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.
I've uploaded another revision of the emperors paper. The best thing about this version is that it's four pages shorter than the previous ones.
Unrelatedly, I've removed the Herbrand restriction from my tree prover. The restriction says that a Gamma node should not be expanded more often than there are closed terms on the branch. But currently, the prover doesn't keep track of the number of closed terms, it only keeps track of the number of function symbols (including 0-place function symbols, i.e. individual constants). So if a lot of s(0), s(s(0)), etc. are on a branch (as in this proof, where I noticed the bug), the prover wrongly applied the Herbrand restriction, thinking all of them are only two closed terms.
All my testcases work just as well without the Herbrand restriction. If you find a case where the performance got worse, please let me know. It shouldn't be difficult to fix it (rather than removing it completely).
Suppose there are at least proper-class many possibilia. Does it follow that some fusions of possibilia are not members of any set? For the last two years or so I thought it does. My reasoning was that if some of the possibilia correspond one-one with all the sets, then some atoms of possibilia also correspond one-one with all the sets (for there cannot be proper-class many fusions of set-many atoms); but since there are always more fusions of atoms than atoms, it follows that there must be more fusions of atoms of possibilia than sets, and hence that some (in fact, most) of these fusions lack a singleton. This does not take into account atomless possibilia, but I always thought the reasoning would easily carry over, by something like the fact that even with gunk
Well, I know what Counterpart Theory is not: it is not a theory according to which ordinary things do not really exist at other possible worlds.
There are two readings of "ordinary things do not exist at other worlds". The first is a neutral reading on which things exist at another world in the way they sleep at another world or win elections at another world: whatever possible worlds are, they somehow represent things as existing and sleeping and winning. In this sense, something exists at a world iff the world represents it as existing. Anyone who accepts possible worlds talk at all accepts that ordinary things exist at other worlds in this sense.
My fellow Germans have donated very generously to the tsunami relief effort. That's good. But it's remarkable that we have donated so much to this cause, and far less to other good causes. 100 Euros given to the tsunami victims could also have been spent, say, to help the refugees in Darfur, or to support the reconstruction of war-torn Uganda or Sierra Leone, to provide medical care for people in Ethiopia or Bangladesh, to prevent deforestation, overfishing and soil erosion, to fight climate change, and so on. Donations are urgently needed all the time.
David Chalmers has an interesting post on the differences between his and Frank Jackson's versions of two-dimensionalism. It turns out that my reading of a certain passage in "Why we need A-intensions" was right: Jackson believes that truth at a world considered as actual is somehow reducible via de-rigidification to truth at a world considered as counterfactual.
The difference between linguistic ersatzism, where possible worlds are replaced by sets of sentences, and modal fictionalism, where the pluriverse of all worlds is replaced by a large set of sentences describing all worlds at once, appears to be small. Nevertheless, I (still) think the analytic power of fictionalism is greatly diminished compared to that of linguistic ersatzism.
One of the great advantages of possibilia is that they provide a unified framework to reduce lots of kinds of things: properties can be identified with sets of possibilia, propositions with sets of worlds, meanings with functions from worlds to extensions, events with functions from worlds to regions, and so on. But suppose possibilia don't really exist, but exist only according to some fiction. Then properties can't be sets of possibilia. By the usual rule of interpreting statements about fictional entities, it will at most be true that according to the fiction, properties are sets of possibilia. But that doesn't help us if we're looking for a unified ontology. We'd like to know what properties really are, not what they are according to some fiction. If as fictionalists we think that properties really are sets of possibilia, then we have to conclude that properties don't really exist, just as the (other-worldly) possibilia don't really exist.