You're given two envelopes, and are told that one contains
twice the amount in the other, but you aren't told which is which. You
tentatively decide to take envelope A, but then reason that there is a
50% chance that B contains twice A's amount and a 50% chance that it
contains half A's amount, with an expected value of 1.25 times A's
amount overall, so it is in your interests to switch. But of course
the same holds in reverse. What is going on? I give a detailed
analysis of this "two-envelope" paradox, including a few
interesting subtleties that are sometimes overlooked. I didn't
publish this as I now think the analysis is incomplete; in effect it
solves the "numerical" paradox but not the "decision-theoretic"
This is a much more recent short paper (2001) that fills in the gap
in the paper above. It sets out a closely related scenario, which
combines elements of the St. Petersburg paradox and the two-envelope
paradox, and use this to diagnose where the decision-theoretic paradoxical
reasoning goes wrong. Published in Analysis, 2002.
These are a few unfinished papers on a variety of subjects, mostly
written around when I was graduate student at Indiana. I set these
aside because I wasn't quite happy with them, or because I didn't
think they were very significant, or because they evolved into
something else, or because I am lazy, but looking at them now I quite
enjoy them. My 1999 self may not endorse every youthful excess
here, but there are some interesting bits and pieces.
An early high-level overview of "first-person" and "third-person"
issues about consciousness. This was Part I of a supposedly 3-part paper
- the two remaining parts got turned into my paper "Consciousness
and Cognition". This part doesn't reach any firm conclusions,
but it captures something of the eternal internal struggle.
This was my inner taxonomist at work. (See my bibliography
for another example of this sad trait.) Following a workshop on humor at
CRCC, during which innumerable jokes were told and dissected, this was
my attempt to fit all of the jokes into a few basic templates. Unfortunately
the jokes themselves are given only one-line summaries, so I wish you luck with recognizing
This has a few jottings on the existence of "spaghetti-sorters"
and other remarkable devices that seem to be able to compute certain functions
faster than any standard computer (a spaghetti-sorter sorts a list of n
numbers in order n time, for example, by cutting n pieces of spaghetti
with the right lengths and banging them against a table).
On a not-too-far-fetched scenario, inspired by contemporary work in
artificial life, in which a Cartesian interactive dualism would have turned
out to be true. Indeed, many of the "simulated worlds" in artificial
life are Cartesian in just this way.
These are a few commentaries I've given at philosophy conferences over
the years. Often I don't write these up, but these may have enough in them
to be worthwhile.
A 1991 commentary (for a St. Louis conference on "Perspectives on Mind") on Andy Clark's "Theoretical Spaces". I
think the idea of "deep systematicity" as the central virtue
of connectionism is quite important, although I haven't got around to developing
it in a real paper. There are also some remarks on the relationship between
evolution and learning.
This was a 1993 SPP commentary on Valerie
Hardcastle's paper "On Determining the Monent of Consciousness"
(published in Philosophical
Psychology), which argues the neural level can help determine some
"Orwell/Stalin" indeterminacies. Here I was in the unusual position
of defending Dan Dennett; at the end Dennett was in the unusual position
of agreeing with almost everything I said.
A 1994 APA commentary on Dan Lloyd's "What is it Like to be a Net?"
Most people at the time thought I was joking.
Old Usenet postings
In days gone by I posted to Usenet, and other mailing lists, quite
a bit. There was an occasional very good discussion - at least one of my
published papers resulted from this sort of thing, and I can see other
traces here and there. Other postings were just intellectual curiosity
or frivolity. The endless discussions of Chinese rooms and consciousness
were too open-ended to excerpt here, but here are a few more specific topics.
I asked this question in sci.math and got quite a few interesting responses.
This message (which is now part of the sci.math
FAQ) is a summary and discussion. Lots of information on the Continuum
Hypothesis can be found here.
A comp.ai.philosophy discussion of Putnam's argument that every ordinary
open system implements every finite automaton. A number of people contributed
to this discussion, which has lots of interesting byways and raises plenty
of deep questions about computation. My paper
of the same title descended from this.
Someone else posted about various "realms" such as those
of matter, representation, and consciousness; here I take the conceit and
run with it, multiplying the realms and discussing various possible relations