Wolfgang Schwarz

Victory

On a more positive note, Prof. Beckermann found my speculations convincing: The next edition of his logic book won't contain "incorrect" quantifier rules any more.

War

I can't count how often I wished to live in that very close possible world in which Al Gore won the presidency (very close in terms of Lewis' similarity standards for counterfactuals, not in terms of overall similarity, sadly).

What worries me most is how many US Americans seem to back the Bush administration. I mean, when Clinton, like so many other people, had an extramarital affair and lied about it, that was a big scandal and caused an impeachment process. When Bush, quite unlike most people, violates the UN charta by going to war against a country that doesn't threaten the US at all, and keeps lying about his alleged knowledge of Iraq's weapons of mass destruction and links with Al Quaeda, Americans just seem to buy it. Then again, they are renaming French fries. There goes my princple of charity... For now, I blame it all on the absence of a free press in the US, but I'm not sure if that's a sufficient reason. I also tried to read blogs of the war-mongers, but that didn't help much, it just left me very depressed for the rest of the day. It's like shopping at Kottbusser Tor.

Oh well, I should better be blogging about quantifier rules in axiomatic systems of predicate logic.

Speculations on the Origin of "Incorrect" Quantifier Rules

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:

On Being Incomprehensible

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.

Why use incorrect rules of inference?

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.

Bashing "Two Dogmas"

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:

Brain Prostheses

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.

Unexpected Side-Effect

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.

Carnap's Higher Order Numbers

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).

Words and PDFs

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.