I add that your link provide a way to recover my old conversation
with Joel Dobrzelewski on the list (28 June 2001), which
presents the simplest version of the Universal Dovetelair
Argument (UDA), i.e. the argument showing that the
computationalist hypothesis (in the bio/psycho/theo/-logical
sciences) entails that physics is ultimately a branch of machine
bio/psycho/theo/-logy. In particular it shows that physics can
be presented as a probability or credibility measure on the relative
computational histories (which are computation as seen from
some first person perspective).
The argument is presented in a step by step way, and begins here:
You can then follow the step by clicking on the right arrow next
"date", and skipping the many threads we were discussing
simultaneously at that time.
People interested can ask questions. Note that the lobian
interview does not necessitate the understanding of the UDA,
but this one provides the basic motivation for some of the
Theaetetical variants of the modal logic G and G*.
I've had this question brewing for some time while I've been pondering
the UDA. So now I've gone through the above thread and I still didn't
find the answer to it.
In the UDA it is said that the Correct Level Of Substitution (I'll call
is CLOS for short) is unknowable. I agree: Just intuitively, in a
closed system, how could we know if something wasn't exactly right? It
would result in the future being different than it would have been, but
we wouldn't be aware of the difference. We would just accept that as
Since the CLOS is unknowable, then we should be able to talk about an
unknowable, yet true, probability P(CLOS) that each substitution is
done at the CLOS. By the way, we know at least P(CLOS) < 1 because the
doctor is guessing, and P(CLOS) = 1 would implies that the doctor knows
and can actually implement it. But in fact I'd say that we really
don't have any lower bound for P(CLOS), but that fact is beside the
point I want to make.
OK, so now for my question. So when we talk about finding a
probability measure on the 1-determinancy (I don't know if that's the
exact right words), don't we have to multiply this probability measure
by the unknown P(CLOS) to get the actual probability measure? But this
would imply that the probability measure is impossible to find out to
any degree that would be called scientific, since it is a function of
P(CLOS), i.e. the step of faith in saying "Yes" to the doctor who
doesn't know anything.
In fact, if each moment is equivalent to a substitution (not
necessarily at the CLOS!), as comp says, then there would be an
exponential decay of our identity, as sort of identity entropy.