Things are counterparts iff they are sufficiently similar to each other.
They needn't be similar intrinsically: For example, in "Individuation by
Acquaintance and by Stipulation" (§2), Lewis allows for counterparts that
are similar in standing in a particular relation of acquaintance to some
person. In fact, they needn't be similar at all: In On the Plurality of
Worlds (§4.4), Lewis accepts that, speaking unrestrictedly, everything
is an individual possibility for anything. However, in "Things qua
Truthmakers" (§5), he denies that things could be counterparts by living in
a world in which there are no unicorns. I wonder why. Lewis says that
such a respect of similarity would be too extrinsic and strike us as too
unimportant. But other eligible respects are extrinsic too, and what
strikes us as important certainly depends on the relevant context. I can
imagine theists who believe that there is a big difference between
living in a world where there is a God and living a duplicate life in a
Godless world. So in some special contexts, those of our counterparts who
live in Godless worlds might be excluded as being too different. Conversely, an atheist might exclude counterparts that live in worlds with Gods a being too different.
Well, what do I mean by "extended"? If "extended" means
"having parts", nobody thinks that extended things lack parts. I guess
what I mean is "existing at several different (space-, time- or spacetime-)
coordinates". For instance, I find it hard to understand how something
could cover all of Berlin without having any part that covers Kreuzberg. I
see that this is precisely how immanent universals are supposed to exist,
but that doesn't help me much, because I find it equally puzzling here.
Perhaps I was wrong when I said that those who
claim that perdurantism is contingent think that things could undergo
intrinsic change without having temporal parts. I've just reread
Haslanger's and Lewis' remarks, and these appear to be compatible
with the view that only things that don't change might endure. For
example, Lewis only mentions the possibility that the spatial parts of a
spinning sphere might persist by enduring. And maybe those parts don't
ever change their intrinsic properties. Probably even the entire sphere
doesn't, because if you copy a particular sphere stage and rotate the copy
by 180 degrees, you still have an exact intrinsic duplicate of the original
stage. This would explain why Lewis doesn't announce a big change of view,
because he always accepted that some special entities, namely universals,
might endure.
My only complaint then is that this doesn't turn perdurantism into a contingent theory of intrinsic change (rather than persistance). And I still find it difficult to understand how extended things could lack parts.
I am not an expert on modal fictionalism, so probably something is obviously wrong with the following objection. But anyway, here it is.
Modal fictionalism claims that any statement S about possible worlds (and other possibilia) is to be analysed as "According to the possible-world-story, S". Now possible worlds are used in reductive analyses of all kinds of concepts: modality, counterfactuals, causation, laws, properties, propositions, meanings, probabilities, supervenience, fictions, etc. For instance, an analysis of indexicals usually talks about extensions in possible contexts of utterance. If fictionalism is right, then this analysis must in turn be analysed in terms of extension in possible contexts according to the possible-worlds-story. And this seems rather odd. Suppose I propose some theory T of indexicals (or laws or whatever). If fictionalism is right then T is correct iff it is implied by some story about possible worlds. Firstly, intuitively this is not at all what I would have thought my theory was about. Secondly, which possible-world-story is relevant here? If we take the five or six claims about recombination and other worlds being of the same kind as ours usually presented by fictionalists (e.g. Rosen 1990), all the analytic projects mentioned above appear to be doomed: That simple story will not imply anything at all about indexicals, or laws, or causation. Unless of course we extend it by some analysis of these notions. Which analysis? The obvious candidate is the analysis we believe to be true, that is, T. But then all the analytic projects mentioned above come out as trivially true: Even the craziest theory will be good enough to imply itself.
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)?