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".
I'm trying to catch up with Dave Chalmers's reading of Scott Soames's Reference and Description. I'm still at chapter 4, and my reaction to it is not quite the same as Dave's. (I began this entry as a comment over there, but it somehow grew way too long.)
Let's stipulate that "Lee" (rigidly) denotes the youngest spy (if there is one). Soames argues that if
Until recently, I thought that there are no quantifiers in ordinary discourse for which a substitutional interpretation is adequate, or helpful. I still think this is true for almost all cases, including quantification over fictional and intentional objects. But here are two cases where a substitutional interpretation looks ok.
First. The world can be completely described in precise vocabulary. There are no vague objects with irreducibly vague bounderies or heights or colours. Rather, for many terms, like "Mount Everest", it is indeterminate exactly which perfectly precise object they denote. But it is very natural to say that Mount Everest has
vague boundaries. Instead of denying it, I'm inclined to offer some kind of reinterpretation, such as: there are different objects slightly differing in their boundaries between which "Mount Everest" is indeterminate; or: for no precise boundaries b is it true that Mount Everest has boundaries b; or: for some precise boundaries b is it indeterminate whether Mount Everest has boundaries b. All these are true, and all of them could be meant by "Mount Everest has vague boundaries".
Call an expression E scrutable with respect to a class of expressions C iff it is a priori that all true sentences involving both C and E are a priori deducible from all true sentences involving only C. Equivalently, E is scrutable with respect to C iff there are no worlds w1 and w2 of which exactly one is in the 1-intension of some C+E-sentence, whereas all 1-intensions of C-sentences contain either both worlds or neither.
Is every expression scrutable with respect to some class of expressions to which it does not belong? If the relevant language has synonyms for all expressions, that's trivial. We should better ask about families of expressions: what classes of expressions are scrutable only with respect to expressions containing other members of their class? Call such classes indispensible. Large classes of expressions like the class of all expressions are obviously indespensible, as is probably the class of indexicals and the class of quantifiers. Dave Chalmers would also add the class of phenomenal expressions. As a type-A materialist, I would rather not.
I don't share Lewis's strong intuitions that shape properties must be purely intrinsic rather than time-indexed. For me, the argument from intrinsic change works much better with certain relations, in particular mereological relations and identity.
Suppose x is part of y at time t1, but not at t2. Perdurantists can say that the temporal part of x at t1 is a part simpliciter of the temporal part of y at t1. Time-indexers will say that the whole of x stands in the part-at-t1 relation to the whole of y, where this relation is not analysable in terms of non-indexed parthood: time-indexed parthood is all there is. But no! Subsets are parts simpliciter of sets, battles are parts simpliciter of wars, the story of the Trojan War is a part simpliciter of the Illiad, geometry is a part simpliciter of mathematics, XPath is a part simpliciter of XSLT, and so on. These things are not part-at-time-related, but part-related.
Thought experiments about reference often focus on cases where a term intuitively refers to something other than what a certain theory would predict. This way, we can find sufficient conditions for reference. I think it is just as interesting to consider cases where the term does not refer at all, which gives us necessary conditions.
For example, suppose "hydrogen" and "Aristotle" refer causally, that is, denote whatever stands in a certain causal relation to our use of these expressions. Then what would it take to find out that hydrogen does not exist? We would have to acquire etymological information about the causal-historical origin of the term "hydrogen": only if something went wrong in that causal path could we conclude that there is no hydrogen.
I have a slight cold, so instead of doing philosophy I've rearranged the music collection on my hard drive and written a LaTeX template to print paper CD cases: template.tex. I've also written a little Perl driven web form that generates a ps file from the template and the entered title/tracks: cdcase.pl. Sorry, you can't test it online, as I don't have LaTeX installed on this server. Here is an example output: cdcase.ps.