Peter Smith's Blog, page 42

The Many and the One, Ch. 1

As Louis MacNiece wrote, “World is crazier and more of it than we think, Incorrigbly plural.” Evidently, then, we need a plural logic! Or so say quite a few. And enough has been written on the topic for it to be time to pause to take stock.

I have just now started reading Salvatore Florio and Øystein Linnebo’s The One and The Many: A Philosophical Study of Plural Logic, newly published by OUP with an open access arrangement which means that a PDF is free to download here. The book aims to take stock and explore the broader significance of plural logic for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct?

I’ll say straight away that Florio and Linnebo write very lucidly in an attractively readable style. Though it is not entirely clear, perhaps, who the intended reader is. The opening pages seem addressed to a pretty naive reader who e.g. may not even have heard of Cantor’s Theorem (p. 3); yet pretty soon the reader is presumed e.g. to understand talk of defining logical notions in terms of isomorphism invariance (p. 22). Again, if the reader really was new to the topic and had never seen before one of the now standard core logical languages for plural logic and its associated core deductive system, the initial brisk outline presentation (pp. 15-20) might perhaps be rather too brisk. But I’m certainly not going to nag about this sort of thing. Whatever F&L’s intentions, I’ll take the likely reader of their book to be someone who has some logical background and in particular has a modicum of prior acquaintance with plural logic and some of the debates about it; and then their brisk early remarks can serve perfectly well as reminders getting us back the swing of thinking about the topic.

So let’s dive in. In the short Chapter 1, ‘Introduction’, F&L highlight three questions which are going to run through their discussion:

Should the plural resources of English and other natural languages be taken at face value or be eliminated in favor of the singular?What is the relation between the plural and the singular? When do many objects correspond to a single, complex “one” and what light does such a correspondence shed on the complex “ones”?What are the philosophical and other consequences of taking plurals at face value?

Not, I think, that we are supposed to take these as sharply determinate questions at this stage: take them as pointers to clusters of issues for discussion. F&L also give early spoilers, indicating some lines they are going to take.

In response to (1) they announce they are pluralists, resisting the wholesale elimination of plurals (while, they say, wanting to resist some of the usual arguments against singularism). On (2) they say — surely rightly — that the question is going to entangle us tricky issues in metaphysics, semantics, and the philosophy of mathematics. We can’t, as it were, argue for a particular line on plural logic in isolation; rather we going to have to “chose between various “package deals” that include not only a plural logic but also commitments far beyond”. On (3) F&L trail their view that many of the claims that have been made for plural logic — such as that it “helps us eschew problematic ontological commitments, thus greatly aiding metaphysics and the philosophy of mathematics” — are, in their words, severely exaggerated. Leaving aside the ‘severely’, I’ll probably find myself endorsing a verdict that some of the claims that have been made for plural logic are somewhat overblown. But I’ll be interested to see to see how the detailed arguments pan out.

To be continued.

The post The Many and the One, Ch. 1 appeared first on Logic Matters.

The Many and the One, #1

As Louis MacNiece wrote, “World is crazier and more of it than we think, Incorrigbly plural.” Evidently, then, we need a plural logic! Or so say quite a few. And enough has been written on the topic for it to be time to pause to take stock.

I have just now started reading Salvatore Florio and Øystein Linnebo’s The One and The Many: A Philosophical Study of Plural Logic, newly published by OUP with an open access arrangement which means that a PDF is free to download here. The book aims to take stock and explore the broader significance of plural logic for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct?

I’ll say straight away that Florio and Linnebo write very lucidly in an attractively readable style. Though it is not entirely clear, perhaps, who the intended reader is. The opening pages seem addressed to a pretty naive reader who e.g. may not even have heard of Cantor’s Theorem (p. 3); yet pretty soon the reader is presumed e.g. to understand talk of defining logical notions in terms of isomorphism invariance (p. 22). Again, if the reader really was new to the topic and had never seen before one of the now standard core logical languages for plural logic and its associated core deductive system, the initial brisk outline presentation (pp. 15-20) might perhaps be rather too brisk. But I’m certainly not going to nag about this sort of thing. Whatever F&L’s intentions, I’ll take the likely reader of their book to be someone who has some logical background and in particular has a modicum of prior acquaintance with plural logic and some of the debates about it; and then their brisk early remarks can serve perfectly well as reminders getting us back the swing of thinking about the topic.

