# 2006

## FOM for neurotic logicians

Maybe it is the advancing years, but occasionally there are those moments of panic. I think “Surely it must be the case that P“, guess I can see how to prove it, check out an obvious source or two, google around, and then am perhaps a bit surprised not to come across a straight proof of P. And sometimes my nerve fails: just occasionally I’ve asked on FOM whether indeed P. I’ve invariably got helpful replies. A couple of days ago, I was asking — in effect — how far up the Friedman/Simpson hierarchy of second-order arithmetics we have to go before we can prove Goodstein’s Theorem (something not mentioned in Simpson’s wonderful book). Before the day was out, I got a couple of really useful private responses, and there are now two brief but equally helpful replies on the list from Dmytro Taranovsky and Ali Enayat. What a fantastic resource this is: I’m not sure how my current book project would be going if it weren’t for FOM and its archives, and I’m immensely grateful.

Oh, and the answer to my question is that ATR_0 is enough. Which I should have got from Sec. V.6 of Simpson (which tells us that ATR_0 is good at handling countable well-orderings).

I’m ploughing on as fast as I can to get my Gödel book finished. I try to keep in mind the good advice that C.D. Broad used to give. Leave your work at the end of the day in the middle of a paragraph which you know roughly how to finish. That way, you can pick up the threads the next morning and get straight down to writing again. So much better than starting the day with a dauntingly blank sheet of paper — or now, a blank screen — as you ponder how to kick off the next section or next chapter. (Or indeed, you start wondering whether the whole thing is worthwhile …) Instead, with luck, you can pick up where you left of and then face the next hurdle while on a roll, with the ideas flowing.

Well, it works for me …

## Real Estate

I’ve been using my old desktop (well, under-the-desk) G4 Mac less and less recently, so I’ve reorganized things so that I can mainly use its fairly new and very nice LCD monitor with my laptop when I’m at home. Wonderful. I can have the TeXShop window with the PDF of the book I’m working on displayed on the external monitor (a full page at 150%), and the TeXShop drawer open too, with all the section hyperlinks: and then the source file of the current chapter and other stuff like BibDesk is on the PowerBook screen. Why on earth didn’t I think of doing this before? It’s LaTeX heaven!

So message to myself: no more lusting after 17″ laptops — keep to a 15″ one for portability, and get the additional real estate when you need it by plugging an the external monitor.

It all seems a very long way from thinking that WordStar on an ACT Sirius was really, really neat …

## What is it like to be a blog?

A blog with that title just has to be worth a link! (It’s by a group of University of Connecticut grad students — interesting content, and there are some nice links out into the philosophical corner of the blogosphere.)

The world inhabited by the philosophy graduate student has been changing fast in the last few years (and in very good ways). Blogs, on-line forums, and the rest obviously can do a lot to counteract the depressing sense of isolation that used to bug people writing their PhD. If local experience is anything to go by, those of us involved in running grad programs need to be thinking more about how best to help students make use of the changing world. Though, on second thoughts, they seem — as usual — to be doing pretty well without us …

## Abebooks

The Advanced Book Exchange is simply terrific, isn’t it? Search over thirteen thousand second-hand book sellers, and — more often than not, in my experience — you can find what you are looking for, and frequently at a decent price.

Of course, there’s a downside. Booksellers can now easily check on-line what is rare and what is not, and check what others are charging. It’s not that many years since I picked up the complete Principia Mathematica for £30: I can’t imagine a bookseller now being so ignorant of its true worth. Still, plenty of bargains are to be had: a copy of Wolfram Pohlers’ Proof Theory has just dropped through the door. I paid all of \$5.95 plus postage.

It’s a bit disturbing, then, to read a paragraph in Private Eye which reports that abebooks have been hiking the commission they charge to booksellers and are about to add more charges. It would a great loss indeed if they price themselves out of having such a wide coverage of booksellers.

## Edinburgh: Gödel, Raphael, …

In a world of such ready e-communication, where people put work-in-progress online, where there are terrific discussion forums like FOM, not to mention blogs and the like, I do wonder about the value of so many conferences. I’m just back from one in Edinburgh on Truth and Proof: Gödel and the Foundations of Mathematics. The first conference I’d travelled to for some time, and to be honest I wasn’t really very encouraged to repeat the experience soon, good though it was to put some faces to some familiar names. In the event, only two papers were directly on Gödel, one by Richard Zach (based on the draft paper which you can read here), the other by Panu Raatikainen (based on his paper which you can read here): both interesting pieces, particularly Richard’s, but I had read them long since. Oh well, …

But Edinburgh of course was quite wonderful, not least because I got to the National Gallery of Scotland more than once. (And a happy discovery since: you can get some impression of most of their major pictures on-line, as e.g. here or here.)

## A spell broken?

Out last night to hear Dan Dennett lecture, talking about his new book Breaking the Spell. A pretty terrific lecture. But the book is, in a word, disappointing. Which is not to deny that it’s full of intriguing insights and illuminating suggestions about e.g. the possible evolutionary sources of dispositions to religious belief. But the structure of the book is surely a little too meandering (I found the first 100 pages dragged), the writing too allusive, to get through to the wide audience he is aiming for. I can see why Dennett often pulls his punches. Full frontal assaults on the frankly dotty aspects of mainstream religious belief-systems would just produce an unthinkingly hostile response, while the cumulative effect of jokes, analogies, biological speculation, just-so stories, reminders of what we all know (e.g. about the variability of religious beliefs), etc., might just get under the defences of some of those he wants to reach, and give them serious pause for thought. I hope so. But the pace isn’t zestful enough, the points not pressed hard enough and clearly enough to really have the impact Dennett wants. In fact, I suspect he should have written two books: a punchier, shorter, less complex book for his desired wider audience and a more fact-strewn, more analytically complex book for those who want the whole story as Dennett currently sees it.

But we’ll see. And certainly, I’m all for his spell-breaking project (the spell he wants to release us from is the idea that we shouldn’t treat religion as a natural human phenomenon with its own biological rationale). Dennett is dead right that we can hardly overestimate the importance of understanding more about religion as a natural phenomenon.

## To begin … a Gödel talk at CUSPOMMS

To blog or not to blog? I’m in two minds. But why not just dive in and see how it goes?

Today was my second outing this academic year to talk to non-philosophers in Cambridge about Gödel, incompleteness and the like. The first time was at a meeting of the Trinity Math. Society. Rather staggeringly, there were more than eighty people there. Perhaps not a brilliantly judged talk, but I did have good fun e.g. telling them about Goodstein’s Theorem. (Having a lot of bright mathmos getting the point and smiling at the cheek of the Goodstein proof made a nice change.)

Today’s outing was to give a talk at CMS to the slightly unfortunately named CUSPOMMS. A very mixed audience, we meet there approximately fortnightly for talks on the philosophy of mathematics, broadly construed. Rather perversely, I suppose, there was less philosophy than in the Trinity talk. In the event, I was explaining one pretty way of proving (a version of) Gödel’s First Theorem without explicitly constructing a Gödel sentence that codes up ‘I am unprovable’. The point of doing this is to counteract that familiar tendency to think that the Gödelian result must be fishy because it depends on something too close to the Liar paradox for comfort.

Paul Erdös had the fantasy of a Book in which God records the smartest and most elegant proofs of mathematical results (have a look at the terrific Proofs from the Book by Aigner, Hofmann and Ziegler). So I was aiming to outline one Book proof: here is a version of the talk.

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