A little light editing …

I have not been exactly full of logical energy! But I’ve been up to a little light re-editing of the already-revised chapters of Category Theory: Notes towards a gentle introduction. I’ve repaired some typos and a few thinkos, slightly speeded up a few sections which added unnecessary complications, and even added a couple of minor theorems. The main changes are at the very outset in the pre-categorial chapter on groups, and in the first two chapters on products.

Some of the typos/thinkos in the previous version are annoying enough for me to want to put the current corrected notes online right away. So I have …

Otherwise covid chez Logic Matters wends its tedious way along what seems to be the now most common trajectory, where the main continuing effect is considerable fatigue outlasting mild-ish cold-like symptoms. Could be a lot worse. Back to music and other postings, I hope, next week.

Not what was planned …

Perugia, photograph by Joana Kruse 2020.

I intended to return from Perugia full of renewed energy, imagination, and zest. It hasn’t quite worked out like that. We have Covid. So far, it’s largely a matter of massive fatigue. Let’s hope that’s the worst it gets. So perhaps not much here on logical matters for a week or two.

Postcard from Perugia

Six days away in Perugia. Where we’d never been before, despite the daily flights from Stansted Airport near Cambridge to the Umbrian airport very close to Perugia. But three weeks or so ago, Mrs Logic Matters saw a very warm review of an exhibition to mark the five hundredth anniversary of the death of Perugino, and that prompted us to get our act together and organize travel and a hotel. (I can’t but wonder, though, what St. Francis of Assisi makes of having an airport named after him …)

And the exhibition is indeed wonderful, more than worth the trip. It is quite beautifully presented, small enough not to be overwhelming, large enough both to give you a sense of Perugino’s mastery and very illuminatingly to put the artist in some context. The photo above is from the Perugino2023 website here (worth exploring). We very much enjoyed taking the exhibition slowly, a couple of times.

Perugia’s centro storico is rather stunning. And as is frequently the way in Italian cities, the ground-floor spaces in the old, often very old buildings, are used to accommodate shops and cafes in (mostly) such remarkably decorous and sympathetic ways. So the streetscape is a visual delight without being in the least a museum piece. The weather was still too chill for people to be sitting outside cafes late into the evening — Perugia is on the top of a hill, and catches the wind. But even so, there was a bustle to the ancient Corso Vannucci, and we found ourselves caught up in its early evening passeggiata.

Away from the very centre, the city starts to tumble down the sides of the hill along  steep narrow roads and down alleys which turn into staircases. We sent a lot of time just wandering around. But then of course there are all the churches worth visiting. And not least there is the Galleria Nazionale dell’Umbria, where the Perugino exhibition was held. The main two-floor gallery in the Palazzo dei Priori had a complete renovation only last year, and the result is a triumph. The spaces are just beautiful and the collection  includes some real masterpieces, wonderfully well displayed. Visit GNU’s website and look through the rooms  to get an impression.

Since we were staying in a hotel rather than an apartment we had to eat out at restaurants every night. Tough, eh? And while in Cambridge you can eat mostly badly or very badly in a dozen different cuisines, in Perugia you get to eat well or very well in the one Umbrian style.

Well, I exaggerate. But only a little. And we had the best meal out in two or three years at Luce Ristorante — wonderful ambience and service, superb food and wine (imaginative without being over-the-top). We paid at most half what a comparable meal would cost in the handful of “fine dining” places in Cambridge.

And as for coffee … Italian cafés have mostly avoided the plague of “artisanal coffee” which makes for undrinkable brews unless drowned in milk in the English way. So the espresso still tastes as the good lord intended. Which is a relief.

In concert: Noa Wildschut plays Bach

I’m hardly exploring the more obscure musical corners in these weekly posts! But no matter. This week, it’s the ridiculously gifted Noa Wildschut engagingly enjoying herself playing Bach with great verve and musicality. A delight to watch as Mrs Logic Matters particularly agreed. Just what is needed after a very busy and rather stressful week!

Subobjects and subobject classifiers

Another update to Category Theory: Notes towards a gentle introduction. This time, I have rewritten and indeed doubled the length of the chapter on subobjects and subobject classifiers. Much improved, I hope! I’ve also added two or three needed results at the appropriate places earlier in the notes, so that the proofs in this newly revised chapter can be snappy, and corrected some random typos I happened to notice.

(I’ll be pausing on categories now for a few weeks, with a holiday break coming up.)

Logic Matters is seventeen!

It’s the blog’s birthday! Let’s party!!

The very first post was back on March 9th, 2006 (and I have just restored the link there to a short talk on Gödel’s theorem for mathematicians which I’d quite forgotten about ). Since then there have been — rather astonishingly — 1630 posts.

Of course, many of these were of merely passing interest (if that). But over the years, there have been some blog posts, or series of posts, of perhaps less ephemeral interest. So I’ve decided to rework the webpage that used to be unhelpfully labelled ‘Varia’ to become more of an ‘Archive’. I plan over the coming weeks not only link to a few papers, book reviews, and other pieces, but also to ‘best bits’ from the blog. It will take a while to organize this; but I’ll hopefully enjoy finding out what earlier time-slices of me thought!

