Wei Dai <[EMAIL PROTECTED]> wrote:
Here's a new question for you, Bruno. What interpretation of probability
theory do you subscribe to? I've been saying that the meaning of
probabilities come from decision theory and specificly a probability only
has meaning if it actually is relevant to making a decision.
I think we discussed this before (when I told you that this position
is not unlike my iridia (ex)-boss position). But probabilities
never really
appeared in that context, credibilities appeared instead, somehow
akin to the
Dempster Shafer evidence theory. You can look at Philippe Smets
webpage
at http://iridia.ulb.ac.be/~psmets/ for links.
So far no one
has posted a disagreement with that philosophy, but perhaps we don't all
agree. Would you like to clarify your position on this issue?
I think I do not disagree with that philosophy. Now in my
approach
the only axiom I really need for the machine's rational beliefs
on
probability is that [P(x) = 1] entails [not P(x) = 0]. (P(x)
is
for probability of event x). This will
correspond to the modal formula []A -> <>A. That is: if
the event A
is necessary then it must be possible. This formula
is called D (for deontic: it is also basic in the modal approach
to
obligation and permission). If D was not a theorem of the Z
logic, I would
have stop the machine interview and would be much more doubtful
about
comp.
It is an open problem how to treat more general notion of
probability
in the language of a consistent machine. With the introduction of
self-
duplication experiment, probabilities becomes very
counterintuitive. That's
why I try to give partial axiomatic and just listen to what a
consistent
machine can say about that, and remaining consistent.
On Wed, Jul 17, 2002 at 04:13:54PM +0200, Bruno Marchal wrote:
> The mind-body problem is hard to formulate purely formally because it
> search a link between the somehow formal body and the non formal mind.
I think you can formalize the problem, or at least an aspect of it, in the
language of decision theory. So perhaps you can come back to this question
after reading Joyce's book.
OK. But honestly my feeling is that "decision" is a
higher concept that
probabilities.
> Come on, I'm sure you see what I mean. (Of course "functional substitution"
> is an interesting concept by itself. It would be just a slight exaggeration
> to say that the lambda calculus and even category theory has been invented
> for making that concept precise). In the uda frame, once the level of
> digital substitution has been chosen, a substitution is functional if it
> preserves the counterfactuals input/output relations of the thing which
> is substituted.
You claimed that the concept of causality is problematic. So how do you
define "counterfactuals input/output relations" without
reference to causality?
Imo, concept like "causality", "free-will",
"decision", etc. are fundamental
and very interesting *high level psychological* notion.
The "counterfactuals input-output relations" are
semantically defined by UD*
the running of all computations. But the "running" is
itself defined
in arithmetic, or in the minimal set of inference rules needed to
formalize
notion of computation. This is confirmed partially by the formal
similitude
of the Z logic and Lewis/Hardegree/Stalnaker quantum like
approach of the
notion of relevance. It is also linked to the non-monotonic
aspect of quantum
logic (cf hardegree). But the only low level notion of causality
is the comp
approach is the classical material implication. A is a cause of B
if A is false
or B is true. From this a pyramid of causality notion can (and
must) evolve.
I'm not sure this can make sense if you have not an idea of the
psycho/physics
comp reversal.
> I have written more in this list than I will ever be able to write in
> a paper. I have begin at least four papers; I don't know if I will
> finish them. "Our field" overlaps too much disciplines. Either the
> papers grow too much, or the paper became relatively incomprehensible.
> Perhaps I should write a book instead. I don't know.
> I must think about that. Advices are welcome.
Sorry, I'm not an academic and have no idea how things work in that world.
Academic are like any human societies. It works like happy
families in the
best cases and like mafia in the worst but fortunately rarer (I
hope) cases.
I just want you to write your ideas down in a comprehensive form that I
can understand.
I guess we are not on the same length wave. It would really help
me to write
that comprehensive form if I knew what is your problem with the
uda, unless
for some reasons you reject the *hypothesis*. I would
really
appreciate if you could tell me at which step of the uda you
stop(*).
The comprehensive paper must begin by the uda, and I don't see
what I can
add.
The AUDA without an understanding of the UDA is just a formal
games.
I am open to the idea that something is wrong or unclear, or
imprecise.
I mean once you understand the difference between 1-person and
3-person, and
once you understand the 1-comp indeterminacy, and once you
understand that
if we are machine we cannot be aware of any delays in
UD-computations (invariance
lemma), then it follows(**) that our futures are determined by
all computations
going through and relative to our actual (1-actual) computational
states.
At first it looks like a refutation of comp because empirically
we have good
reasons to believe in negative amplitudes of probability, which
intuitively
does not seem to appear through comp, but then taking into
account the
godelian incompleteness, through the translation of UDA in
the consistent
machine language shows that the probability matter is more subtle
than
intuition.
(*) if *anyone* find a flaw or even imprecisions I would be
grateful
letting me know it. (links
http://www.escribe.com/science/theory/m3044.html ).
(**) Easily with some Occam Razor. Less easily without Occam; you
need the
Movie Graph Argument if you don't accept Occam.
