Imagine a world with nothing but infinitely many duplicate dragons, aligned in one long row. Consider the second dragon in the row. Call it "Fred".
Fred could have failed to exist. There are many worlds where he does not exist. (The actual world is probably one of them). Some of these worlds where Fred does not exist contain no dragons at all, others contain some of the other dragons in Fred's row. In particular, there are worlds where all the other dragons exist, but not Fred. The dragons are after all distinct existences, and there are no necessary connections between those.
Robbie Williams pointed out that in my recent musings on worms and stages, I ignore the following straightforward characterizations:
Worm Theory: the semantic value of predicates like "rabbit" is a set of 4D worms.
Stage Theory: the semantic value of predicates like "rabbit" is a set of 3D stages.
He's right. I believe that these theories both cannot work, so I don't want to define stage and worm theory that way.
I've set up a new server, so that now this blog should support LaTeX commands. As a test, here is what I take to be the most general version of the fixed Principal Principle:
![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%24%5Cmathrm%7BC%7D%28A%5C%3B%7C%5C%3BH%29+%5C%3B+%3D+%5C%3B+%5Csum_%7Bx%7D%5C%2C%0D%0A%5Cmathrm%7BC%7D%28%5Cmathrm%7BP%7D%28A%29%5C%21%3D%5C%21x+%5C%3B%7C%5C%3B+H%29+%5Ccdot+%5Cmathrm%7BC%7D%28A%0D%0A%5C%3B%7C%5C%3B+H%29%24)
Hm. The 'x' is a bit blurry.
As usual, I ended up rewriting the entire paper when I just wanted to add some footnotes to deal with timetravel and fission. Here's the new version. I still believe there is something wrong with the conclusion (which I also still find dull), but at least the characterizations of Counterpart and Fusion Theory now look better to me.
Turns out that I mostly use my Ned editor for making and editing websites and web-applications nowadays. So I've just fixed some bugs (like the problem with tab characters) and added some features (like switching character encodings and a zip & download option).
I'm somewhat stuck with the parts/counterparts paper. One of the problems is to find an acceptable semantics for time travel situations.
Part of the problem is that I'm often unsure what to say about these cases. I guess if time travel were more common, we would need some new linguistic conventions. Anyway, here are some sentences that seem true to me in the following scenario: Tina decides in 2025 to meet her younger self back in 2005. So at some time t in 2005, the younger Tina is in the living room and weighs 60 kg while the older Tina is in the kitchen and weighs 70 kg. Now, these all seem true to me:
I've written a little paper about the difference between theories on which ordinary things are fusions of parts located at various places, times, and worlds, and theories on which they instead have counterparts there. The dull conclusion is that there is no difference. I'm not sure I believe anything in there, and it's all quite rough, so comments are welcome: Parts and Counterparts (PDF).
Update 2005-03-08: Robbie Williams points out that my translation between Counterpart and Fusion Theory does not handle fission cases correctly. I should at least (following Lewis's translation scheme) say that names in the fusion language are indeterminate between all maximal eligible fusions of the corresponding counterparts from the counterpart language. But this is only a partial fix. I hope to come up with something better soon, though as I'm on the road for the next couple of days, that will probably have to wait until the weekend.
Ordinary objects - persons, planets, rivers and tables - are unextended atoms. They occupy only one point of space at only one time at only one world.
At first sight, this might sound absurd. Don't ordinary things
obviously exist at many different places, times and worlds? Isn't the
Yangtze clean in Geladandong and dirty in Shanghai? Wasn't it clean in Shanghai in 1500? And isn't it clean in Shanghai now at some other possible world?
Fortunately, Atomism need not deny any of this. For even though the
Yangtze is an unextended atom that strictly speaking only occupies a
single point, it has many counterparts at other points. And
these counterparts make all those statements true.
Note to self: I sometimes say that metaphysical modality is of S5 type, when I should rather say only that it satisfies the characteristic axiom of S5, Mp -> LMp.
It isn't clear to me that metaphysical modality obeys all the S5 principles because it isn't even clear that it obeys T. One of the problems is what to say about Lp if p contains names of objects which may exist only contingently. The two most obvious proposals are: a) Lp is true iff p holds at all worlds where the named objects exist (in this sense, Hesperus is necessarily Hesperus, even though Hesperus exists contingently); b) Lp is true if p holds at all worlds (in this sense, Hesperus is not necessarily Hesperus, but it is necessary that if Hesperus exists then Hesperus is Hesperus). Either way violates T. On (a), let "F" express the property of coexisting with Hubert Humphrey; then "L(F(Hesperus) & F(Humphrey) -> F(Hesperus)) -> L(F(Hesperus) & F(Humphrey)) -> LF(Hesperus)" is false, even though it's an axiom of T. On (b), "L(Hesperus = Hesperus -> Hesperus = Hesperus)" is false, even though it's a theorem of T.
According to the Stage View, ordinary objects are temporally unextended timeslices. "Ted sleeps" is true iff the present Ted-stage sleeps.
What if there is no present stage, as with "Socrates is wise" and "Socrates exists"?
The question is not what to say about "Socrates was wise" and "Socrates did exist". These are true because at some time in the past, there is a wise Socrates stage (see pp.27f. of Ted Sider's Stage paper). The problem is the tenseless "Socrates is wise".