Heavens: I’ve just realized that if I start the clock when I got my first job, the blog has been going for about a third of my academic life. Doesn’t time fly when you are having fun.

In concert: András Schiff plays Schubert D 946

The weeks seem to rattle round too fast. Here, to slow down and pause over, is Sir András Schiff playing the late Drei Klavierstücke D 946 [29 mins]. I have always thought that the second of the three pieces in particular [starting here at 8.45] is one the most magical of Schubert’s piano works. And Schiff is one of my favourite Schubert pianists. Enjoy!

Philosophy of mathematics, also disappearing over the horizon?

Long ago, I posted a piece here under the mournful title “Logic disappearing over the horizon ….”.

I’ve just had an invitation to give a talk at the University of X, a distinguished place, with a philosophy graduate community of about fifty (according to their website). So I checked out how much logic/phil maths is going on, what I could reasonably take as given. Zilch. Apart from a first year course perhaps approaching the level of my intro logic book, nothing at all, as far as I can tell. Which leaves me a bit bereft of anything to go to talk about. But more to the point, it means that for students at X a central swathe of the work of lasting value from the last hundred years has disappeared over the horizon. Which is, shall we say, a pity.

My sense is that this is happening more and more in UK universities. I’d be delighted to learn that I’m wrong.

There was some discussion on the blog at the time, not very cheering. And my current sense is that the situation is getting worse and worse. How many logic-orientated posts in philosophy departments have been advertised and filled in the UK in the last dozen years? Very few, as far as I know.

And things are just as grim, if not more so, with the philosophy of mathematics. Here is Jeremy Avigad, in a recent essay which I’ve just noticed:

A recent analysis of tenure-track positions advertised in Jobs for Philosophers in the 2021–2022 academic year doesn’t even mention philosophy of mathematics in its categorization. Digging into the data shows that the phrase “philosophy of mathematics” occurs in only three of the 201 advertisements, in each case listed among multiple areas of potential interest. Surely this is an indication that the field is no longer viewed as important. It is sad that a discipline that was so central to the philosophical tradition from ancient times to the middle of the twentieth century now barely registers a pulse.

An Avigad now would, it seems, have a pretty hard time getting an academic post in philosophy. Sad indeed.

Is it always the fate of those in their declining years to think important bits of their world are falling apart? Probably so. But we’re not always wrong to thing so ….

Stochastic parrots

I thought that this piece on chatbots from New York magazine was worth reading and thought-provoking.

I was amused/alarmed by one Christopher Manning who seems to think we are stochastic parrots, and “the meaning of a word is simply a description of the contexts in which it appears.” Really? Apparently, the idea that meaning has anything to do with how words hook up to the world and to our interactions with the world and each other is antiquated, the “sort of standard 20th-century philosophy-of-language position.” Well, that’s us told.

I was pointed to this piece by a post on Mastodon. I still occasionally look at the old bird site because that’s where posts about music and other cultural stuff still are mostly to be found. But these days, quite apart from not wanting to have too much to do with Musk Enterprises Inc., the more genial atmosphere of Mastodon, on my instance anyway, suits me fine.

Category theory notes updated again

I’m trying hard not to be logically distracted from the long-promised revision of the old Beginning Category Theory theory notes. Which makes for a very dull blog! And indeed, this is just another of those “I’ve updated more chapters” posts. Exciting or what?

This time I’ve updated Ch. 16 on limits, Ch. 17 on pullbacks and pushouts, and Ch. 18 which proves the completeness theorem that a category with terminal objects, binary products and equalizers has all finite limits.

However, in doing this, I found that the version of the completeness proof in Beginning Category Theory was hopelessly confused. Ouch. I guess that’s the first real foul-up that I have discovered in revising the notes, so I suppose I shouldn’t be too upset. But it does means that it is time to fully retire those old notes, and finally take them offline.

Therefore I’ve replaced them by Category Theory: Notes towards a gentle introduction which — as of February 28 — has the eighteen newly revised chapters but now followed by the same number of old unrevised chapters. So everything, revised and waiting-to-be-revised, is conveniently in one pdf.

What next? Over the coming weeks, I will be revising and expanding the rest of Part I, meaning the chapters before we start looking at functors between categories in Part II (when, many would say, the real categorial fun starts). So I will be revising the chapter on sub-objects, splitting and then improving the chapters on natural number objects and groups-in-categories. I also envisage adding to Part I a preliminary look at the idea of a topos if I can organize a dozen sensible and useful pages.

Having knocked Part I into an overall shape that I’m happier with, I intend next to polish up these chapters to make them more consistent in level and friendliness. Which is another way of saying that I won’t be getting round to revising Part II for some months. But I may well set up an at-cost paperback “beta version” of Part I for people to comment on, as so many (including me) prefer working from a printed version. We’ll see …

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