Peter Smith's Blog, page 49

A few thoughts about self-publishing

A very enjoyable walk down to my favourite library, the Moore library, in the winter sun. But not, sadly, to then read and write, and think, and idly look out of the windows, and take a coffee break, and write again. It will be a good while yet before all that is possible. I was just donating, via their dropbox, copies of IFL2 and GWT.

Time for an update, perhaps. How have things gone since I got the copyright back from CUP, and have been able to give away IFL2 and IGT2 as freely downloadable PDFs? I’ve just checked: since late August, IFL2 has been downloaded over 3.6K times. And after a quite crazy initial flood (when someone posted a direct link at Hacker News, without saying that the link was to a full book!), IGT2  has been downloaded another 4K times. The two books have sold well over 200 each of the inexpensive print-on-demand versions. (It is very early days for GWT … I’ll report back on that in the New Year.)

I didn’t at all know what to expect. Or rather, I was expecting something like that ratio of freely downloaded PDFs to bought copies: but I had little idea how many would be tempted by the books overall. I guess I am pretty pleased.

And it certainly seems to have been worth the small effort of making the print-on-demand versions available. I did ask online, and got enough responses to suggest that there is a significant minority of readers who significantly prefer to work from “real” books as opposed to onscreen PDFs (which is one reason that libraries should have hard copies available); and some of that minority said that they are prepared to pay a modest amount to get the hard copy too. And so it has turned out.

By the way, as I’ve remarked before, I wasn’t thrilled to bits to be using the Amazon-provided service. But for this kind of enterprise, it does seem the best and easiest option on various counts. And since sales are small, and I’ve only rounded up the price from the minimum possible by pence (in order to cover costs of getting proof copies, sending copies to copyright libraries etc.), you are at least not adding much to Amazon’s grossly undertaxed profits by buying a copy.

In some respects, then, isn’t this an ideal way of publishing book-length projects? Provide freely downloadable PDFs; and make as-inexpensive-as-possible print-on-demand copies available.

Well yes, but only up to a point. It works if you e.g. already have a book or two to your name and you don’t particularly need the imprimatur of a respected academic press for people to think that your book might be worth taking seriously. And if you don’t need that imprimatur for promotion purposes either. And  if you can find enough friends and acquaintances to give honest critical feedback at key writing stages (eventually doing the work of a publisher’s readers). And if you know your way around a document processing package like LaTeX well enough, and have a good enough design eye, to produce pages which look professional.  And if you can find enough other friends and acquaintances who will happily check for typos and thinkos (doing the work of a publisher’s proof-reader). And if you have enough internet presence via a blog or whatever to get the word out there beyond the small circle of those friends and acquaintances!

That’s quite a few rather big “if”s.

So traditional publishers do still have a role to play. Or at least some of them. Mind you, we can all think of publishers like Spr*ng*r where the quality control is minimal, and unheralded books (published at ludicrous prices) fall stone dead from the press. However, you can these days publish with an academic publisher and negotiate to be allowed to keep a PDF freely downloadable (some even put e.g. chapter-by-chapter PDFs open access on their website). CUP, OUP and MIT seem to allow this sort of thing sporadically, though I’m not sure what the principles of choice are. And then there is e.g. the very promising new BSPS Open initiative: the plan is to publish open access monographs under the supervision of an editorial board to maintain quality. It will be interesting to see how initiatives like that develop over the coming few years: for surely, with the gross pressure of costs on libraries (let alone the impoverishment of young academics) the days of publication solely by the £80 monograph must be numbered …

Meanwhile, if it can work for you, I can recommend the self-publishing route!

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Logic: A Study Guide — Basic Model Theory

I’m continuing work on the update for Teach Yourself Logic: A Study Guide. So there are now five chapters in the new Logic: A Study Guide.

There are three preliminary chapters, giving an introduction for philosophers, an introduction for mathematicians, and a guide-to-the-guide. Then there is a long chapter on FOL. I’ve previously posted versions of these.

The fifth chapter is on entry-level model theory. There’s an overview introducing a few elementary results, intended to give a flavour of the enterprise. There follows the usual sort of reading guide.

Here then is the Guide including this new  chapter. Need I add? — all comments very gratefully received.

