The principle of recombination states what other possible worlds there must
be, given the existence of some possible worlds. In sec. 1.8 of On the
Plurality of Worlds, David Lewis suggests something like this:
L) For any parts of any worlds there is some world containing
any number of duplicates of all those parts, and nothing else , provided that they all fit
into a possible space-time.
Daniel Nolan argues in "Recombination Unbound" that the clause 'and
nothing else' should be dropped, because if some thing B consists of two
duplicates of A, there couldn't be a world containing one B, one A, and
nothing else. Unfortunately, without the clause the principle doesn't
exclude the necessary coexistence of distinct possibilia. In fact, it is
even compatible with all possibilia having duplicates in all worlds. I
think it would be better to leave the clause and instead restrict the
principle to distinct parts of worlds.
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.
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?
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?
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.
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)?
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.
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.
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.
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.