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? http://iridia.ulb.ac.be/~marchal/

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 me.

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 "substance".

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 developed).

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 ;)



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