In particular I’m sure I can do better at the end of the displayed box on p. 34. I say earlier in the chapter that — although the focus is of course on standard first-order model theory — it is worth at this stage knowing just a bit about second-order logic/theories (so you get e.g. a glimmer of why first-order arithmetic isn’t categorical which a second-order arithmetic can be). But what short and accessible reading on second-order logic would you recommend at this stage? Later in the Guide we’ll be taking a serious look at the topic: but what brisk (perhaps arm-waving but still helpful) intro could be offered at this point?

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Gödel Without (Too Many) Tears published!

Brought to the front — short version: GWT is available on Amazon, print on demand.

Long version: Gödel Without (Too Many) Tears is based on notes for the lectures I used to give to undergraduate philosophers taking the Mathematical Logic paper in Cambridge. Earlier versions were available here online, and have been much downloaded for a decade (and I know they have been used for seminars/lecture courses elsewhere). As occupational therapy in this time of pandemic, I have now considerably tidied-up the notes into a book format — and many thanks to all those who have helped along with way with suggestions and corrections. You can think of the result as a much cut-down version of big Gödel book; it is just over a third of the length, but still aiming to explain some of the key technical facts about the incompleteness theorems.

The book is now available as a very inexpensive, at cost, print-on-demand book for less than $5/£4/€4.5. See e.g. US link, UK link; you can ‘look inside’ from the linked pages. For other Amazons, use the ASIN identifier B08L5MQLRQ. (Sorry about using Amazon; but they bought up the CreateSpace platform …)

The book will also eventually become freely available as a PDF download. But if you want to get a free copy right now, then here is how. Email (a version of) the following note to the relevant university librarian, copying me in (peter_smith at logicmatters dot net):

Please order the following two books for the library:

Peter Smith, An Introduction to Formal Logic (2nd edition, originally published by Cambridge University Press 2020; now available as an inexpensive Amazon print-on-demand book; ISBN 979-8675803941; ASIN B08GB4BDPG.)

Peter Smith, Gödel Without (Too Many) Tears (Logic Matters 2020; available as an inexpensive Amazon print-on-demand book; ISBN 979-8677892196; ASIN B08L5MQLRQ.)

I’ll reply to your email with a PDF of GWT. If your library uses a web-based form, bounce on to me the order acknowledgement — or do something else similarly convincing ;-) As you’ll see from the prices, the royalties coming my way will be trivial. What I do really care about is making sure that the two books are indeed in libraries (especially for the significant number of students who, for one reason or another, much prefer to work from printed texts). And so I hope this tiny bribe of the early free PDF will encourage people to ask for library copies!

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Logic: A Study Guide — First Order Logic (again)

I’ve updated the chapter on FOL in the new-style Guide. Here again are the preliminary chapters (which you can ignore if you know the basic idea of the Guide, inherited from TYL), plus the revised chapter.

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Logic: A Study Guide — First Order Logic

I have started working occasionally on an update for Teach Yourself Logic: A Study Guide. It now has a slightly different format — and a marginally snappier title, Logic:  A Study Guide.

After three preliminary chapters — an “Introduction for Philosophers”, a shorter “Introduction for Mathematicians”, and a chapter on “Using this Guide” — the first substantial chapter of the new Guide gives, as you would expect, basic reading recommendations on first order logic. Here then is a draft of those preliminary chapters together with the new Chapter 4. (The earlier chapters will only be of any interest to those not familiar with the general intention of the Guide: everyone else can start reading at p. 12.)

All comments and suggestions very gratefully received, as always.

“Ok, it looks prettier, but the principal recommendations haven’t changed!” I’m afraid not. I have been doing a lot of enjoyable and indeed instructive re-reading over the last couple of weeks, but I do seem to have ended up not changing my verdicts about very much. Fancy that!

“So after all that effort, it’s a bit like Ford Prefect updating his entry for the Earth in the Hitchhiker’s Guide to the Galaxy from ‘Harmless’ to ‘Mostly harmless’?” Harsh but embarrassingly close to the truth …

… Still, there are enough minor changes, perhaps, to make it all worth while!

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Philosophy of mathematics — a reading list

A few people recently have quite independently asked me to recommend some introductory reading on the philosophy of mathematics. I have in fact previously posted here a short list in the ‘Five Books’ style . But here’s a more expansive draft list of suggestions.

