Mary Leng’s Mathematics and Reality, Chs 5 & 6

We are reading Mary Leng’s book in the Thursday Logic Seminar for the second part of term. It fell to me to introduce discussion of Chapters 5 and 6, and I found myself yesterday writing (very rapidly indeed) these brisk notes in trying to get my own thoughts clearer before the meeting. There was an excellent discussion which has led to a few after-the-event changes. But mostly these notes stay in the same rough-and-ready form, and I’m not going to have time to do better: so caveat lector! However, they might be of some interest to others intrigued by Mary’s project.

Intro Logic Lectures

Here’s another helping of the overheads for my first-year logic lectures 4 to 10 this term. This is the block of seven lectures on basic propositional logic via truth-tables. I’ve already posted the links to the first three very introductory ones — though you can catch up here. The new slides are “dynamic”, revealing one bullet point at a time because there is often over-writing, or the dynamic filling-in of truth-tables etc.: for the best effect, select “View > Page Display  > Single Page” in Adobe Reader.

The overheads are there to help speed things up, rescue students from having to read my terrible blackboard writing, and to keep me on message. Needless to say, I do embroider around and about them in the live show, and throw in other remarks as the mood takes me. So the content of the overheads is pretty basic and conventional. Don’t expect wild excitements! But for what they are worth, here they are:

  1. Three Connectives
  2. Bivalence; Evaluating Propositions
  3. How to Test Arguments, a Sketch; Introducing PL
  4. Tautologies
  5. Tautological Entailment
  6. The Material Conditional; PLC
  7. ‘Only if’; The Expressive Adequacy Theorem

Piling up on my desk

Term rattles on, leaving little time for doing much reading other than for the two logic seminars for grads (this term we looking at Mary Leng’s book on Mathematics and Reality in one, and Sara Negri and Jan von Plato’s Structural Proof Theory in the other). So the books that I’ve recently bought start to pile up on my desk. Perhaps if I briefly mention there here, they will feel slightly less neglected.

So at the bottom of the pile, there from just before the beginning of term, you’ll find the new Cambridge Companion to Frege co-edited by my colleague Michael Potter who came into the project late. The collection looks a bit of mixed bunch, as is the way of these things. But the three pieces I’ve read so far (by another colleague Alex Oliver, by Richard Heck, and by Peter Sullivan) are impressive. Though the high sophistication of these pieces makes me wonder a bit who the Companion is for.

Next up the pile is the Alan Weir’s Truth Through Proof: A Formalist Foundation for Mathematics. As you might expect if you’ve met Alan at all, this has the most engaging possible preface! — and it should be a provoking read. Formalism lives? In 2010??

Then there is Oded Goldreich’s P, NP and NP-Completeness: The Basics of Computational Complexity which has just come out too. Having read the first two chapters, this promises to be highly accessible, a sort of warm-up exercise to see if you want to tackle his ‘big book’, Computational Complexity. In fact I really must try to read the rest over the coming few days, as a refresher since I want to say something about P-vs-NP in my first year lectures (just for fun, and to keep the mathematically ept awake).

Next up is William Henry Young and Grace Chisholm Young’s The Theory of Sets of Points. Published in 1906. And reprinted last year in CUP’s “Cambridge Library Collection”. Why is that in the pile, you ask? Because I want to see what set theory — the actual theory that mathematicians use(d) — looked like after Cantor had been initially digested but before Zermelo. I very much enjoyed reading the first few chapters in a coffee shop after buying it, probably because the style is so very reminiscent of old maths books from the 30s and 40s from my father from which I learnt maths as a school boy.

Top of the pile, and only just published, is W. D. Hart’s The Evolution of Logic which promises to be an intriguing but bumpy ride. Here’s part of the blurb:

After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post’s problem, and Morley’s theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.

How well will Hart pull this off? He certainly hasn’t made things easy for the reader by going along with about the lousiest bit of maths typesetting I’ve seen since the days when books were done on electric typewriters. All the symbols are in the same roman font as the rest of the text (see what I mean by following the Google preview link on the CUP webpage for the book). It makes the symbol-heavy pages ludicrously and utterly unnecessarily hard going. What on earth were CUP thinking of? Still, Hart’s topics are central enough for me to still want to make the effort. But when term finishes.

5-4-3-2-1 …

There are just five more lectures to go in (my segment of) this year’s 1A logic course. Which means that — after, ye gods, forty years in this game — there are only five more lectures to go in (probably) my last ever intro logic lectures.

It has to be said: it does in a way feel rather strange. But will I really miss giving them? I suspect not. I have been rather enjoying this last trip around the block. But I’ve written up and elaborated the lectures in my Intro to Formal Logic some years back, revised less than two years ago, so I hardly think I’ll be depriving the world if I don’t give the live show again. And by the time I’ve spruced up the slideshow, strutted my stuff, and recovered from the excitement, that’s two-and-a-bit hours out of my life for each lecture, and I’ve much more interesting logical things to do while I still have the energy.

