Peter Smith's Blog, page 114

LaTeX for Logicians — any suggestions?

I’ve just been (belatedly) sprucing up LaTeX for Logicians again, and repairing a regrettable number of broken links. Some of those broken links were due to changes at CTAN;  but a few were due to people who had useful pages on their personal websites now apparently going off the radar.

The only new addition is a link on the Natural Deduction page to the CTAN archive for lplfitch, a package “for typesetting Fitch-style proofs a la Language, Proof, and Logic, by Jon Barwise and John Etchemendy.” (It was originally written by John Etchemendy, with modifications by Dave Barker-Plummer and Richard Zach, and looks excellent.)

I know a lot of people out there use LaTeX for Logicians (for example, that page of info about Natural Deduction packages was visited over 7000 times in the first six months of the year). And I very rarely get any corrections, suggestions for additions, etc. Which I guess is a good sign (presumably the pages are quietly succeeding at doing what they are intended to do). However, if you’ve been meaning to send me any ideas, requests, pointers towards new stuff, etc., now’s the time, while L4L is at the front of my mind for a day or two.  So, over to you …

 

Typos, typos …

Leszek Wroński of the Jagiellonian University has kindly sent me a list of typos in IGT2. Quite cheering as these things go, as the needed corrections are tiny, and certainly no readers are going to be led astray by them.

Joseph Jedwab of Kutztown University has even more kindly sent me a second list of typos for the supposedly corrected version of IFL. This isn’t so cheering, as he has noted some silly foul-ups which could confuse students as well as a whole rash of smaller mistakes. The composite list of needed corrections is now quite embarrassingly long. The good news is that CUP will print a corrected version at the next reprinting (maybe later this year).

To make the corrections for IFL, I’ll have to edit the PDF which is a real pain compared with editing the source document, were that possible. But the original was typeset using a proprietary program that no longer runs on macs under OSX. Huh. Moral: don’t, really don’t, use proprietary programs (whether document processors, layout programs, bibliography managers, or whatever) for stuff that needs to last. LaTeX and its companions rule, OK?

Alex and Tim have published a book

For quite a while, the favourite Cambridge example of a collective plural predication has been ‘Alex and Tim are writing a book’ (said with a teasing tone, as it was a long drawn out business). But our example will, at last, have to change. For the book is now published, as Plural Logic, out from OUP. Here’s their blurb as a taster (if you don’t already know some of their earlier papers on plurals):

Alex Oliver and Timothy Smiley provide a natural point of entry to what for most readers will be a new subject. Plural logic deals with plural terms (‘Whitehead and Russell’, ‘Henry VIII’s wives’, ‘the real numbers’, ‘the square roots of -1′, ‘they’), plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’), and plural quantification (‘some things’, ‘any things’). Current logic is singularist: its terms stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once; in other words, there is such a thing as genuinely plural denotation. The authors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration.

I in fact saw a late draft of the book which Alex and Timothy kindly asked me to comment on, which I did with enthusiasm here and scepticism there, so I’ll be really interested to discover how this final published version works. It wouldn’t be appropriate for me to write a formal review  in one of the journals, even if asked, as I wouldn’t have the requisite distance. But that certainly won’t stop me giving some informal thoughts here over the next few weeks. Watch this space, then: and meanwhile, get yourselves a copy of the book!

Kicking the bar

Staying near Welshpool in Montgomeryshire for a few days, we drove over the Cambrian mountains the sixty miles through Llangurig and Devil’s Bridge to Abersytwyth. The journey on a sunny day was as stunning as ever.

It was the first time we’d been back to Aber for at least a dozen years. The town itself, once so neat and quietly respectable, full of “real” shops, seems to be rather run down. There are supermarkets now on the outskirts, and so the streets in the centre are too full of shabby “saver” shops: so much looks depressingly scruffy and ill-kempt. Our old house and its neighbours — once family homes lived in by university colleagues — seem to have sunk into multiple occupancy. All rather sad. (Was it just nostalgia setting us up for disappointment? In Agnelli’s, a rather good little Italian café/deli at the top of the town, we talked to the Milanese proprietor, and she spoke of how she’d seen Aber declining over the last ten years …)

For old times’ sake, we walked the length of the prom, and — as many generations of Aber people have done — “kicked the bar” (yes, kicked the railings at the end of the sea-front). And then we cheered ourselves up by driving up the coast to Machynlleth and back over the hills through Llanfair Caereinion to where we started, another sixty miles of some of the most beautiful countryside in the land. It isn’t for nothing that Montgomeryshire is called the Paradise of Wales.

TYL, #16: The Teach Yourself Logic Guide again

Oh dear. I seem to have spent much more time than I meant over the last week revisiting various logic books and updating the Teach Yourself Logic Guide, and it seems to have somehow grown by another nine pages. So I’m calling a halt, and have uploaded the June version a little early. You can find it here. Do spread the word to anyone you think might have use for the Guide.

The previous, April, version has been downloaded well over 1200 times in under two months, so it certainly seems that it is worth putting the effort into the project, and it is fun (of a sort) to work on. I’ll no doubt upload another version in a couple of months. But,   for the moment, I really must get back to other things.

What do you think of Enderton’s Mathematical Introduction to Logic?