Let’s begin with an entry-level book first published twenty years ago but not yet superseded or really improved on:

Stewart Shapiro, Thinking About Mathematics (OUP, 2000). After introductory chapters setting out some key problems and sketching some history, there is a group of chapters on what Shapiro calls ‘The  Big Three’, meaning the three programmatic ideas that shaped so much philosophical thinking about mathematics for the first half of the twentieth century — i.e. varieties of logicism, formalism, and intuitionism. Then there follows a group of chapters on ‘The Contemporary Scene’, on varieties of realism, fictionalism, and structuralism. This might be said to be a rather conservative menu — but then I think this is just what is needed for a very first introduction to the area, and Shapiro writes with very admirable clarity.

By comparison, Mark Colyvan’s An Introduction to the Philosophy of Mathematics (CUP, 2012) is far too rushed to be useful. And I would say much the same of Øystein Linnebo’s Philosophy of Mathematics (Princeton UP, 2017). David Bostock’s Philosophy of Mathematics: An Introduction (Wiley-Blackwell, 2009) is more accessible, but — apart from a chapter on predicativism — covers similar ground to the earlier parts of Shapiro’s book, but has little about more recent debates.

A second entry-level book, narrower in focus, that can also be warmly recommended is

Marcus Giaquinto, The Search for Certainty (OUP, 2002). Modern philosophy of mathematics is still in part shaped by debates starting well over a century ago, springing from the work of Frege and Russell, from Hilbert’s alternative response to the  “crisis in foundations”, and from the impact of Gödel’s work on the logicist and Hibertian programmes. Giaquinto explores this with enviable clarity: this is really exemplary exposition and critical assessment. A terrific book.

Then, before moving on, I have to mention that most accessible of modern classics:

Imre Lakatos, Proofs and Refutations (originally published in 1963-64, and then in expanded book form by CUP, 1976). Textbooks tend to present developed chunks of mathematics in a take-it-or-leave-it spirit, the current polished surface hiding away the earlier rough versions, the conceptual developments, the false starts. Proofs and Refutations makes for a wonderful counterbalance. A classic exploration in dialogue form of the way that mathematical concepts are refined, and mathematical knowledge grows. We may wonder how far the morals that Lakatos draws can be generalized; but this remains a fascinating read (I’ve not known a good student who didn’t enjoy it).

Next, having got from Shapiro a sense of some of the core problems, you should certainly sample some classic papers. Here are two extremely useful sourcebooks taking us up to the turn of the century:

Paul Benacerraf & Hilary Putnam (eds), Philosophy of Mathematics: Selected Readings  (CUP: NB you want the 1983 2nd edition of this classic collection).
Dale Jacquette (ed), Philosophy of Mathematics: An Anthology (Blackwell, 2002).

Then, for further discussions of debates old and new, the obvious next place to look is:

Stewart Shapiro (ed.) The Oxford Handbook of Philosophy of Mathematics and Logic (OUP, 2005). The editor’s introductory essay is in fact called ‘Philosophy of mathematics and its logic’, which should surely also have been the whole Handbook’s title — for of the twenty-six essays here, twenty are straight philosophy of mathematics, and the logic essays are mostly closely relevant to mathematics too. Large handbooks of this general type can often be very mixed bags, containing essays of decidedly varying quality; but this one really is a triumph. Some of the essays are very substantial, and as I recall it none is a makeweight. There are often pairs of essays taking divergent approaches (e.g. to contemporary logicism, to intuitionism, to structuralism). Of course, there are variations in the accessibility of the individual essays: but Shapiro seems to have done wonderful work in keeping his very well-selected authors under control! So for any serious student now — perhaps beginning graduate student — this must be the place to start explorations of issues in more recent philosophy of mathematics.

Following up interesting-seeming references in the Handbook essays will enable you to begin to explore the then-state-of-play in various areas in as much detail as you want: I therefore needn’t add more references here to important earlier work by a whole range of philosophers. And so, with a gesture towards the amazing resource that is the Stanford Encyclopaedia of Philosophy — which has some characteristically excellent long entries on various topics in the philosophy of mathematics, all with many further references — we could stop an introductory list at this point. Except I should perhaps mention another giant handbook. After all, if you are interested in the philosophy of maths, it helps to know some maths! For a guide with some wonderfully lucid essays, see the masterful

Timothy Gowers (et al., eds) The Princeton Companion to Mathematics (Princeton UP, 2008).