So, short of some major bribery, I think this will be the end. And just when I was beginning to get the hang of it too. But that’s life …

Belcea Quartet

I have been meaning for some time to write recommending the Belcea Quartet‘s Schubert recordings. There’s one double disk of the G major, Death and the Maiden, and the Quintet, and another disk of the Rosamunde Quartet, the E flat, and the Quartettsatz. Both seem to me (and not just to me!) to be quite stunning — surely comparable with the Lindsay’s great recordings (and indeed, I suppose not dissimilar in their whole approach).

But I got to see the quartet playing live for the first time tonight in the very intimate setting of the Peterhouse Theatre here in Cambridge (part of a series of concerts which includes the  remarkable prospect of Viktoria Mullova playing in this tiny space which seats less than 200 people). In their new line up — with a new second-violin — they played the first of the late Haydn Op. 77 quartets, the Grosse Fuge(!), and then after the interval  the first Rasumovsky. All jaw-droppingly good (though I confess I do prefer hearing the Grosse Fuge played as the culmination of Op. 130; coming at it without the preparation of the journey there, it can seem too extreme, too outlandish).

The Belcea’s Rasumovsky in particular was as good as I have ever heard, live or on disc — everything that that recent feeble performance by the Endellion wasn’t. Passionate, by turns driven and etherial, utterly engaged (and stunningly together given the very recent change in line-up, with an intense rapport).

Music doesn’t get better than a great quartet in full flow; and quartet playing doesn’t get better than tonight’s.

Godel Without (Too Many) Tears. Episode 4

I’m afraid that life has been rather distracting recently, with little time for more-than-minimal blogging. I hope, however, that things will get back to normal after a few more very busy days catching up with life. Here, in the meantime, are the notes for this week’s lecture.

Having had a swipe at the deeply disappointing Endellion Quartet a few posts ago, however, I will just prove that I’m not really a mean-spirited curmudgeon by adding a quick but very warm recommendation for the Atos Trio, caught on radio while driving. A quite terrific performance of the Schubert E flat.

Godel Without (Too Many) Tears. Episode 2

The first episode of the new version of Gödel Without Tears was downloaded over 1650 times in seven days: there seems to be some interest, which is good to see!

Anyway, here’s a very marginally revised version, together with the next episode from today’s lecture.

Comments are open for corrections and queries: as I said before, there’s a (as yet unused) dedicated GWT comments page here.

Not even close

Given the choice, I prefer hearing a good string quartet play to almost any other concert-going.

When we lived in Sheffield, we were spoilt by being able to go to see the Lindsays in their prime (and we also got to see other quartets visiting the series of concerts they organized, from the likes of the Tokyo Quartet, down to new young ensembles just starting out). Coming to Cambridge we missed all that a great deal. We tried early on going to see the Endellion, the quartet in residence here, but really didn’t enjoy the experience. But perhaps we were disposed to find fault and find them over-rated. And perhaps we were too swayed, as well, by the marked differences between the Sheffield occasions and the Cambridge concert in ways that were no fault of the quartet — the much less intimate setting of the concert hall here, the seeming stiffness of the antique audience.

Well, a number of years further on, with various people encouraging us to give them another chance, we went to hear the Endellion again last night. The audience was as stiff  as before. And as for the music? … “lacklustre”, said Mrs LogicMatters. You can tell she is kinder than I am.

They played the Haydn Op 33, no. 1, lacklustre indeed at the outset, and only just about getting into it by the last movement. Then Shostakovich’s 8th quartet (which is a quite startling piece, and admittedly their best effort of the night — but Mrs LM had heard the Takacs Quartet play this quartet while we were in NZ, and she thought them in an entirely different class). Then after the interval the First Rasumovsky. Sigh. This was really pretty thin and unconvincing stuff (especially from the leader), with even the aching slow movement quite failing to grip the soul. If they’d been a recording they’d have been switched off long before the end.

Or is this unfair? I’ve just been listening again to the Vegh Quartet playing the Beethoven; heart-stopping eloquence. And within reach I have stunning recordings by the Busch Quartet and the Hungarian Quartet too, and equally fine and emotionally gripping newer recordings by the Lindsays in two versions and the Takacs (not to mention three or four other pretty good versions). So is it that, those paradigms having become so  familiar, I have just become primed to expect almost impossibly much from a live concert? (Does the easy availability of the best performances of the last seventy or more years tend to spoil our ability to enjoy anything but the extraordinary?)

No, I really don’t think it is that at all. We have been, for example, to concerts by young quartets who perhaps have quite a way to go, yet which have been just wonderful — where you are swept along for a couple of hours by their vision of the music, by their intense desire to communicate with their audience, by the sense of a shared journey. But last night was not even close to that.

The Endellion remained at a distance, then bowed stiffly in their tail coats, and walked off-stage just leaving me deeply disappointed.

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