvan, and Richard Zach with the very promising title An Introduction to Proof Theory: Normalization, Cut-Elimination, and Consistency Proofs. How did I miss that before? Here’s the blurb:

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader’s understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen’s consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach’s introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

Surely, especially given these authors, exactly what we need! There are a few more details here.  I really look forward to reading this. And a bonus point to OUP, by the way, for bringing out this 432 page paperback for a very reasonable price.

Website woes (updated again)

For a day, all the comments here on blog posts and on static pages oddly disappeared. But by magic they have now reappeared. By magic, because I spent a couple of hours online with Bluehost without resolving the problem. (I can’t be too cross about that, apart from the annoying waste of time —  Bluehost have been absolutely stars at sorting issues in the past). And now, in some random fiddling on seemingly unrelated aspects of the site, the comments have reappeared. Hey ho.

But still, maybe this is all telling me that — after more than ten years — it is really well past time to update the WordPress theme, and do various other under-the-bonnet updates. I’ve been putting this off for too long. Bluehost have set things up so I can play with a test site for a while before going live. So there’s a project for rainy evenings …


A number of distractions (good distractions!) from logical writing projects recently. For a start, we spent some days near the Suffolk coast, a few miles inland from Aldeburgh. The first time we’ve stayed away from Cambridge in these days of Covid. Initially, we were quite irrationally tentative about doing that — but this seems a quite common reaction after more than a year of restrictions. But we had a great time. The weather was good enough for lots of breezy walks. And being by the sea always very much lifts the spirits.

Back home to hours of nerdy amusement for me, playing around with a new bit of serious software, Affinity Publisher. Extraordinarily inexpensive but powerful alternative to Adobe InDesign. Lots of terrific reviews, and certainly seems quite excellent to me. Have used it to design good-enough covers — still big and red but slightly snappier — for hardback versions of the Big Red Logic Books, and I’ll use the same redesign for the republished paperbacks. More about this when the first hardbacks become available, shortly I hope.

Not least among the distractions, my new 24″ iMac has arrived. Entry-level in blue, since you asked.

Took a day to clear my study into a fit state to have somewhere to put it, and half another day to set it up, transferring files across, installing software and so on. But I’m bowled over by the result.

I’ve not had a desktop machine for well over a decade. So the difference between this and my trusty (but soon-to-be-traded-in) six year old MacBook Pro is wonderful. The big screen in particular is amazing. For LaTeX, being able to work with source code and PDF output side-by-side in big windows is a delight. And LaTeX compiles a large diagram-heavy file about 2.5 times faster too, which is a nice bonus.

The iMac itself is a thing of beauty (significantly better in reality, I’d say, than in the adverts). Even Mrs Logic Matters is impressed. The front-side colour is pleasingly muted. And those “white bezels” which Mac forums were complaining about a lot when the machine was launched in fact strike me as something of a design triumph. They aren’t glaring white — but a sort of slighty-grey off-white and so, in use, the edges of the screen shade off in your peripheral vision into your background wall (at least, if your background wall is fairly neutral like my study wall), in a way which works very well. I could go on. But if you were wavering about whether to get one, I’d say just do it!

Going back and forth

You might have missed Jacob Plotkin’s comment a week ago about about a reference (by me!) to “Cantor’s back-and-forth proof”:

Cantor did not invent/discover or use this method of proof. That honor belongs independently to Felix Hausdorff and E.V. Huntington.

Jacob gave a reference to the short paper where he spells out the evidence. I’ve now had a chance to read it, and it is interesting and instructive (and after all, it is always better to get our history right rather than wrong). So let me add a link to where you can find the paper!

Scroll to Top