As I said, I have surely provided more than enough introductory reading! Still, let’s ask: what has been published of note since around the time of the Handbook (while letting that do the work of pointing to previous contributions). There was a short collection edited by Otávio Bueno and Øystein Linnebo called New Waves in the Philosophy of Mathematics (Palgrave, 2009), which has moderate interest. Some of the papers collected in Paolo Mancosu (ed.) The Philosophy of Mathematical Practice (OUP, 2008) are worth reading. And of course, the journal Philosophia Mathematica continues to publish many good articles. But what of books?

Ian Hacking’s Why is There Philosophy of Mathematics At All (CUP, 2014) is an idiosyncratic though accessible and engaging ramble by an always-interesting philosopher. Penelope Maddy, who has a paper on ‘naturalism’ about mathematics in the Handbook has published two characteristically readable works developing her position, Second Philosophy (OUP, 2007) and Defending the Axioms: On the Philosophical Foundations of Set Theory (OUP, 2011). One position under-represented in the Handbook is outright fictionalism: Mary Leng’s Mathematics and Reality (OUP, 2010) mounts a defence. She argues that we have no reason to believe that mathematical objects exist, and then takes on the task of explaining how it can still be that mathematics is can be crucially useful in the formulation of scientific theories. You might well not end up agreeing: but engaging with Leng’s lucidly presented arguments will force you to get clear about a range of central issues.

We are now perhaps going up a level in difficulty. Charles Parsons has been one of the most insightful philosophers of mathematics for half a century. His early collection of papers Mathematics in Philosophy (OUP, 1983) is still well worth reading. But his long-awaited major book is Mathematical Thought and Its Objects (CUP, 2008) is quite tough going — it is not easy to work out the subtle position he is trying to develop as he negotiates his way between different kinds of structuralism.

Every philosopher of mathematics should at some point read Michael Dummett’s Frege: Philosophy of Mathematics (Duckworth, 1991). The later neo-Fregean project of Crispin Wright and Bob Hale’s The Reason’s Proper Study (OUP 2001) has rather run out of steam. But it did inspire important work on Frege and on more loosely Fregean themes: see for example Richard Heck’s two books of papers Frege’s Theorem (OUP, 2011) and Reading Frege’s Grundgesetze (OUP, 2012), and also the very interesting John Burgess, Fixing Frege (Princeton UP, 2005) which will also point you to more on the project of so-called reverse mathematics.

Philosophers continue to worry about the foundations of set theory — having, let’s hope, done their initial homework on Michael Potter’s excellent Set Theory and Its Philosophy (OUP, 2004), and perhaps also on José Ferreirós’ historical Labyrinths of Thought (Birkhäuser, 2007). We’ve mentioned Maddy’s work. For a new discussion see Luca Incurvati, Conceptions of Set and the Foundations of Mathematics (Cambridge, 2020). A smaller number of philosophers worry about the foundations of category theory: you’ll find some scattered papers with further references in Philosophia Mathematica.

My sense, though, is that after a period in which the philosophy of mathematics really flourished, there has perhaps been something of a lull more recently. However let me finish with a stand-out recent achievement, more wide-ranging than just philosophy of mathematics: Tim Button & Sean Walsh, Philosophy and Model Theory (OUP, 2018).

And let me leave it there for the moment. What would you add?

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Corrections, corrections …

I at last hit the “publish” button for Gödel Without (Too Many) Tears as an Amazon print-on-demand book; and within less than a day of its going live, I received a list of corrections and suggestions based on a late draft. Of course.

This is the kind of thing which would be so very very annoying with a book published the old-school way — I’d be kicking myself repeatedly for missing the obvious typos that couldn’t be corrected until a later reprint, perhaps years down the road. But in this case, I had a corrected version done within hours, and Amazon had approved it within another few hours. No more than two dozen very early adopters will have the original version (sorry!); from now on you should receive a copy which says on the verso of the title page “This revision: 5.xi.2020”.

In fact — rather a relief! — the caught mistakes turned out to be minor, a few obvious typos, a few clumsy errors like using “then” twice in a sentence. There are just two places where you could possibly be led astray, if you do have the original version. (1) Theorem 72 starts “Under the given conditions …”. Context should make it clear but I didn’t say that the conditions include the relevant theories including enough arithmetic to code consistency sentences. (2) In talking generally about the Second Theorem and Hilbert’s Programme I should have footnoted that the Second Theorem doesn’t rule out all informative proofs of consistency, but leaves room for e.g. Gentzen-style results. I’ve added a quick footnote. If I come to do a second edition of GWT, perhaps I should say more on this second point — though perhaps not: I’d set myself the goal of keeping GWT to a third of the length of IGT2, and I have already overshot a little …

A general comment though. Corrections to any of the three Big Red Logic Books are still welcome (or at least, corrections which e.g. note obvious mistakes, or stylistic infelicities, or uses of English which are opaque to someone who isn’t a native speaker). Dealing with such corrections is very straightforward: so keep them coming!

