Sunday, March 29, 2009

Cameleon report

Well, the Cameleon weekend is over. Something of a success, I think (though the main CMS building at the weekend is a rather bleak empty space, not very conducive to socializing between papers, and the catering-arrangements could have been better; these things matter -- don't they? -- to getting a really good feel to an occasion).

I talked about the incompleteness theorems. The exercise of trying to pack some headline news into three sessions was very useful (to me, at any rate) -- though I'm afraid that I became rather conscious of some inadequacies in my book in the process. Enough of the audience seemed gratifyingly surprised by simple observations that e.g. generic Gödel sentences (fixed points for ¬Prov) can be false, and that there are provable "consistency" sentences, to make it worthwhile going over some basics again. I wrote a 43 page handout, though I think I'd like to tidy it up just a bit before publishing here. So watch this space.

Thomas Forster talked about countable ordinals, and there's a rough-and-ready version of some notes here. I've heard him talk about these things before, but I like his way of thinking about ordinals, and I want to get clearer still about these things before getting back to writing about Gentzen.

John Truss presented some work on countably categorical structures, Fraissé theory, and the "classification of countable homogeneous multipartite graphs", all with enviable lucidity. I don't know enough -- or have the right interests -- to really understand why this might be interesting. I had a sense that denizens of a mathematical zoo were being pointed out and classified (giving, as it were, the natural history of part of the abstract realm). I guess my tastes run to more abstract theory.

For me, though, the high points of the weekend were Wifrid Hodges's talks on the history of logic. His question was: why did modern logic take so long to arrive? And his tour through various episodes from the history of logic, and his diagnosis of some causes for stagnancy from Aristotle to Leibniz, was absolutely fascinating. Do visit his website and look at some of the other historical pieces there too.


David Auerbach said...

you say:
", and that there are provable consistency sentences"

I think that should be:
and that there are provable so-called consistency sentences

Followed, of course, by an explanation of why, superficial appearances to contrary, they aren't really consistency sentences. (What with their not expressing consistency and all.)

Peter Smith said...

Well, indeed ... Let me add some scare quotes! It is fun to alert people to some of the minor subtleties here about what happens if you use "consistency minded" proof predicates.

David Auerbach said...

The intuition-feeding version I like to use yields:
The largest consistent subsystem of P is consistent.

(which is a) trivially provable in P and b) "says" that P is consistent.