The fact that it turned out so difficult to explain my
question in sci.logic made me have a closer look at common axiomatic
systems of the kind I was critizising. This was a good idea, because I
found out that the systems used by Mendelson and Hodges are not of that
kind after all. The only such system is the one used by Kutschera and
Breitkopf, and as their logic book is German (and post-war), it is
not surprising that nobody understood my problem. It is however
interesting to compare the Kutschera/Breitkopf system with the systems of
Mendelson, Hodges and others:
Posting to newsgroups has some clear advantages over lonesome blogging.
Most notably, when I write something
incomprehensible in a newsgroup, somebody
will tell me that I do. Whereas here in this blog, nobody ever
complains even when I post absolutely unintelligible gibberish.
Maybe adding a comments section would help. But then I don't really have
a lot of readers. Maybe I should just add an "incomprehensible" button
under each entry, which when pressed would send me an email asking for
clarification.
Call for logicians: I have to convince Prof. Beckermann to drop an
incorrect rule of inference from the axiomatic system for predicate
logic used in his logic book. The incorrect rule is that from
A 
B
one may derive
A 
x B(t/x)
provided that t does not occur in A.
Christian has to write an introductory paper on Quine's "Two Dogmas". I
wouldn't like to do this. I think "Two Dogmas" is excessively overrated,
and should only be read in courses on the history of American philosophy.
Unfortunately, Christian seems to agree with most of my misgivings.
Maybe I find some opposition here.
"Two Dogmas" consists of three parts: §§1-4, §5 and §6. In §§1-4 Quine
argues that there is no distinction to be drawn between analytic and
synthetic statements. His argument appears to be as follows:
The world's first brain prothesis is interesting for several reasons:
Firstly, of course, it illustrates that when philosophers disagree about what would happen in a particular thought experiment, it is of very little help to carry out the experiment in reality: Will these rats become zombies?
Secondly, they are creating a hippocampus prosthesis. I guess they will also try what happens if that prosthesis is stimulated from the outside. There is a slight chance that this will have considerable effects on learning. I don't expect that we might one day learn just by stimulating the prosthesis. But we might learn much more easily by doing so.
In the metro I've just been reading a couple of pages from Luce Irigaray's Ethic de
la difference sexuelle. It was a fascinating experience because I
didn't understand a single sentence. I couldn't even find out what the
book is about, except that it has something to do with sex.
This reminded me of a puzzling phenomenon I've noticed for some time now:
The longer I study philosophy, the less I understand most
philosophers. I remember that when I read Kant's Kritik der reinen
Vernunft after leaving school, I thought I understood at least roughly
what is going on. A while ago, I had to look up his "refutation of
idealism" and felt completely lost.
In §27 of Meaning and Necessity, Carnap announces that all
mathematical concepts can be defined without the use of any class
expressions. The basic idea is to use Frege's system, but to replace all
occurrences of class variables with higher order variables. In particular,
the cardinal number of a property F is defined as the second order property
of being equinumerous to F (definition 27-4). "Thus, for example, '2' is a
predicator of second level" (p.117).
It appears that I'm allowed to make my thesis on Lewis available online. I've put it on a separate page where I might at some time add a couple of other papers I've written.
If anyone knows how to create PDF files that are readable on computer screens from PS files created by OzTeX, please let me know. I've already tried a) ps2pdf on Linux, 2) export as PDF from MacGSView, 3) Acrobat Distiller on Windows, each with all kinds of different settings. I always get files that look nice when printed, but crumbled on screen.
Apple was very quick shipping the (free) replacement adapter.
I've decided to bring order into my thoughts about Fregean thoughts by
writing a little paper. If all goes well, I'll hand it in as the termpaper
required for my MA. Since my last entry on this topic, I've found out that
there is a lively discussion among Frege scholars about the structure of
thoughts. Some, in particular Dummett, argue that Frege is, or should be,
committed to this view:
My notebook's AC adapter is broken, and I have to wait for Apple to ship a replacement. In the meantime don't expect much blogging or answering of emails.
I hope I won't be arrested by the time the adapter arrives: Today I received my tax assessment for 2001, and somewhat suprisingly it turns out I have to pay 40.000 Euros for that year in which I've earned about 3.000 Euros.