Re: possible solution to modal realism's problem of induction

From: Bruno Marchal <>
Date: Thu, 16 Jun 2005 18:12:35 +0200

Le 14-juin-05, à 18:26, Brian Holtz a écrit :

> Hi everyone (in this world and all relevantly similar ones :-),

Welcome to the list Brian. Thanks for the link to Alexander R Pruss'
web page, which seems quite interesting (and which I will comment a
little bit too, here or in a next post).

> I like the solution to the Induction / Dragon / Exploding Cow problem
> that I see in work by Malcolm, Standish, Tegmark, and Schmidhuber.

It is equivalent to the "white rabbit problem" we talk indeed about,
all along this list, and which is *almost* "solved" in my phd thesis
(to be short). May I attract your attention to it by referring you to
my web page?

It is a good occasion to sum up the main differences and the main
similarities between Standish, Schmidhuber, Lewis, Tegmark, Levy,
Ruhl, Mitra, Mazer, Finney, ... and my own. All approach are indeed
form of modal realism, and this is indeed what the everything-list is
all about.

Now I want to be short and I apology in advance for some
oversimplification, and please, any of you, don't hesitate to correct

To simplify the comparison I think it could be useful to compare them
from their ontology and their epistemology, and the way they tackle the
"Dragon" problem.

Finney, for example, (a pillar of the list) borrows Bostrom's notion of
"observer-moment" (OM). He argues they are fundamental, and its "modal
realism" consists to accept or postulate *all observer-moments*
Then he borrows a computationalist hypothesis from Schmidhuber, and
associates to each OM a finite binary strings.
Then he tackles the dragon problem by attaching to those binary
string/OM their Kolmogorov complexity from which he infers a absolute
measure. Little strings will have higher measure, and this should make
the dragon disappearing through Bostrom Self-sampling assumption SSA,
taken in some absolute version of it: ASSA.
My critics: OM are described by Bostrom as first person subjective
construct, and it is not clear how they can or should be related to the
strings, in such a way that we can make personal prediction. The dragon
disappear, but then in one second I will be a bacteria!

Schmidhuber postulates a "big programmer" which runs all programs. He
postulates some universe and he postulates the possible universes are
computational objects. Then he try to find some prior explaining the
importance of short programs at the origin of one universe capable of
sustaining self-aware structure like us.
My critics: there are simply no notion of first person available.
Worst, Schmidhuber is obliged to postulate some totally unknown
physical reality. So the epistemology is empty and the ontology is
unknowable, though, according guessable (this is quite close to
traditional physicalism).

Tegmark, in his first paper, suggest the existence of ALL Mathematical
Structures. This is ontologically much interesting than Schmidhuber
frame, imo. Unfortunately it is too big, and Tegmark seems not to know
the failure of all mathematician to capture all of mathematics
mathematically. I have discussed elsewhere in the list, at lenght, some
cardinality problem related to Tegmarkian approaches. In Tegmark there
is an embryo of distinction between first and third person point of
view, but it is either vague, or locally clear only under the
assumption of QM, but then it is exactly the (very interesting)
difference between the subjective and objective knowledge already
introduced in Everett basic papers. The mind body problem is still
under the rug.

Both Tegmark ande Schmidhuber assumes unclear relaltion between
observer and universe, which in general presuppose Aristotle theory of

In that regard, epistemologically, Malcolm has the same physicalist
attitude. He describes quite clearly three sort of *physical*
"theories", having in their intended model (in logician's sense) either
one universe toward having all logically possible universe, and he
defends, quite convincingly (imo) that last sort of theories. But he
discusses to quicky the relation between universe and information so
that I cannot really say more.
Main critics: the approach relies to much on some aristotelian notion
of universe, and the 1-3 distinction is not really tackled.

Standish is not yet enough clear about its assumptions, but seems to
get a pretty derivation of schroedinger equation, which is an
improvement. He does assume time, with the topology of the reals, which
is my main critics. The 1-3 distinction is present and used in an
anthropic way, but I have not yet understood it precisely.

George Levy is completely aware of the 1-3 distinction, and makes the
1-person at the origin of a purely first person "plenitude". Well, so
much that it is not clear for me if the plenitude is really suited for
being described in a 3-person theory, and this explains some its
silence in the list.

Note that some people, like Wei Dai, the list's master, but also late
James Higgo, have oscillate between approaches. Notably on the Absolute
versus Relative SSA. This is a key distinction. Saibal Mitra defends
the absolute version and Jesse Mazer a relative one. Mazer is quite
aware of the 1-3 distinction and of the necessity of having a theory of
consciousness to solve the dragon problem (which is what I have

Sorry for being short, and probably unfair, and unclear, but I must go
now. In a nutshell my approach is quite different. I take seriously the
1-3 distinction and I propose a proof that if we take the hypothesis
that "we" (or I) are digitalizable entities, then ontologically there
is no primitive physical universe (no big 3-everything), and
epistemologically the appearance of physics must be recovered from, let
us say, the gap between computer science and computer's computer
science. that gap is well described by the mdoal logic of
self-reference (Solovay), which makes it possible to translate the
proof in the language of (any) sufficiently rich (I say "Lobian)
machine. From this I can infer that the logic of physical proposition
obeys some precise modal logic of Lewis-Stalnaker counterfactuals, and
to show they agreed until now with quantum logics. Weakness: highly
technical (the "dragon problem" is transformed in an arithmetical
renormalization theory) and to much counter-intuitive for the average
aristotelian naturalist. But note it is quite "natural" (pun!) for the
Pythagoreans, the Platonist, and some neoplatonist like Plotinus.

I will add comments later and I will try to be more precise, and also
to comment your conversation with Alexander Pruss. About Lewis I love
its "counterfactuals". In the last edition he corrects some of its
argument against seeing worlds as "maximal consistent extensions" like
in my thesis, and then thanks to a paper by Hardegree (ref in my
thesis) this makes quite close my approach with his.

Actually I think it would be quite useful if, like we have done
"joining post", each of us could summarize its own approach in a
reasonably short post. The present post was just for showing you the
richness of the our hunting-dragon in the everything (modal) landscape.

If only pointing to David Lewis could motivate the people here to
invest a little more in ... (modal) logic ;)

Received on Thu Jun 16 2005 - 12:17:06 PDT

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