Wolfgang Schwarz

Non-Standard Escape Routes

I've been busy working on the logic book, playing with music software, meeting friends, lazing around, looking after Magdalena (who was ill again), protesting against the war, and thinking that it was a good idea to have voted for Livingstone (as I did when I lived in London). I hope to get back to philosophy soon.

Teaching Predicate Logic

I'm thinking about how to introduce the semantics of predicate logic to beginning philosophy students. In particular, I'm interested in the interpretation of predicates and quantifiers. Last year in logic class, it seemed that most students were rather unhappy with the formal recursion on truth we were teaching them.

So I've just picked 15 random logic textbooks to see how they are doing it.

Group 1 (functions and sets): Interpretations are introduced as entities that assign to each n-ary predicate symbol a class of n-tuples of elements of the domain. (Machover, Beckermann, Bostock, Newton-Smith, Mendelson, Kutschera, Allen/Hand, Bühler)

Creation by Definition

Hereby I stipulate that "fb13" is to denote the first human born in the 13th century. Hence it might seems that "fb13 was born in the 13th century" is analytically true, true by definition. But if analytic truths are closed under logical implication, "somebody was born in the 13th century" would also be analytically true. Which it is not.

I don't think tinkering with closure under logical implication will help. Hereby I stipulate that "fb23" is to denote the first human born in the 23rd century. However, if recent progress in civilization continues, there might well be no humans in the 23rd century. And if no humans are born in the 23rd century, "fb23 is a human born in the 23rd century" is false. So it cannot be true by definition.

Even More Thoughts about Thoughts

In my last posting, I argued that to escape the cardinality problem for thoughts Frege perhaps has to give up

1) For any things there is at least one concept under which all and only those things fall.

Now (1) is clearly false if, as I think, all there is are objects -- that is, if it makes sense to quantify over absolutely everything. But if not, as Frege thinks, denying (1) is not an option. A concept is a function from things to truth values. Given that functions are not themselves things, how could there fail to be such functions?

Too Many Thoughts

A while ago, I was discussing Adam Rieger's alleged paradox in Frege's ontology (here, here, and here). I'm still confident that the Russellian version of the paradox can be blocked. But on second thought, the cardinality version of the paradox appears to be much more difficult. Here it is again.

1) For any things there is at least one concept under which all and only those things fall.

2) For each of these concepts, there exists the thought that Ben Lomond falls under it.

3) All these thoughts are different.

4) All thoughts are objects.

From (1)-(3) it follows that there are more thoughts than objects (2^k if k is the number of objects), contradicting (4).

Silly Question

Ulrich Blau is professor of logic in Munich. For the last 30 years or so he's been working on an enormous book in which he solves all known and several unknown problems in logic, foundations of mathematics, and philosophy in general. If you ever come across that book (it's not published yet), I'd strongly recommend you just skip the non-technical introduction (and conclusion). It's really getting much better where the formulas begin. Anyway, in the introductory chapter I found a silly question that I once discovered myself when I still went to school:

Does this question have an answer?

(In Blau's version, it goes "Can you answer the question you are now reading either affirmatively or negatively?")

A Quine

When I take a break from philosophy I often find myself creating utterly useless computer programs. Today, for example, I've spent some hours on Quines. A Quine is a program that outputs its own source code. (Quines are so called because Quine, in "The Ways of Paradox" if I recall correctly, introduced the self-denoting expression "'appended to its own quotation' appended to its own quotation".) Making Quines is a lot of fun, and also a good training to avoid use/mention mistakes. I've just written several JavaScript Quines. Here is a particularly neat one (try it!):

Done.

I've finished my thesis on Lewis' metaphysics. I'll make it available online as soon as I've found out that I'm allowed to do so. (Only "unpublished books" are accepted at the contest, and I don't know if online publication counts as publication.) Anyway, it's German, and doesn't contain many new ideas, especially if you've been reading my blog for the last couple of months.

Next, I have to find out how to register the thesis at my university. Then I will officially be given 4 months to finish it. I also have to find out if it's okay to hand in the finished thesis before registering.

Choosing the best of all possible worlds

I've been thinking about yesterday's problem from Brian Weatherson's interactive philosophy blog. Instead of a solution I've found a name: "Forrest's Paradox" (see §2.5 in Lewis, On the Plurality of Worlds).

Knowing the name, it is now easy to create even stranger problems of the same kind. First a reformulation of the original problem.

Deadline

I'm trying to finish my thesis before February 1st. So this David Lewis blog might eventually become a more general philosophy blog again soon. For the remainder of this month, I probably won't be blogging very much.

By the way, I made a fool of myself by asking physicists about whether elementary particles are extended. As expected, the answer is that the question doesn't make sense in quantum mechanics.