Colour at the Fitzwilliam

Book of Hours, Use of Rome, The Three Living and the Three Dead, Western France, c.1490-1510. Photograph: Michael Jones/The Fitzwilliam Museum

Book of Hours, Use of Rome, The Three Living and the Three Dead, Western France, c.1490-1510. Photograph: Michael Jones/The Fitzwilliam Museum

So there you are, out for a spot of hunting and general enjoyment, and these killjoys turn up to remind you of the fate which must, in the end, befall you.  No wonder you don’t look too pleased …

This is from one of the illuminated manuscripts on display in the wonderful new Fitzwilliam Museum exhibition, COLOUR: The art and science of illuminated manuscripts (on until the end of year, free entrance). As now usual at the Fitz, this is a quite beautifully mounted show, and many of the manuscripts on show are little less than astounding. There is a five star review in the Guardian, with links to more illustrations, so I need say no more here. You can also explore further on the museum’s website. We’ll certainly be back. And it is quite definitely worth a trip to Cambridge.

(Tip for non-Cambridge people. Come on a sunny day, as the exhibition should be quieter, with fewer tourists tempted to shelter from the rain.)

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Not minding my ‘P’s and ‘Q’s

Books are never really finished.

But the pressure to publish, to have something to show for your time, becomes too great. Or your friendly publisher goes from merely nagging to threatening to take back even your meagre advance if you delay delivery any more. Or you simply can’t, for the time being, face another rewrite. Or all three, in the case of the first edition of An Introduction to Formal Logic. 

As I work through that book again — and fingers crossed that the Syndics of the Press formally agree to a second edition, as I’m now about 100 pages into a rewrite — I’m struck what a really mixed bag that edition is. There are some quite nice episodes, which I still like and which need little reworking; other episodes where things need to be smoothed but which are basically on the right lines; but also far too many places where I need to do a lot better.

And in some of those cases it isn’t just presentational changes that are needed. There are thoughtless foul-ups that require sorting out. There I am, in the old Chapter 10, giving a sermon on minding our ‘\textsf{P}’s and ‘\textsf{Q}’s (propositional letters in a formal language) and distinguishing them from ‘A’s and ‘B’s (schematic variables helpfully added to logicians’ English to help us, inter alia, generalize about wffs in our formal language). And then, dammit, in Chapter 11, when talking about the expressive adequacy of a language with conjunction, disjunction and negation as the built-in connectives,  I find that they are places where I do things in terms of  ‘\textsf{P}’s and ‘\textsf{Q}’s where really I needed, for the intended generality,  ‘A’s and ‘B’s. Hell’s bells. How on earth did I not notice that before, when it should have been glaringly obvious all these years? After all, this is baby logic…

One of those occasions, then, for those uncomfortably mixed feelings known to authors lucky enough to get a second shot at a book (I remember the sensation well, from when I was revising my Gödel book). There is horror at the earlier foul-up, relief that you have spotted it and can make it good, and sheer panic at the thought that if you managed to make that egregious mistake without noticing it for years, there could well be other things, equally bad, that are still passing you by.

Oh, the joys of logical authorship. Wouldn’t be without them for the world, of course.

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Duet Display again


I posted about this six months ago. But let me repeat myself, by way of a public service announcement!

If you have e.g. a MacBook of some description (or indeed a Windows machine), and an iPad, you can use the iPad as an additional display. Duet Display works over a USB cable, so it is very much smoother and vastly less flakey in operation than old implementations of the general idea using e.g. local wifi. OK, it won’t magically increase your “productivity” but it assuredly reduces the irritations of window-juggling when working. Above, there’s my current source code for a LaTeX chapter in a TeXShop window on the left of the 15″ MBP screen, the PDF of the book on the right — and off-loaded to a standard-sized iPad, the TexShop console and a BibDesk window. Of course you could put something more distracting on the secondary screen!

Once you’ve told Duet Display how you have placed your iPad and laptop relatively to each other, the cursor magically goes from screen to screen (and the current menubar moves with it), just as with a more standard multi-monitor set-up. It really does work a treat and is extremely stable. And by the way, you can hit the home button on the iPad to navigate to other open apps in the usual way, and then return to Duet Display to pick up where you left off.

You can get Duet Display for the iPad from the app store, and then download the free OSX or Windows companions from their site. If you don’t know it, a very warmly recommended bargain.

[Added: Updating to MacOS Sierra hasn’t actually broken Duet Display, but leads to some unwanted effects – apparently Apple’s fault. Still useable, but not as seamlessly smooth.]

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Why not ask your local friendly logician?

Logicians are perhaps of rather limited use to the world (as I’m occasionally reminded by Mrs Logic Matters). But they can be tolerably helpful when you are in danger of inadvertently confusing  use and mention, or if you want to avoid getting into muddles about variables, and so on.

Consider this:

A set is merely the result of collecting objects of interest, and it is usually identified by enclosing its elements with braces (curly brackets).

