I'm in Bielefeld at the GAP5 conference. The overall quality of the talks so far hasn't been very good, but I'm told it's always like that at philosophy conferences.
One of the most tedious presentations was Manfred Kupffer's discussion of arguments for the claim that we don't know a priori whether Hesperus is Phosphorus. In contrast, it was much more enjoyable to listen to Karl-Georg Niebergall who suggested that all of mathematics is in fact about certain concrete lines (straight ones, triangles, rectangles, and circles, to be precise) infinitely many of which exist somewhere in our universe. The lesson is that arguing for an obvious truth is generally much worse than arguing for something absurd. (I asked Kupffer whether anybody ever denied what he is arguing for, and he said Scott Soames did. If that's true then Soames has learned that lesson.)
Another note on FOL75: In his talk, Wilfried Hodges argued that the logician's conception of logical consequence differs a lot from the ordinary conception. One of his points was that not all valid arguments are valid in any of our technical senses because the latter don't account for conceptual implication. That's of course true. But Hodges also claimed that consultation of Google shows that the ordinary conception of logical consequence is even further away from what most logicians think. For if one excludes results from sites about philosophy and logic the top results (e.g. 1, 2, 3, 4, 5) all look like this (from 5):
The second edition of Ansgar Beckermann's Einführung in die Logik has just been published. Here are my solutions to all the exercises. I hope there aren't too many errors left (both in the book and in the solutions). If you spot one, please let me know.
To my relief, there have been a few more advanced talks later at the FOL75 conference of which I understood very little. Here I just want to link to a new Gentzen-like deductive system that was presented at the conference by Kai Brünnler and the research on relativity theory several people currently work on in Budapest.
I'll be moving house tonight. In the new flat I don't have telephone/internet connection yet, so I might neither blog nor read emails for until I return from Bielefeld on Friday next week.
Things went not at all according to plan.
The biggest shock was that all presentations so far were fairly easy. Even Dan Willard's discussion of interesting theories in which interesting variants of Gödel's Second Incompleteness Theorem don't hold was easy for me to follow. I had expected the presentations to be like readings from a JSL volume.
The other surpising thing I noticed was how little most attendants know of what the others are doing. For example, when Hintikka talked about (surprise, surprise) the superiority of IF logic, the participants in the discussion seemed to know very little about it. (In this particular case that might be because those who know more about IF, like Hodges, have already given up arguing with Hintikka long ago.)
In the next 10 days I'll be attending two philosophy conferences. The first, starting tomorrow and ending on Sunday, is the FOL75 logic conference here in Berlin. My plan for this is to sit quitely and nod or frown from time to time so that it doesn't show too much that I don't understand a word of what the speakers say. I'll also look at how some other people behave of whom I know that they also won't understand much. I guess for me this conference will be more like a field study in academic sociology.
The other conference, Monday through Friday next week, is the GAP5 conference at Bielefeld. I haven't really made up my mind on what I'll be doing there, but I hope to do some philosophy. If all goes wrong, I can still spend some time at the excellent library of Bielefeld university, catching up on the literature I'm missing in Berlin.
Lewis does not want to take the worldmate relation (that holds between two things iff they belong to the same world) as primitive. He proposes two alternatives. The first is that things belong to the same world iff they stand in ("analogously") spatiotemporal relations to each other. According to the second, more general, proposal things belong to the same world iff they stand in fundamental external relations to each other, whether or not these relatios are (analogously) spatiotemporal. I'm not sure if I fully understand the difference between these three alternatives. Here is why.
I think this only works with simple sentences containing short and familiar words. To test this, I wrote a little bookmarklet: scramble! If you bookmark this link (by using the context menu) and open it on any webpage, it will scramble the words on it. (If you click it, it will scramble the words on this page.) It should work in all browsers that support the W3C DOM, but I've only tested it in Mozilla.
[Update 2003-09-23]: I've updated the bookmarklet so that it doesn't count punctuation marks as parts of words any more.
[Another update 2003-09-23]: Sorry, there was a typo in the previous code.
Re dense worlds, Dave Chalmers asks in what sense worlds that differ only in which intrinsic properties play which roles are indistinguishable. That's a very good question, and I'm afraid I don't have a good answer. He notes that those worlds differ in lots of respects, including their laws and quite probably the perceptions of their inhabitants.
What I want to say is that the worlds are somehow 'structurally alike', or 'isomorphic'. But that's hard to cash out. Is every Ramsey sentence that is true of one of them also true of the others? Then I would first have to restrict the 'old' terms of the Ramsey sentence. But that's a minor problem. What's worse is that this doesn't take care of more complicated rearrangements, where different parts of roles are played by different properties. Here the quantifiers of the Ramsey sentence would have to range over very gerrymandered (though intrinsic) properties. And given that gerrymandered properties are generally supposed to be causally inefficacious this is dubious. And finally, even if the Ramsey sentence account would work, I would still have to say why worlds that cannot be distinguished by Ramsey-sentences (or are otherwise 'structurally alike') are in any reasonable sense indistinguishable.