Strolling through the library, I just came across George Tourlakis' Lectures in Logic and Set
Theory. I wouldn't recommend it as a textbook for logic courses in
philosophy, unless you want to torture your students with a full
proof of Gödel's Second Incompleteness Theorem. But it's nice to have
that proof available somewhere. The second volume on set
theory (unfortunately only on ZFC) also looks useful, if only because there
are so few thoroughgoing introductions to set theory.
Now I'm in a friend's flat, where a lot of books and a TV set have
consipred to distract me. Yesterday I've read Szpilman's "The Pianist" and
watched "The Matrix". I found the latter rather silly and unoriginal, but
maybe I've entirely missed the point. I'll try to find out what's supposed
to be the point as soon as I get a chance to access the net without
increasing other people's telephone bill.
The Frege paper is
finished, by the way. And yes, it's in German.
I've just moved out of my flat. Next I have to find a flat to move into.
This time I've even managed to throw away most of the notes and copies of
papers I used to carry with me each time I moved. I've also thrown away
some other stuff, like two of my three pairs of trousers, so I feel like
quickly approaching my dream lifestyle.
In the meantime, the new semester has begun. I'll probably visit just one
seminar, which is supposed to be about classical logic, though I'm not sure if
e.g. Dov Gabbay's fibring
logics should really be called "classical". Well, maybe I've missed the new era while reading Frege.
If nothing goes terribly wrong, I will finish the Frege paper tomorrow. Though I'm not sure if it's really the same Frege paper I mentioned previously.
Initially I just wanted to put together all the comments on
Fregean thoughts and Rieger's paradox that I had already posted to this
weblog. That looked like a cheap way to get a termpaper. For some reason
however the paper has now evolved into a discussion about the prospects and
dangers of developing a semantics that can be applied to its own
metalanguage.
I'm still working on the Frege paper. Obviously, so far this weblog hasn't cured my perfectionism, which I hoped it would.
Apropos perfectionism: That new (and not very informative) entry on Turing Machines in the Stanford Encyclopedia reminds me of a Turing Machine simlulation I've worked on back in 2000. Here is the rather unusable latest version of that attempt. I've stopped working on it mainly because I wanted the page to automatically draw a flow chart for any machine table that is specified. But I couldn't find an algorithm that prevents overlapping arrows wherever it is possible. (Here is an example of the latest, somewhat funny looking version.)
Magdalena told me that Jay Wallace will offer a seminar next semester here in Berlin. In this respect I fully support the "love it or leave it" messages from the American right, as long as they bring good philosophers to Old Europe...
Battleground God says that there are three contradictions in my views about God. Of course I don't believe my views are contradictory. Here are the alleged contradictions:
First, I accepted both of the following as true:
4. Any being which it is right to call God must want there to be as little suffering in the word as is possible.
12. If God exists she could make it so that everything now considered sinful becomes morally acceptable and everything that is now considered morally good becomes sinful.
Is this a contradiction? I'm not quite sure whether (12) is an indicative or a subjunctive conditional, but I think if it was subjunctive it would have to go "If God existed ..." or "If God would exist ...". So I think it's meant to be indicative (in the sense of "If God exists, then it is the case that: She could ..."). Like most people, I find it difficult to evaluate indicative conditionals with false antecedents, but at least for today I felt like embracing the Grice-Jackson-Lewis view that they are true. The website complained that I "say that God could make it so that everything now considered sinful becomes morally acceptable". But that's not what I said!
I've fixed a couple of (five, to be precise) problems in Postbote.
On Friday, I wrote:
Conclusion 2: If we want to avoid Bradley's regress, there is
no reasonable way to defend the principle that every meaningful expression
of our language has a semantic value. (Russell's paradox is an independent
argument for the same conclusion.)
Today, I was trying to prove the statement in brackets. This is more
difficult than I had thought.
Semantic paradoxes usually (always?) arise out of an unrestricted
application of schemas like
Friends who know English better than I often tell me that when I write English, my sentences get too long and complicated. So I noticed with considerable relief this resolution from the University at Buffalo on open source software.
Frege believes that predicate expressions have semantic values (Sinne and
Bedeutungen) which can't be denoted by singular terms. Hence "the
Bedeutung of 'is a horse'" does not denote the Bedeutung of 'is a horse'.
Before the discovery of Russell's paradox, the only reason he ever gave for
this view -- apart from claiming that it is a fundamental logical fact that
just has to be accepted -- is that otherwise the semantic values of a
sentence's constituents wouldn't "stick together". The more I think about
this reason, the less convincing I find it.