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.
Fictionalism about a certain discourse is the view that statements belonging to this discourse are to be interpreted like statements in fictional discourse.
Now as Brian has observed, on the common account of fictional discourse, "Fictional(Fa)" implies "(Ex)Fictional(Fx)" (even though it normally doesn't imply "(Ex)Fx"). So one might think that on the common account, fictionalism can't do with fewer entities than realism, even though it can do with different entities. However, the common account is not committed to "Fictional(a != b)" implying "(Ex)(Ey)(x != y)". After all, it usually allows for "(Ex)(Fictional(Fx) and Fictional (not-Fx))", so why not allow for "(Ex)(Fictional(x != b) and Fictional(x = b))"? So maybe one could endorse fictionalism about mathematics and the common account of fictional discourse without being committed to an infinity of entities by claiming that all the "numbers" talked about in mathematics are in fact identical.
Allan Hazlett, in his Against Fictionalism, says that if
numbers exist then "there is a fact of the matter about which sets numbers
are", even if we can't find it out. I don't think realism and
reductionsism about numbers implies this kind of determinatism. (Sorry,
"determinism" was already taken.)
The point is general. I believe in psychological states, and I believe
that psychological states are really just neurophysiological states. But I
don't believe that it is possible to isolate a single brain state that
realises the pain role, or the believes-that-the-meeting-starts-at-noon
role. The problem is that folk psychology is probably far too unspecific
to have a unique realisation. (This is not the problem of multiple
realisability, or not quite. Multiple realisability is usually taken to be
the problem that pain is or might be differently realised in different
individuals. It would be interesting to know more about the relation
between the two problems.)
Similarly, I believe in mountains, and I believe that mountains are really
just mereological sums of rocks, stones, sand, etc. But I don't believe
that it is possible to isolate a single sum of rocks etc. that is
(determinately) Mt. Everest.
Assume some sentence "Fa" is neither determinately true nor
determinately false. This might be due to the fact that
1) It is somewhat indeterminate exactly which object "a" denotes.
or
2) It is somewhat indeterminate exactly which property or condition "F"
expresses.
If neither (1) nor (2), then "a" determinately denotes a certain object A
and "F" determinately expresses a certain condition F. So whence the
indeterminacy? Maybe