Now I’m back from my Bahamian break, I’m intermittently doing some reading, preparing for another version of the Teach Yourself Logic Guide to be put online at the end of the month. I’ve just been taking another look at Enderton’s much used, and often recommended, A Mathematical Introduction to Logic (to which I perhaps gave rather short shrift before). It strikes me as a good book, meeting it again after a long gap, now in the guise of its second edition. But it also strikes me as tougher going than it purports to be. So my summary verdict, from the draft page-and-a-bit that I’ll be adding to the appendix on the Big Books on Mathematical Logic, is that Enderton’s Chs 1 and 2 would make good supplementary reading if you’ve already read a more user-friendly text on first-order meta-theory, and that his even-more-action-packed Ch.3 would make good consolidatory reading if you’ve already read something more introductory on incompleteness (like IGT, for example!).

But what do/did you think of Enderton’s text as a teacher/student? I’d be interested to hear as it is still recommended so often.

Gödel Without Tears, again?

Last year, a couple of thousand people downloaded Gödel Without (too many) Tears, and the notes continue to be downloaded at the same rate. Which makes me think I could usefully update/expand the notes so that, for a start, they integrate better with the new edition of IGT.

Oh, should I flag that up?

IGT2 is now available in the USA. Hasten to Amazon.com or your local friendly bookseller. Go on, you know you want a copy. As do your logical friends and relations. Total bargain, of course, and full of timeless truths, which is more than be said for most philosophy books. (And don’t forget to tell your uni library to get lots of copies).

 Ahem. As I was saying. I’ve been wondering about re-doing GWT. Perhaps in two halves, say eight or ten instalments for the [UK] autumn term/semester later this year, and then another bunch of instalments for the beginning of 2014. I’m not inclined to do any accompanying lecture-style videos (if only because I get bored watching such things myself: reading is so much quicker than listening/watching!). But I am turning over the idea of setting up a forum for questions/discussions. A heavily moderated forum, so as avoid everything being hijacked by the swivel-eyed loons who want to disprove Gödel’s theorems, or by the likes of those who troll math.stackexchange by inciting people to waste their time explaining standard bookwork.

I’d be interested, though, to hear from (or be put in touch with) anyone who has experience using a discussion forum like this. Would it get used? Is it more hassle than it is worth? (And practically, any recommendations of forum software to use? If you or anyone you know has set up a mathsy forum in a way that allows contributors to use MathJax to render LaTeX symbolism nicely, then I’d be particularly interested to hear about how that was done!) Any suggestions/thoughts about how to proceed with this sort of thing welcome!

Postcard from the Bahamas

Another year, another trip to the Bahamas. Familial duty trip. But these things need to be done, you understand. Just have to put up with the crowded beaches and leaden skies as you can see …

Holiday reading so far: Kate Atkinson, Emotionally Weird (not her best, I think, but laugh-out-loud funny); Julian Barnes, Flaubert’s Parrot (re-read with enormous pleasure); Ivan Turgenev, Rudin (Turgenev’s first novel, which I’d never read before; again not his best but I enjoyed it a lot); Scott Fitzgerald, The Great Gatsby (decades since I read this: but surely comparatively over-rated, no?); currently Anthony Horowitz, The House of Silk (Holmes pastiche, huge fun). And no logic books.

How relevant is relevant logic?

Review essays in the genre “Recent work in X” are often extremely useful, if only to confirm your suspicion that you can probably live pretty happily without getting too exercised about the latest lucubrations of X-ists.

I’ve just read a preprint newly posted by Mark Jago, “Recent work in Relevant Logic”. Now, I’m not resistant to logical reformisms (having various interests in intuitionism, plural logics, ancestral logics, predicative systems), but I’ve never really been able to get worked up about issues of relevancy. Or at least, such small itches as I’ve had about e.g. arguing past a contradiction are sufficiently soothed by Neil Tennant’s style of relevant logic which minimally mutilates classical (or intuitionist) systems.

Does Jago point to anything that might get me more excited? Well, apart from some sketchy hints at the end that you can perhaps tie together issues about relevant logic with ideas about truth-making and truth-makers, I’m not persuaded that the ingenious technical constructions that he reports link up to anything I can get very interested in (either when wearing my philosophical hat or my mathematical hat). But your mileage may very well vary, so do take a look at Jago’s very clear and useful piece for yourself.

An open problem about Rosser sentences?

Fix on a provability predicate Prov for a suitable theory T (there’s a lot of choices to make

here, starting of course with a choice of Gödel coding). Then any Gödel sentence in the sense of a fixed point for Prov is provably equivalent in T to the consistency sentence not-Prov(0=1). So these Gödel sentences are all equivalent. That’s all familiar.

Now Rosserize the provability predicate in the usual way, and consider Rosser sentences, meaning fixed points for this doctored predicate. The question was recently asked on math.stackexchange: are these Rosser sentences also provably equivalent with each other?

I knew there was a relevant paper by D. Guaspari and R. Solovay, ‘Rosser Sentences’, Annals of Math. Logic vol 16 (1979), pp. 81-99. And their key relevant result about Rosser sentences is this. There are some ‘standard’ provability predicates whose Rosser sentences are all equivalent, and there are other ‘standard’ provability predicates whose Rosser sentences are not all equivalent. (Being standard is a matter of satsifying two of the usual derivability conditions.)

The proofs of these results need quite a bit of apparatus: and the authors remark that the situation with respect to the “usual” provability predicate constructed in the normal way without fancy tweaking “seems to be very difficult” and is [or rather was at that time of publication, 1979] unsettled. But is the question still unsettled?

Well, I note that in Buss’s *Handbook of Proof Theory* (1998), p. 496, it is still reported as an open question whether there is a reasonable notion of “usual” provability predicate for which it can be settled whether or not all Rosser sentences for such a predicate are equivalent. It is interesting that the problem should be this intractable. I just don’t know whether there is any more recent work which sheds further light. Any offers?