So let’s dive in. In the short Chapter 1, Introduction, F&L highlight three questions which are going to run through their discussion:

Should the plural resources of English and other natural languages be taken at face value or be eliminated in favor of the singular?What is the relation between the plural and the singular? When do many objects correspond to a single, complex “one” and what light does such a correspondence shed on the complex “ones”?What are the philosophical and other consequences of taking plurals at face value?

Not, I think, that we are supposed to take these as sharply determinate questions at this stage: take them as pointers to clusters of issues for discussion. F&L also give early spoilers, indicating some lines they are going to take.

In response to (1) they announce they are pluralists, resisting the wholesale elimination of plurals (while, they say, wanting to resist some of the usual arguments against singularism). On (2) they say — surely rightly — that the question is going to entangle us tricky issues in metaphysics, semantics, and the philosophy of mathematics. We can’t, as it were, argue for a particular line on plural logic in isolation; rather we going to have to “chose between various “package deals” that include not only a plural logic but also commitments far beyond”. On (3) F&L trail their view that many of the claims that have been made for plural logic — such as that it “helps us eschew problematic ontological commitments, thus greatly aiding metaphysics and the philosophy of mathematics” — are, in their words, severely exaggerated. Leaving aside the ‘severely’, I’ll probably find myself endorsing a verdict that some of the claims that have been made for plural logic are somewhat overblown. But I’ll be interested to see to see how the detailed arguments pan out.

To be continued.

Postcard from Monmouth

We have been staying in a cottage near Monmouth for a few days. The countryside here is indeed a particularly green and pleasant land; we can sit outside the cottage looking over many rolling miles towards the Black Mountains. The ruins of Tintern Abbey are close by, as is Raglan Castle (both so very well looked after by Cadw for the Welsh Government, and both sites surprising quiet). There is a lot of wonderful walking here, through local woodlands, and in the Usk valley and the Wye valley. The weather has been kind. So a delightful escape from Cambridge.

With brilliant timing, the day before coming away, when I should have been concentrating on things domestic, Logic Matters got hacked. Or rather — since “logicmatters.net” then delivered a Chinese language advert, which hardly looked like a hack aimed at the typical reader here — I suspect some WordPress plugin had been hacked. (I’d been experimenting with different plugins while giving this site a fresh coat of paint). It took a while for me to find the source of the trouble; but then someone kindly recommended the Wordfence security plugin which quickly pinpointed where the evil code been added. Fingers crossed, but I hope the site is now more secure from such exploits. A long afternoon quite, quite wasted though. Not good for the blood pressure.

Calm was restored driving down to Monmouth and stopping at Kiftsgsate Court Gardens and then on to High Glanau, both gardens real works of art. We will visit Coton Manor Garden on the way home, which is even more stunning in its way (though perhaps I prefer the slightly wilder, less perfectly kempt style of Kiftsgate). I have said before, that gardens are a form of art the English both do particularly well and particularly love. Is there, I wonder, anything attractively and insightfully written by modern philosophers on the aesthetics of gardening? (A genuine question!)

LaTeX for Logicians — a new look (and time for new content?)

Here are the new-look pages for LaTeX for Logicians.

The LaTeX for Logicians front page got over 35K visits last year, with some of the other individual pages getting 15K visits. So these pages are evidently still being found useful. I haven’t updated some of them  for well over two years, and I am certain to have missed some more recently added LaTeX resources that will be of interest to users of these pages.

So this is your moment: as I update these pages, do please let me know what’s missing!

… and back again

Update on the Logic Matters website. You can get lost down the infinite rabbit hole of WordPress customizations. But I’ve managed to escape, fixed on a theme, suppressed most of its fancy options, aiming for simplicity verging on starkness, and have got to work … Lots still to be done (for a start, in making more tablet and phone friendly), but you’ll get the basic idea. Any helpful comments/suggestions will of course be welcome.

Update on the hardback of Gödel Without (Too Many) Tears. Hooray! — a copy (from UK Amazon) has arrived at last, and another copy (from Blackwell’s, one to send on to the British Library) arrives tomorrow. UK and US Amazon are both now promising very speedy delivery.

I must say that I am very pleased with the result, it is really decently produced. So that, together with the sales figures, encourages me to organize hardback library copies of IFL and IGT. More about that anon. But for the moment, do please remember to get your local friendly librarian to order the hardback GWT for the library! — details here.

LaTeX for Logicians — a new look (and time for new content?)