No: what gets surrounded by curly brackets in forming an expression identifying a set are expressions designating the elements, not the elements themselves. (And odd to say that sets are usually identified this way, using lists enclosed in curly brackets, when that only works for finite sets!)

Or how about this:

A property is a statement that asserts something about one or more variables. For example, the two statements “x is a real number” and “y \in \mathbb{R} and y \notin \mathbb{N}” are clearly properties that assert something, respectively, about x and y.

Ok: it makes sense to say e.g. that

\pi is a real number” asserts something about \pi,

because  \pi is a denoting term. But it doesn’t express any complete claim to say that

 ” x is a real number” asserts something about x

if “x” is left as a dangling free variable. And we can’t tidy up by imagining there is a governing quantifier, as you can’t quantify across quotes. Anyway, a property isn’t a statement of any kind (even if we allow open sentences with unbound variables to count as statements) — properties are what are expressed by open sentences, or are their semantic values, or some such.

How about this?

[An example of a compound sentence is]

P \land Q (means  “P and Q” and is called conjunction)

What convention on quotation marks is in play which would make it right to have the quotation marks this way round? And, being pernickety — but why not? —  it is certainly not the case that the wff is called “conjunction”! It is a conjunction.

Quite rightly, any logician would balk at write each of the above. Not so the mathematician Daniel Cunningham in his brand new book Set Theory: A First Course (CUP, 2016). Those quotations are all from the first six pages.

This seems a huge pity as the book later promises well as an introductory set theory text. I’ll report back in due course on the real content, once the book gets going. But it really is worth talking to your local friendly logician to avoid silly foul-ups like these.

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Solomon Feferman (13.xii.1928 — 26.vii.2016)


I’m sad to hear that Solomon Feferman, an intellectual hero of mine, has died.

There is a very warm tribute here from the Stanford philosophy department.

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Those Brexit blues again

The admirable John Lanchester, writes on Brexit in the latest London Review of Books, which has made his piece freely available.

If you are not all Brexited out, then this strikes me as particularly insightful about some of the social currents at work, and more than usually worth a read.

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Reaching peak Apple: the Macbook 2016

I have not wanted to post about the really pretty miserable political news even though it has been much occupying my thoughts (for I have nothing new or insightful to add about Brexit,  about the incompetent narcissist supposedly leading the Labour Party, or about the new UK government, let alone about the disasters in the wider world). And I’m afraid that spending a lot of time tinkering with little presentational issues in the early chapters of my introductory text book as I slowly work towards a second edition doesn’t exactly provide inspiration for exciting logical posts here either.

So let me tell you about my new MacBook instead.

Headline news: if you are thinking of splurging out on new Apple kit, the revised 12″ Macbook is just terrific. Go for it.

Slow news: I’d been using as my portable (for libraries, cafés, sofa-surfing on my lap) a Macbook Air, now approaching five years old. Still a great bit of kit. But, and it’s quite a big ‘but’ for someone spending a lot of time writing, the on-screen text on the MBA now does seem decidedly blurry. Compared with modern retina screens on my iPhone, iPads, and a big and not-very-portable MacBook Pro used as my main home machine — yes, I really am reaching peak Apple here  — the elderly MBA screen is just not so great. Hence, initially pretty much for that reason alone, when a larger-than-expected royalty cheque arrived, I splashed out on the recently revised 12″ MacBook. Space gray, since you asked.

Six weeks in, I’m more than delighted. Some have commented adversely on the keyboard. But unless you are a very heavy-handed typist, you should find it excellent. Despite its different feel, going from this keyboard to the MacBook Pro and back really presented zero problem after just a day or two ‘s use. The screen is simply amazing. The lack of ports is also no problem at all for me, since all my work files live in DropBox, and everything else lives in various clouds too. And — now this was a very big surprise — the added portability (and added ease of use on a lap!) seems completely out of proportion to the actual change in size and weight compared to the MBA. Finally, the MacBook is even more gorgeous than the MBA, and I think aesthetics matter if you are spending so much time up close and personal with something!

Whether it would suit you as a sole machine, I can’t say: read the usual forums for advice on that. But for anyone looking for a very portable second machine to take out and about, this works a treat in every way. You’d have to be very hard to please not to be delighted!

Nerdy note: I initially got the entry-level model, but then returned it for the upgrade to the fastest m7 chip which does make a noticeable difference working with LaTeX: I’d recommend the small extra outlay for that reason. More on this, with some timings, here.

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The Arcanto Quartet with Maximilian Hornung play the Schubert Quintet

By chance, we just caught this BBC broadcast, available for 30 days, of a truly fine performance of the Schubert Quintet by the Arcanto Quartet with Maximilian Hornung as the additional cellist. An hour’s suitably reflective respite from the grimmest of news,  which others might appreciate too.

