11 07 2006

The conference of the Australasian Association for Philosophy was just last week, and it was a lot of fun. The probability stream in particular I found quite interesting – there were some interesting pairings of talks, with both Rachael Briggs and Mike Titelbaum talking about updating on indexical beliefs and applying it to sleeping beauty; Matt Weiner and me talking about infinitary decision theory and versions of the two-envelope paradox; and Jonathan Shaffer and Antony Eagle talking about the (in)compatibility of non-extreme chances with determinism.

There were a couple other talks I found quite interesting as well. Brendan Jackson and Sam Cumming gave interesting talks on formal semantics (Brendan on analyticity coming from semantic structure alone, and Sam on discourse-referent-based approaches to Frege’s puzzle). And Peter Forrest posed a problem for general relativity in that its ontology calls for space-time to be a differentiable manifold, which requires not only a set of points and a designated colleciton of “open” sets, but also a collection of functions mapping these sets to real numbers in order to give the differential structure of things. He pointed out that it’s quite unclear in what sense these functions have any physical reality, and proposed some ways to minimize this ontology, some of which seemed to have consequences for views on time.

Finally, Zach Weber (a student at Melbourne) gave a very interesting talk presenting some of his results using naive Fregean set theory, in a relevant logic to avoid triviality. He’s been able to prove, fairly simply, the existence of inaccessible cardinals, the axiom of choice, and many other interesting results that one wouldn’t necessarily expect to get so easily. Whatever one’s thoughts on paraconsistent logics, I think there’s probably interesting stuff here to motivate some sort of principle to transfer some of these results to classical set theory, if possible.

Anyway, in addition to all these talks, the conference was quite a nice environment to talk to people from all over Australia (and the US, and other places) about various philosophical topics, and was a nice way to spend my last week in the country. Immediately afterwards, I left for the US, and I’m now teaching at the Canada/USA Mathcamp until early August, before returning to Berkeley. So I might not have as much time for posting in the next month. But it’ll probably be more mathematically oriented than a lot of what I’ve been posting recently.




One response

13 07 2006

Alan Weir’s been working for a while on setting naive set theory within paraconsistent logics. But he told me sometime last year he thought he’d figured out a way to do everything consistently in a stronger, non-paraconsistent logic. I don’t know the details, but it’ll be interesting to see how strong the background logic is, and how it compares to, say, relavant logics for philosophical appeal.

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