The material conditional — analysis or replacement?

Update. I posted a couple of chapters, just 22 pages, hot off the laptop, from a bit later in the draft second edition of my Intro to Formal Logic about the material conditional. I’m now a little unhappy with them, and CUP are unhappy about me posting too much from the book here. So I have now removed the chapters. Comments from early downloaders still most welcome.

Generating truth-tables in LaTeX

I have just added to the “Logicians’ miscellany” page of LaTeX for Logicians a new heading “Help for generating truth-tables”. There is now a link there to a Truth Table Generator webpage by Michael Rieppel. This page contains a JavaScript program which will generate a truth table given one or more well formed formulas of sentential logic, and provide you with LaTeX source for the table.

Thanks to Sara Uckelman for the pointer to this. Any other recommendations for similar or even better resources?

Unsatisfying satisficing

There’s no getting away from it. You know perfectly well you can’t try to optimize a book — that way madness lies (or at least, never finishing). You know perfectly well you have to satisfice. But that is oh so unsatisfying. When I had to finish books for work reasons, I gritted my teeth and let stuff go. Now I’m retired, it’s more difficult not to keep on keeping on editing and (hopefully) improving. I need a contract settled for the second edition of IFL to concentrate the mind. But CUP’s wheels are grinding slowly (fingers crossed that that isn’t a bad sign), and so are mine.

Updated: link to draft chapters removed.

Plural Logic, again

515t0r0vqcl-_sx331_bo1204203200_ A second, paperback, edition of Plural Logic by Alex Oliver and Timothy Smiley is now out from OUP. As the cover says, it is ‘Revised and Enlarged’ – in fact it is almost fifty pages longer, with some new sections and a whole new chapter on Higher-Level Plural Logic. So you should certainly make sure that your library gets a copy.

I did read and comment on a version of the original edition pre-publication. But that was not at a good time for me, and I remember much less detail than I should: so I really want now to re-read the book. One reasons is that, in reworking my Introduction to Formal Logic, I want to excise unnecessary set talk, e.g. when giving the semantics of QL. So I want to remind myself how Oliver and Smiley handle this. And there is also a tenuous potential connection too between thinking about plurals and another interest, my on-the-back-burner introductory discussion of category theory. For I need to think through how far we can get in elementary category theory by conceiving of categories plurally rather than as set-like, thereby avoiding certain problems of ‘size’ hitting us too soon.

Category Theory in Context

51rmanvawtl-_sx331_bo1204203200_ Congratulations to sometime Cambridge student Emily Riehl, now at Johns Hopkins. Her very illuminating lecture notes, aimed at beginners in category theory (albeit mathematically perhaps rather sophisticated beginners) have become a book, Category Theory in Context, published in a new series of ‘Modern Math Originals’ by Dover Books. This is available now in the US, and at the end of the year in the UK.

There has been a link to Emily Riehl’s evolving notes on the category theory page here for a couple of years, and the publishers have kindly allowed her to continue to host a free PDF copy of the book. So you can take a look already if you don’t know her work — but at this low price, it will be really nice to have a paper copy (and of course, tell your library).

Postcard from Paris

Raphael, La belle jardinière, The Louvre
Raphael, La belle jardinière, 1507
The Louvre

So, as it happened, we left for Paris on the day of the Presidential Election, and woke up in our hotel to the grim news the next morning. At least, being away from home, with so much else to distract us, we haven’t been glued to the television, internet, and newspapers as we might have been. But the result is, assuredly, a catastrophe.

Depressed by all that, we have found ourselves repeatedly seeking out balm for the soul, especially in the Louvre and the Musée d’Orsay. Here’s just one painting that I find particularly affecting.  (Almost no one stops to look at it as the crowds push past into the adjoining room with the Mona Lisa — yet wouldn’t you rather live with the Raphael, if you could?)

Paris has been rainy and cold — thank heavens for the wonderful Metro! — but still as beautiful as ever.

