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Do Escher's "impossible pictures" really show impossible situations? Andrew Lipson and Daniel Shiu have built Lego models of the waterfall, the infinitely ascending stairs, and the Relativity picture. And Sugihara Kokichi made some more impossible objects out of paper. (Via der Schockwellenreiter and the Cartoonist).
At first, I thought teaching students an informal semantics for predicate logic was only a compromise we had to choose because the real thing, formal model theory, is just too difficult for beginners. But now I'm inclined to believe that the informal semantics is itself the real thing. Maybe for those of us who have no quarrals with set theory, the difference is only superficial since both accounts assign the same truth conditions to all sentences, and truth conditions are all that matters. But that's not quite true. For example, when we talk about all sets (or all classes, or all things whatsoever), standard model theory is in trouble. I think it's silly to conclude that we can't really talk about all sets or classes or things. We obviously can do so in English, and we can also do so in (interpreted) first-order logic.
I've already mentioned that I moved into a new flat recently. This in itself isn't very remarkable as I'm used to moving house every couple of months. What's remarkable is that this time I've actually rented the flat. I still don't really know why I did that. It's a nice flat in Prenzlauer Berg (near Helmholtzplatz) with two rooms, a balkony, and Ofenheizung, but it's far too big for me and my two bags of personal belongings. So if you're visiting Berlin and need a cheap place to stay, drop me a line.
I've been running MacOS 8.6 for more than a year now. Since many programs I like aren't available on MacOS Classic at all (like any reasonable web server), or aren't updated any more (like Mozilla), I finally decided to make the switch, and I switched to Debian Linux. I've never used Debian before and I've never used Linux on a Mac, so I'm not sure what to blame. At any rate, I found the installation rather painful. It took me several days to set up the basic system with a working X server and a working dial-up connection. Then, last week, I tried to install a different kernel in order to get my ethernet card to work. The result is that now the system completely ignores my keyboard. Since I can't even login without the keyboard I don't know what to do next. Maybe I'll read some philosophy.
Luckily, I've put the new system on a new (well, second-hand) hard disk, so for now I'm back to MacOS 8.6.
Suppose we are relativists about moral judgements. That is, we believe that, for example,
"One should not engage in premarital sex"
may be truely asserted by somebody iff according to his moral code (or the moral code of his community, or something like that) one should not engage in premarital sex. The important part here is of course "truely". Noone denies that if you believe that one should not engage in premarital sex then if asked about it, you should say so. That's not relativism. Relativism as I understand it holds that what you said then would be true.
The GAP conference is over. There have been a couple of nice symposia on the a priori: George Bealer and David Papineau discussed the significance of a priori reasoning in philosophy, and Frank Jackson and Brian McLaughlin talked about a priori physicalism. I would like to comment on this, and also on some talks I heard about relativism and contextualism, but at the moment I'm a bit tired of philosophy, and my arms also aren't well. So I decided to do something useful for a change and went to Munich to save the rainforests. I'll be back in Berlin on Monday.
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.
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