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Solutions

Back to life. Here is the solution to the Christmas puzzles:

1. The king said that one day somebody will find a sound proof that he hasn't always said the truth. Now either this is true or it isn't. If it isn't, the king hasn't always said the truth. If it is, somebody will find such a proof, and since the conlusion of any sound proof is true, again the king hasn't always said the truth. So in any case, the king hasn't always said the truth.

2. The king had uttered only two sentences. By the above argument we know that one of them must be false. But we also know that the first one was true: Somebody really found the requested argument. So the second sentence must have been the false one. It said that the person who finds the argument will get the kingdom. Hence it was logically impossible to give the kingdom to the court jester.

A Christmas Puzzle

I'm too sick to blog. In the meantime, here is a puzzle I've made up for the second edition of Ansgar Beckermann's Einführung in die Logik. In fact, it's two puzzles.

Once upon a time an old and reticent king made the following announcement: "One day somebody will find a deductively sound argument proving that I haven't always said the truth. To this person I will bequeath my kindom." It was the court jester who first presented such an argument. How did the argument go?

Soon afterwards, the king died, and it came to be known that the above announcement was in fact the only sentences the king had spoken in his entire life. Thereafter, the court jester was refused the kingdom -- for logical reasons. Why?

On the contingency of perdurantism

Several people have claimed that perdurantism is only contingently true, or at least a posteriori: Mark Johnston expresses something like this at the end of "Is There a Problem about Persistence?"; Sally Haslanger in "Humean Supervenience and Enduring Things"; Frank Jackson in section 2 of "Metaphysics by Possible Cases"; and David Lewis in section 1 of "Humean Supervenience Debugged".

One of the arguments for this claim seems to be that both perdurantism and endurantism are to some degree intelligible, which is why philosophers still disagree about the issue. I find that strange. Philosophers also disagree about the existence of universals, arbitrary mereological fusions, possible worlds, and numbers. Are these also contingent matters?

Fred is a woman

Apropos colour, a fact not very well known among philosophers is that some women have not three but four kinds of cones. More interestingly, it seems that these women also have colour discriminating abilities that go beyond those of the rest of us. It's not yet proven whether they have different phenomenal experiences though.

Update 04.01.03: A somewhat better link.

Reduction is not a decision procedure

There are some arguments against the reducibility of tensed propositions to tenseless propositions about times and things at times. But I've never seen the following argument:

The reductionist claims that there are other times and that things have all kinds of properties at those times. Clearly, it would be circular to say that there are exactly those times that once existed or will exist, and that x has F at some past time iff x once was F. The reductionist must not use tensed statements in specifying exactly what times there are and what things instantiate which properties at those times. But it seems hopeless to find a completely tenseless, general, and yet accurate rule.

This is silly, because a reduction is not the same things as a decision procedure. Of course, if you reduce A-facts to B-facts, complete knowledge of B-facts must in principle suffice to deduce all A-facts. But specifying all the B-facts is in no way part of the reduction.

Isn't it puzzling that this silly kind of argument keeps being brought forward against Lewis' reduction of modal facts to facts about possibilia (e.g. in Lycan, "Two -- no, three -- concepts of possible worlds", Proceedings of the Aristotelian Society (91): 1991; Divers and Melia, "The analytic limit of genuine modal realism", Mind (111): 2002)?

Is modal realism innate?

It seems to be: I've never heard of anyone being converted to modal realism, or giving it up. In particular, Lewis himself endorses it in his earliest papers, e.g. in the conclusion of 'Convention'. According to this article from the Daily Princetonian, he "worked on" the topic already at the age of 16. Strange.

Is the empty set false?

In "Two Concepts of Modality", Alvin Plantinga argues that propositions aren't sets of worlds, because "you can't believe a set, and a set can't be either true or false" [208]. I think this argument is better than it might appear in the rather Ungerian context of Plantinga's paper, where he uses several arguments of the same kind to support completely crazy views, like that Lewis is an antirealist about possible worlds.

The traditional job description for propositions says that they are a) the ultimate bearers of truth-values, b) the content/object of propositional attitudes, and c) the meanings of declarative sentences. Plantinga is right that sets aren't the most intuitive candidates for this job: Is the empty set an 'ultimate bearer' of the truth-value false? Is it the content of Frege's belief in Axiom 5? Is it what you have to know in order to understand Axiom 5? Well, intuitively not, but I don't think intuition is to judge questions like these. More importantly, there are reasons against the identification of sets with propositions.

Counterfactual confusion

I'm currently writing a chapter on modal realism. I don't like this topic because it always confuses me. Here is one such confusion.

In some world w, pretty much resembling our world, there are two individuals A and B. Let 'A-in-w' be an extremely rich descriptions of A that implies every qualitative truth about w, similarly for 'B-in-w' and B. Now the following two sentences might both be true:

1) If I were A-in-w, I would do X.

2) If I were B-in-w, I wouldn't do X.

Diffbot

I often visited blogs and other websites just to see that nothing has changed there. No more. To save these wasted minutes I've wasted some hours on writing a little script that keeps track of the latest updates of all those websites and displays them using diff.

Lewis on worms and stages

It is easy to overlook that David Lewis has revised his worm view of ordinary things in 'Tensing the Copula', Mind 111 (2002). Here is the passage (p.5):

In talking about what is true at a certain time, we can, and we very often do, restrict our domain of discourse so as to ignore everything located elsewhere in time. Restricted the domain in this way, your temporal part at t_1 is deemed to be the whole of you. So there is a good sense in which you do, after all, have *bent simpliciter*.

In other words: Terms for ordinary things are indeterminate. They don't always pick out worms. Sometimes they pick out segments, and sometimes just stages, depending on the contextually determined domain of discourse.

I think this is an improvement over the worm theory. Is it general enough? Lewis says that our terms pick out the sum of all those temporal parts of the relevant worm that are inside the domain of discourse. But don't we also attribute bent-simpliciter to the whole of me in "I'm bent now, but I wasn't bent yesterday"? Yet here the domain contains yesterday's parts as well.

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