When I prepared my talk at Heidelberg, I noticed some errors and oddities in the paper I had written. There were also a few interesting points raised in the discussion which I wanted to address. So in Switzerland, I almost completely rewrote the paper. Here is the new version: "Emperors, dragons and other mathematicalia".
[Update 2004-12-31: I've corrected another mistake: condition (1) on singleton relations should say that they are injective functions, not just that they are functions.]
I'm back. The conference was good; and Switzerland was quiet, white and beautiful.
The mountain whose rather flat slope you can see in the foreground is called "Um Su". It is a mountain without a summit.
I'm on my way to the German-Italian philosophy conference in Heidelberg. After that, I'll spend some days in the Alps. I won't have internet access there. (Also, my computer didn't want to boot this morning. Hopefully it was just too cold.)
I've made the script driving the Lewis tracker available for download here. (I have a couple of further ideas and even half-finished pages for david-lewis.org, but they currently suffer from a lack of time and money. Suggestions about useful content are of course welcome.)
I keep wavering between two different uses of "analytical". This entry is meant to remind me of the difference and of why I should prefer the one over the other.
On the first use, a sentence is analytical if it has a universal A-intension. On the second, a sentence is analytical if one can't understand it unless one believes it (this is what I, unoriginally, proposed last year). The first is the better explication.
It consumes energy and emits electromagnetic radiation. It contains a small wire filament. It is widely used all over the world. It was invented by Heinrich Göbel in 1854, though Americans often attribute its invention to Thomas Edison. What is it?
The electrical light bulb, of course.
But hold on. Is there really something that satisfies these conditions? What kind of thing would this be? It can't be any particular light bulb, say, the one in my bathroom. For this light bulb is used only in my bathroom, not all over the world, and most Americans don't even know that it exists. Nor can it be any other particular material thing. Nor can it be a mental object, something like the idea of a light bulb: ideas don't contain small wire filaments. This alleged thing, the light bulb, is a very strange kind of object. It is not a light bulb (all light bulbs are concrete, particular light bulbs), but like all light bulbs it contains a wire filament, consumes energy and emits electromagnetic radiation. It is is located in time (as it didn't exist before 1854), but presumably not at any particular location in space.
I've been assigned some boring administrative work, but that's finished now, I hope. Here are some rough thoughts on indifference and Adam Elga's Dr. Evil paper (PDF).
There are many possible individuals whose mental state is subjectively indistinguishable from my current mental state insofar as they all share my current phenomenal experiences and my (real or quasi-) memories. Some of them inhabit worlds that are exactly as I believe the actual world is, and are located in that world exactly where I believe I am located in the actual world. Others occupy very different places in very different worlds: they are brains in vats or inhabitants of gruesome counterinductive worlds. How should I distribute my credence among all these possibilities?
Oops, last night I exceeded my webspace quota. Apologies for the failures and error messages that this caused all over the place. Please let me know if something is still not working.
Trying (for some reason) to keep myself busy in the evenings, I've started creating music again. So here, for a change, is a song: "Wie Mohn und Gedächtnis" (Ogg Vorbis format, 5.1 MB).
(In case anyone is interested, the song was created in the excellent Cheesetracker, recorded with Ardour, via Jack, and slightly edited with Audacity. All Free and free.)
I've been invited to this year's German-Italian Colloquium in Analytic Philosophy, for which I've put together some remarks on the philosophy of mathematics: "Emperors, dragons and other
mathematicalia" (PDF). I mainly argue that mathematical sentences should be interpreted as quantifications over possibilia. Technically, this isn't really new. Daniel Nolan in particular has made a very similar suggestion (PDF). What hasn't been emphasized enough, I believe, is that this interpretation not only works from a technical point of view, but is quite attractive for various philosophical reasons. (Unlike Nolan, I argue that it isn't a reform, but a faithful interpretation of mathematics.)