Life’s choppier waters

51obksckqzl-_sx320_bo1204203200_My non-logical readings are rather random, except for one pretty firm rule — I try to alternate between reading something new (or at least, new to me), and re-reading something familiar (or at least something that would be familiar, if only my memory for novels and the like wasn’t so terrible). Otherwise, there is no method to it. When I finish one book, I just hunt around the house for something that seems to fit my mood and inclination to read next.  So just recently, I’ve read Sarah Perry’s much praised  The Essex Serpent (which I rather enjoyed, but thought lost its way towards the end), Giuseppe Tomasi di Lampedusa’s The Leopard (which I must have read at least twice before, and which I enjoyed even more this time) and Ian McEwan’s The Children Act (which will go straight back to the Oxfam shop where I picked it up a few weeks ago — a quite unconvincing waste of McEwan’s considerable literary firepower). And I am now re-reading what is surely the best work by one of the best English prose writers of the late 2oth century, namely Jonathan Raban’s remarkable Passage to Juneau. This is proving, if possible, even better than I remember; I am absolutely gripped again.

For those who don’t know Raban’s work, let me link to this sensitive short essay  from the Guardian, whose title I have stolen, which says something about why it is so fine, and which might well (I hope) encourage a few others to read the book.

The Greeks win (2)

On the question of metavariables — relaxed italics versus Greek letters. Which do you prefer? Those who voted in the poll  (and too late, I realized I should have had added a  “really don’t care” option), preferred Greek letters by 4 to 1.

Not just for that reason, I decided a couple of weeks ago (before my brain was shut down by a cold) to go for Greek letters. And returning now to the decision, yes, that is still what I am going to do.

Or rather, I am going to do something just a bit more complicated — but I hope even better than an always-italics or an always-Greek  solution.

In the very early chapters of my logic book where everything is still very informal, arm-waving, motivational, I continue to use talk of patterns of argument like  ‘All F are G, n if F, so n is G‘ in that familiar and relaxed philosophy-classroom way which is surely good enough for very introductory purposes. Though I soon point out it is of course arbitrary what we use for placeholders, so long as patterns of recurrence stay the same.

I also then point out quite quickly that it is a bit murky how such informal notation is used (are we representing patterns in the surface form of everyday arguments or patterns in some supposed underlying logical form or what?). We don’t have to worry about this matter much for very introductory purposes (just as we skim over issues about sentences vs propositions, for example).

However, after the half-dozen intro chapters, we very quickly go formal in IFL, saying that we are going to be dealing with everyday arguments by a two-step process: we regiment these everyday arguments into a nice suitable formal language, and then develop tools for assessing arguments in these formal languages. So we quickly find ourselves talking about formal languages and wanting to talk e.g. about patterns of argument in these formal languages — and now I adopt the convention that placeholders/metavariables added to English to help us talk about wffs and other expressions of our formal languages will be Greek letters. And we have a perfectly precise story about what these variables run over (everything is cleanly superficial and syntactic).

So, in short, italic letters used in a loose but good-enough way for relaxed pre-formal use (as in our philosophy lectures when sketching the form of an argument, say); Greek letters are used when we really are talking about formal languages. Neat and perspicuous. No? (Well the proof is in the pudding, but having done some rewriting along this plan, I think it works well!)

The Greeks win (1)

To the Cambridge Greek Play a dozen days ago. Every three years, student actors and a professional directing team put on one or two plays, in the original Greek — this year, a double bill of Antigone (predictably wrenching) and Lysistrata (predictably bawdy and funny) at the Arts Theatre.

And if you think this is bound to be of minority interest, just try to get tickets for one of the eight performances if you don’t book weeks ahead (and if you get tickets, you’ll find yourself in perhaps the most age-mixed audience of any night of the year). There is no attempt to recreate a fake antiquity. The plays are re-imagined, the stagings are modern. In comedies, contemporary references are freely updated, so in  Lysistrata, a messenger and magistrate become Donald Trump and Boris Johnson  (who end up tap-dancing — don’t ask!). But there is every attempt to get the complex rhythms of the ancient language to sing again (and indeed the chorus does sometimes burst into song), in a way that can be spectacularly effective.  Translations-by-surtitles mean you don’t have to rely on  dim memories or sneaky glances at the programme, and work brilliantly.

Again, as with the previous Prometheus/Frogs double bill,  a  fantastic night at the theatre. Creon, who doubled as Donald Trump, and Lysistrata herself were quite outstanding. Though it was just a little sobering to realize that the last time the Cambridge Greek Play  did Antigone, a performance that I saw as a schoolboy, was over fifty years ago.

(We thought, though, that we might have been coming down with “a bit of a cold” that evening. And oh heavens, yes. Hardly been able to stir from the house since. Which in my case goes with a woolly brain, and logic not even on the back burner — the light turned right off until today. Apologies to those to whom I promised some revised chapters of IFL2 to look at. I hope to get back to light logical duties tomorrow!)

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