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.
Another nice
problem from Brian Weatherson's weblog: Farrington is 50% confident
that it's after 4:30, and 50% confident that a certain coin
landed tails. Now he comes to know that iff the coin landed tails, some
researchers create a brain-in-a-vat duplicate of himself at exactly 4:30
today. What are the probabilities he should assign to the 5 open
possibilities:
This appears to be a problem for Lewis' theories of causation:
Let A,B,C,D be any events such that B depends counterfactually on A, and D
on C. Now consider the conjunction (fusion) B+C of B and C. If A had not
occurred, B+C would not have occurred. For then B would not have occurred,
and presumably B+C can't happen without B. And if B+C had not occurred, C
would not have occured either, so (unless the absence of B has some
surprising effects on D), D would not have occurred. Hence there is a
chain of counterfactual dependence between A and D. But since A,B,C,D were
arbitrary, this means that every cause causes every effect.