Lewis does not want to take the worldmate relation (that holds between two things iff they belong to the same world) as primitive. He proposes two alternatives. The first is that things belong to the same world iff they stand in ("analogously") spatiotemporal relations to each other. According to the second, more general, proposal things belong to the same world iff they stand in fundamental external relations to each other, whether or not these relatios are (analogously) spatiotemporal. I'm not sure if I fully understand the difference between these three alternatives. Here is why.
I think this only works with simple sentences containing short and familiar words. To test this, I wrote a little bookmarklet: scramble! If you bookmark this link (by using the context menu) and open it on any webpage, it will scramble the words on it. (If you click it, it will scramble the words on this page.) It should work in all browsers that support the W3C DOM, but I've only tested it in Mozilla.
[Update 2003-09-23]: I've updated the bookmarklet so that it doesn't count punctuation marks as parts of words any more.
[Another update 2003-09-23]: Sorry, there was a typo in the previous code.
Re dense worlds, Dave Chalmers asks in what sense worlds that differ only in which intrinsic properties play which roles are indistinguishable. That's a very good question, and I'm afraid I don't have a good answer. He notes that those worlds differ in lots of respects, including their laws and quite probably the perceptions of their inhabitants.
What I want to say is that the worlds are somehow 'structurally alike', or 'isomorphic'. But that's hard to cash out. Is every Ramsey sentence that is true of one of them also true of the others? Then I would first have to restrict the 'old' terms of the Ramsey sentence. But that's a minor problem. What's worse is that this doesn't take care of more complicated rearrangements, where different parts of roles are played by different properties. Here the quantifiers of the Ramsey sentence would have to range over very gerrymandered (though intrinsic) properties. And given that gerrymandered properties are generally supposed to be causally inefficacious this is dubious. And finally, even if the Ramsey sentence account would work, I would still have to say why worlds that cannot be distinguished by Ramsey-sentences (or are otherwise 'structurally alike') are in any reasonable sense indistinguishable.
Yesterday I said that Lewis might just shrug off arguments about other-wordly people who, despite being in the same evidential situation as we are and despite using the same kind of reasoning, get the laws of nature and the reference of their terms completely wrong: He could agree that such people are just as possible as similarly deluded people in counter-inductive worlds or even more deluded brains in vats.
But Lewis himself uses an argument of the same form against the non-indexical account of actuality (Pluarlity, p.93):
My attempts to get a copy of 'Ramseyan Humility' were unsuccessful, so I searched the web in the hope that somewhere somebody might have said something about what Lewis says in that paper. This is how I came across Paul Mainwood's BPhil Thesis Properties, Permutations and Physics (PDF). It's a very good thesis and contains (in section 4) an extended discussion of some of the problems I'm struggling with.
I'm confused. It seems to me that the Dense Worlds Argument refutes Lewis' Humean Supervenience thesis: Not all facts about worlds without alien properties are determined by the distribution of fundamental properties over space-time points. But that's not what really worries me.
What worries me is that I don't know what to blame. I don't see any move that doesn't lead into further difficulties. Consider blaming HS. If HS is false, then our world either contains extended things (as opposed to points) that instantiate fundamental properties, or it contains things that stand to each other in fundamental but not spatio-temporal relations. Let's focus on the second possibility. It is certainly conceivable that fundamental properties are instantiated by extended things. But does this help? Suppose all fundamental properties are instantiated by cubes with a volume of 1 nm^3 (or stages of such cubes with volume 1 ns*nm^3). Then the same kind of shuffling as in the dense worlds argument still shows that the interesting facts about our world are independent of the distribution of fundamental properties. But this time HS is not among the assumptoins, so we can't use the argument as a reductio against it.
This is a rewrite of last week's posting, which I now find rather
obscure. Basically, I'm trying to introduce A-intensions in a way
different from the possibilities discussed in David Chalmers' "Foundations". The "contextual" approaches he discusses look
like non-starters to me, and I don't like his own "epistemic" account,
partly because of worries about his use of ideal language and partly
because I would very much like to explain a priori knowledge with knowledge
of A-intensions rather than the converse. Most importantly, I think there
is something wrong with the very question he asks. Or at least there's
something wrong with where the question is asked.
In his paper on
Imaginative Resistance, Brian Weatherson says that the impossibility
theory can't be true because "there are science fiction stories, especially
time travel stories, that are clearly impossible but which do not generate
resistance". Since you're reading this blog, you've probably also read the recent
entry on TAR where Brian discusses time travel
movies. Interestingly, he begins by noticing that "some [of these movies]
seemed unintelligible even on relatively generous assumptions". I agree,
and I would say that these are cases of imaginative resistance: A story
tells me that certain facts obtain, but I find it unintelligible how these
facts could obtain. Maybe we don't get the kind of immediate phenomenal
resistance experienced in paradigm examples of IR, but I don't think this
has any philosophical significance. I think it is largely due to the fact
that we are not clever enough: We can't be struck by an impossibility if
noticing the impossibility requires careful reasoning and keeping track of
exactly what happened at various earlier passages in the story.
Assume that all facts in our world are determined by the distribution of basic intrinsic properties at space-time points. Some of the space-time points in our world might be empty, that is, no basic intrinsic property might be instantiated there (either by some particle or by the point itself). If so, consider another world which is exactly like ours except that at all these empty points some basic intrinsic property is instantiated (say, the basic intrinsic property that plays the role of a certain mass in our world -- "some mass", for short) which however has no effect at all on what goes on in the world. (So if that property is some mass, the laws of nature at this world must be different from the laws at our world since our laws don't accept masses that have no effects.) By the definition of "intrinsic" and a rather weak principle of recombination, such a "dense" world is possible. And obviously, it is in principle indistinguishable from our world.
One of my problems with Lewis is that he published so little on issues where he thought he had nothing new to say. Sometimes it's tricky to figure out what his views on these issues might have been. Knowing people who knew him personally, or having access to some of his communications would probably help. Have there already been efforts to collect his letters, or even to make some of his unpublished writings available somehow? (If this is really Lewis' computer, the data on it definitely should be backed up soon before it completely turns to dust...)
