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.
The exam was okay. It now looks like I will continue to work on my
Lewis thesis so that it may be published as a book. My wrists are better,
but not yet fully recovered. I'm thinking about spending another week
without computers and pens in Switzerland.
I'll be in Bielefeld tomorrow for my final exams, and then in Poland for a couple of days, so don't be surprised if I don't answer your emails.
The state of my wrists is slowly improving. Maybe I will get back to blogging next week.
Since it doesn't look I will be able to finish the new version of my Tree Proof Generator anytime soon, I've now added a rough fix for the problem with unrecognized old terms.
Sorry for the recent lack of postings. I'm taking a break from typing to rest my wrists.
Not only my hands, but also my computers are now threatening to fall apart. While I unfortunately forgot to make backups of my hands, I've just copied all important data from my computers to the server. Most of it is not worth letting the googlebot know, a possible exception being two German scripts (1, 2) I wrote last year about recursiveness, representability, and Gödel's first incompleteness theorem, largely based on chapters 14 and 15 of Computability and Logic, 3rd ed. I've also uploaded some of the songs I made during the past 10 years to this directory, though as with all bad music, it's much more fun creating it than listening to it.