Here are new-look pages for LaTeX for Logicians (the link is to temporary versions, in their future Siteground home).

The LaTeX for Logicians front page got over 35K visits last year, with some of the other individual pages getting 15K visits. So these pages are evidently still being found useful. I haven’t updated some of them for well over two years, and I am certain to have missed some more recently added LaTeX resources that will be of interest to users of these pages.

So this is your moment: as I update these pages, do let me know what’s missing!

If you hit the “Logic Matters” header on those new pages, you’ll be taken to a temporary version of the main site, again under (re)construction.

I’m testing on five different-sized Apple devices and things are beginning to fall into shape. The site pages certainly load much faster now, and are handled much better on an iPhone.

Two notes: The page footers with links to other blogs, my tweets, etc. do not appear on the mobile version on purpose, to make for neatness. And there’s a little visual glitch with a search box not closing gracefully, but that seems to be a Safari-specific issue not a site issue.

Any thoughts/advice/suggestions on the redesign will be very welcome.

… and back again

Update on the Logic Matters website. You can get lost down the infinite rabbit hole of WordPress customizations. But I’ve managed to escape, fixed on a theme, suppressed most of its fancy options, aiming for simplicity verging on starkness, and have got to work … If you want to see a temporary version of Logic Matters in its new home with its new look, you can take a peek and look around here. Lots still to be done (for a start, in making more tablet and phone friendly), but you’ll get the basic idea. Any helpful comments/suggestions will of course be welcome.

Update on the hardback of Gödel Without (Too Many) Tears. Hooray! — a copy (from UK Amazon) has arrived at last, and another copy (from Blackwell’s, one to send on to the British Library) arrives tomorrow. UK and USA Amazon are both now promising very speedy delivery.

I must say that I am very pleased with the result, it is really decently produced. So that, together with the sales figures, encourages me to organize hardback library copies of IFL and IGT. More about that anon. But for the moment, do please remember to get your local friendly librarian to order the hardback GWT for the library! — details here.

Down the rabbit hole …

This Logic Matters site currently lives on Bluehost. But for various reasons, I’m in the middle of moving to a different hosting provider, Siteground: significantly more expensive (after the initial year’s discount) but by very many accounts also significantly better. Certainly, an experimental test version of the site runs there a lot faster, both on my iMac and even more so on an iPhone. As I’ve said before, the whole site could do with a good deal of tidying under the bonnet. So the needed update will keep me from fretting about the state of the world for a week or two.

I’ll need then to chose a modern WordPress theme that maintains the uncluttered look I like. I’ll ignore the pricey paid options. That only leaves about eight thousand free themes to choose from. So this is going to be dead easy. Down the rabbit hole I go …

Beginning Mathematical Logic again

I have uploaded a slightly revised version of Part I of the Study Guide, with just a few changes to the arm-waving chat and a couple of additions to the recommendations in the Computation/Arithmetic/Gödel’s Theorem chapter. You can download it here.

I’m working away at Part II, mostly enjoying the (re)reading around. An earlier time-slice of myself might have persisted in reading the less fun books out of a misplaced sense of duty. Now I tend to think that if someone really can’t be bothered to write with transparent clarity and make some honest attempt to take their reader along with them by e.g. providing enough signposts along the way, then maybe I can’t be too bothered about struggling with their ill-written texts. So I move on much more quickly to find something more logically entertaining.

Big Red Logic Books: now available in Australia!

Short version: paperbacks of An Introduction to Gödel’s Theorems,  An Introduction to Formal Logic, and Gödel Without (Too Many) Tears are now available from Amazon in Australia.

Slightly longer version: An Australian version of Amazon’s KDP print-on-demand service has been up and running since the beginning of the year. Initially, however, it couldn’t handle books in the format of the Big Red Logic Books. But (though they haven’t told authors!) I have just discovered in the last hour that the books are now available locally. The prices are set to the minimum possible (the fixed printing and distribution charges are higher in Oz, but I’ve set the royalties to zero to compensate).

So please spread the word Down Under. The books have been available as PDF downloads for a year, but there are quite a few who much prefer to work from printed books. And do tell local librarians (you might need to do a bit of explaining/cajoling too, as librarians tend to hold their professional noses over self-published books, and don’t approve of Amazon either! — but other publication routes would have been much more expensive).

I’d be interested to hear how the physical copies turn out  (the UK printed ones are really surprisingly good, apart from slightly flimsy covers, given the price point).