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 Have there already been efforts to collect his letters, or even to make some of his unpublished writings available somehow?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...)
"Content" and its cognates are rather theoretical notions. We need them
to do semantics and psychology, but we don't have immediate acquaintance
with them. That's why I find it slightly puzzling when people say that the
content of a sentence or a mental state can be represented by, say,
a set of possible worlds or some kind of labeled tree, whereas in fact it
is no such thing. What do these people think the content is in fact?
Anyway, let's assume that (at least for a certain fragment of English)
sets of centered possible worlds can do duty for (or represent) the content
of sentences. On this account, the content of "it is raining" is
identified with a certain set of centered worlds, namely the set of worlds
where it is raining at the center. By the semantics of negation, the
content of "it is not raining" is the complement of this set. Analogously,
the content of "language exists" is a certain set of centered worlds,
namely the set of worlds where language exists, and the content of
"language does not exist" is the complement of that set.
It's great that John Burgess makes all his interesting drafts of papers and books available online. It would even be better though if he'd publish them in a format that I can actually read (without having to buy a certain software). So if you're John Burgess or somebody else publishing on the web, please convert your documents to pdf or ps before uploading them.
I'll resume regular blogging as soon as either my wrists get better or they don't get better (despite staying away from typing). So by Tertium Non Datur, this blog will return to scheduled programming eventually.
I'm back.
In the meantime, Marcus Rossberg has kindly looked up the translation of Frege's third letter to Russell that I was talking about recently. He writes:
I checked the reference and the apparently false negation is in there!
It's on p. 141 in Gottlob Frege's _Philosophical and Mathematical
Correspondence_, ed. by G. Gabriel et al., Oxford: Blackwell 1980:
"But the difficulties here are not the same as in transforming the
generality of an identity into an identity of ranges of values."
I guess you're right that the translation is based on the
_Wissenschaftlicher Briefwechsel_, Hamburg: Meiner 1976, at least it says
"originally published as..." in the front of the English edition.
I'm off to Switzerland for a week or two.
John Hawthorne has some
nice arguments for the view that knowledge is closed under known
implication. I don't know much about knowledge, but it seems to me that
there is a good reason to believe that at least justification -- and hence
presumably also justified true believe -- is not so closed. The reason
is this:
E is some evidence, H and S are alternative and incompatible hypotheses.
(Obvious examples are skeptical scenarios, like E = visual evidence of
a zebra, H = there is a zebra, S = there is a mule disguised as a zebra.) E
strongly supports H: It raises its probability of truth from about 0.3 to
about 0.9. And H implies Not-S. Yet E does not raise the probability of
Not-S. On the contrary, it raises the probability of S.
Let "S(p)" abbreviate "p is strongly supported by the availble evidence".
The picture shows that
S(p) and S(p -> q) does not imply S(q);
S(p & q) does not imply S(p); (let p=-S, q=H)
S(p) does not imply S(p v q); (let p=H, q=-S).
When I prepared for my exam, I noticed something curious.
Richard Heck, in "The Julius Caesar Objection", claims that
In a letter to Russell, Frege explicitly considers adopting
Hume's Principle as an axiom, remarking only that the 'difficulties here'
are not the same as those plaguing Axiom V [p.274 in Language, Thought
and Logic].
The claim is repeated by Crispin Wright and Bob Hale in the introduction
to The Reason's Proper Study (p.11f., fn.21). The letter Heck,
Wright and Hale refer to is xxxvi/7 from July 1902.
Berislav Zarnic from the University of Split has translated my tableau prover into Croatian.