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IFL2: a first instalment

OK, I have been tinkering with the opening chapters of my Introduction to Formal Logic, trying to improve them for the planned second edition. Here then are the early chapters up to and including the first Interlude, in an initial re-draft [updated Aug 31]. Some quick notes:

  • I haven’t yet revised the end-of-chapter Exercises.
  • If you don’t know my book, then as in the first edition, Chapters 1 to 3 correspond roughly to e.g. the preamble chapter in Benson Mates’s book. Then Chapters 4 and 5 say something about showing invalid inference are invalid by the counterexample trick, and about showing valid inference are valid by coming up with multi-step proofs.
  • The old Chapter 6 has disappeared, however, with some material working into the end of Chapter. 5. I plan now to talk more about the validity of arguments with contradictory premisses later, and no longer think it good policy to muddy the waters by discussing this too soon.
  • This version, then, is 44 pages rather than 52 pages as before. I hope the result is overall crisper, clearer and better focussed, and certainly some repetition has disappeared. (To be honest, I cringe a  bit at some passages in the first edition!)
  • So … comments and corrections are most welcome! Regular readers here, please do, do chip in if you have anything useful to say. But also, if you have some students, beginners or recent beginners, who would be interested in giving feedback, please do point them this first excerpt from the book. In fact, encourage them by telling them that, when I asked for advice/comments on chapters from the second edition of my Gödel book, there was no correlation at all between seniority and the usefulness of suggestions.
  • Comments are probably better sent by email (rather than using the comments box — since this is much easier for your writing and a bit easier for my reading). If you have lots of comments, the ideal is perhaps to return a marked-up PDF. But whatever works for you! Use ps218 at cam dot ac dot uk
  • I’ll keep the current version fixed now for a few weeks, rather than revise piecemeal as comments arrive.

Enjoy, as they say!

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Most arguments are not arguments

Here’s a strange claim — or rather, something that ought to strike the uncorrupted mind as strange!

An argument consists of a set of declarative sentences (the premisses) and a declarative sentence (the conclusion) marked as the concluded sentence. (Halbach, The Logic Manual)

We are told more or less exactly the same by e.g. Bergmann, Moor and Nelson’s The Logic Book, Tennant’s Natural Logic, and Teller’s A Modern Formal Logic Primer. Benson Mates says the same in Elementary Logic, except he talks of systems rather than sets.

Now isn’t there something odd about this? And no, I’m not fussing about the unnecessary invocation of sets or systems, nor about the assumption that the constituents of arguments are declarative sentences. So let’s consider versions of the definition that drop explicit talk of sentences and  sets. What I want to highlight is what Halbach’s definition shares with, say, these modern definitions:

(L)et’s say that an argument  is any series of statements in which one (called the conclusion ) is meant to follow from, or be supported by, the others (called the premises). (Barker-Plummer, Barwise, Etchemendy, Language, Proof, and Logic)

In our usage, an argument is a sequence of propositions.We call the last proposition in the argument the conclusion: intuitively, we think of it as the claim that we are trying to establish as true through our process of reasoning. The other propositions are premises: intuitively, we think of them as the basis on which we try to establish the conclusion. (Nick Smith, Logic: The Laws of Truth)

And the shared ingredient is there too in e.g. Lemmon’s Beginning Logic, Copi’s Symbolic Logic, Hurley’s Concise Introduction to Logic, and many more.

Still nothing strike you as odd?

Well, note that on this sort of definition an argument can only have one inference step. There are premisses, a signalled final conclusion, and nothing else. Which seems to “overlook the fact that arguments are generally made up of a number of steps” (as Shoesmith and Smiley are very unusual in explicitly noting in their Multiple Conclusion Logic). Most real-world arguments have initial given premiss, a final conclusion, and stuff in-between.

In other words, most real-world arguments are not arguments in the textbook sense.

“Yeah, yeah, of course,” you might yawn in reply, “the textbook authors are in the business of tidying up ordinary chat — think how they lay down the law about ‘valid’ and ‘sound’, ‘imply’ and ‘infer’ and so on. So what’s the beef here? Sure they use ‘argument’ for one-step cases, and in due course probably use ‘proof’ for multi-step cases. So what? Where’s the problem?”

Well, there is of course no problem at all about stipulating usage for some term in a logic text when it is clearly signalled that we are recruiting a term which has a prior familiar usage and giving it a new (semi)-technical sense. That’s of course what people explicitly do with e.g. “valid”, which is typically introduced with overt warnings about no longer talking about propositions as valid, as we do, and so on. But oddly the logic texts never (almost never? — have I missed some?) seem to give a comparable explicit warning when arguments are being officially restricted to one-step affairs.

In The Argument Sketch, Monty Python know what an argument in the ordinary sense is: “An argument is a connected series of statements intended to establish a proposition.” Nothing about only initial premisses and final conclusions being allowed in that connected series!

So: I wonder how and why the logic texts’ restricted definition of argument which makes most ordinary arguments no longer count as such has continued to be propagated, with almost no comment? Any suggestions?

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