Peter Smith's Blog, page 140

Apologia pro iPad sua

("Are you sure that 'iPad' is feminine?" Err …. Now you mention it, no. But let's not fuss about that!)

I really didn't intend to buy an iPad. Let alone buy one on the first day of availability in the UK. But there they were in the Apple store as I was passing, and the early queues had subsided, and I got a chance to play with one undisturbed for three quarters of an hour … So here I am.

A wild extravagance? Well, not that wild. I'm always a bit surprised, in fact, by the odd attitude...

Field on the no proposition view

If you are a deflationist of sorts, you might reasonably toy with the thought that, when 'that's true' is said of an attempted assertion which misfires so badly that no proposition is expressed, then the purported endorsement of a saying misfires too. The suggestion naturally leads to the view that the Liar sentence doesn't express a proposition. Field briefly touches on the view at p. 132 of Saving Truth from Paradox, and brusquely rejects it (without mentioning any of its defenders):

I...

Another Cambridge bookshop gone

It must be almost fifty years since I first bought a book at Galloway and Porters. But I've just bought my last book there as they are closing down at the end of the month, after trading for over a hundred years.

In recent years, G & P have largely sold remaindered books, or "damaged" books (in that odd sense beloved by university presses, used when the only damage is by a red stamp reading DAMAGED across the title page). But they have been a continuing source of unmissable bargains — for...

Hydra games, anyone?

Ok, there's the foundations-significant Kirby/Paris hydra battle, where we can show that Hercules always wins, by a transfinite induction up to ε0.

Now, there must be lots of other hydra games — maybe some of them even a bit interesting! — that terminate (or at least terminate on best play) with a win for Hercules, and can be shown to do so by inductions along smaller ordinals.

Does anyone happen to know if there's a discussion out there of examples of such shorter games?

[Full disclosure: I'm ...

Curry, Lukasiewicz, and Field (revised)

As I said in the last post, we've fairly recently started working through Field's Saving Truth from Paradox in our reading group.

It fell to me to introduce Ch. 4 on Curry's Paradox and (infinite valued) Lukasiewicz logics yesterday. I very speedily dashed off some introductory remarks (expecting, rightly, that few there would have actually read either Curry or Lukasiewicz so some scene-setting background might be helpful). For what little they are worth, here are my notes, now very slightly ...

Curry, Lukasiewicz, and Field

As I said in the last post, we've fairly recently started working through Field's Saving Truth from Paradox in our reading group. It fell to me to introduce Ch. 4 on Curry's Paradox and (infinite valued) Lukasiewicz logics yesterday. I very speedily dashed off some introductory remarks (expecting, rightly, that few there would have actually read either Curry or Lukasiewicz so some scene-setting background might be helpful). For what they are worth, here are my notes.

Squeezing arguments

When I was in NZ, I gave a talk at four universities on the prospects for a squeezing argument to prove Church's Thesis. But in fact half of the talk had to be about the very idea of a squeezing argument (as I discovered early on that almost no one had heard of Kreisel's paradigm example). Kreisel's star has perhaps rather fallen of late — and the Hintikka vol. in the Oxford Readings in Philosophy which reprinted his 'Informal rigour and completeness proofs' is long out of print and off...

Proving FLT

Colin McLarty has posted a preprint of a forthcoming BSL piece "What does it take to prove Fermat's Last Theorem?'. I don't pretend to understand everything here. But even if you don't get all the details, the paper still should give you a handle on the question of the role in Wiles's proof of  assumptions that go beyond ZFC. Impressive stuff.

Bell's The Axiom of Choice

A fun talk this afternoon in CMS from John Bell on "The Axiom of Choice in a Constructive Setting", delivered with really engaging zest: went home with renewed enthusiasm to read the rest of Bell's recent book which I started a few days ago (yes, yes, I should be concentrating on writing my book, but that's another story).

If you don't know it, The Axiom of Choice was published last year by College Publications (which is an admirable outfit, publishing some really good logic books at

More logic matters

David Marans has posted a slideshow "Logic Matters" which has a sequence of familiar and not-so-familiar quotations on logic (and thumbnail sketches of their originators).