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Frate Filippo di Tommaso dipintore

In another world, we would have gone to Florence again this year before spring, before the tourists really return. Out of season, the city becomes a delight,  the galleries and churches peaceful, the cafés and restaurants recovered by the locals. But it was not to be.

So, among other distractions, I’ve had to be reading art books instead. One that I have very much enjoyed is Megan Holmes’s Fra Filippo Lippi: The Carmelite Painter (Yale, 1999). (That detail is from the Annunciation that Lippi painted for Le Murate around 1443, and forms the cover.)

This is rather beautifully produced, as Yale’s large art books usually are. Indeed, I confess I initially bought it for the many illustrations. For Lippi is one of my favourite artists (if I could smuggle just one painting home from the National Gallery in London, it might well be the Annunciation there). So there was huge pleasure to be got just from a slow look at the reproduced paintings in Megan Holmes’s book. But then I found myself becoming thoroughly caught up in her project of trying to understand how Lippi’s work is bound up with his ambiguous relation to his friary. This is perhaps not the best written art monograph ever: it can be a little repetitive and sometimes overdoes the scholarly detail at the expense of the narrative flow.  But still,  I not only learnt a great deal about the particular artist recorded in the Carmine’s records as ‘Frate Filippo di Tommaso dipintore’, about his use of Carmelite imagery, and about the relation between his paintings and their particular varied religious settings. I also learnt — very late in the day for me! — important lessons about how to look at early renaissance paintings more generally.  So, warmly recommended.

A footnote: You can still get Megan Holmes’s book second-hand, but significantly more expensively than when I bought my copy a couple of years ago. Moral: get art books when you are first tempted by them (whether exhibition catalogues or monographs like this one)! They far too readily go out of print and then aren’t reprinted. For example, about the time that I bought this book, I bought Jean Cadogan’s Domenico Ghirlandaio: Artist and Artisan (also Yale, 2001): that now costs at least four hundred pounds second-hand. So if there’s an art book you’ve been hankering after, don’t hesitate, snap it up now for a life-affirming lockdown treat!

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Gödel Without (Too Many) Tears published!

Short version: GWT is available on Amazon, print on demand, ASIN identifier B08L5MQLRQ. 

Long version: Gödel Without (Too Many) Tears is based on  notes for the lectures I used to give to undergraduate philosophers taking the Mathematical Logic paper in Cambridge. Earlier versions have been here online and much downloaded for a decade (and I know have been used for lecture courses elsewhere). I have now considerably tidied-up the notes into a book format — and thanks to all those who have helped along with way with suggestions and corrections. You can think of the result as a much cut-down version of IGT2, just over a third of the length, but still aiming to explain some of the key technical facts about the incompleteness theorems. And the book is now available as a very inexpensive print-on-demand book from Amazon: US link; UK link.

The book will become freely available as a PDF download in 2021. But if you want to get a free copy right now, then here is how. Email (a version of) the following note to the relevant university librarian, copying me in:

Please order the following two books for the library:

Peter Smith, An Introduction to Formal Logic (2nd edition, originally published by Cambridge University Press 2020; now available as an inexpensive Amazon print-on-demand book; ISBN 979-8675803941; ASIN B08GB4BDPG.)

Peter Smith, Gödel Without (Too Many) Tears (Logic Matters 2020; available as an inexpensive Amazon print-on-demand book; ISBN 979-8677892196; ASIN B08L5MQLRQ.)

I’ll reply to your email with a PDF of GWT. If your library uses a web-based form, bounce on to me the order acknowledgement — or do something else convincing ;-)

As you’ll see from the prices, the royalties coming my way will be trivial; what I do really care about is making sure that the two books are indeed in libraries (especially for those students who, for one reason or another, much prefer to work from printed texts). And so I hope this bribe of the PDF will encourage people to ask for library copies!

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Pause for meditation, Thomas Tallis

Needed today, more than ever.

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