Le 08-mars-08, à 21:09, George Levy a écrit :

> Hi Brian
> As Russell said, we have been discussing this topic for at least a
> decade. We all respect each other. I am sure that Bruno did not mean
> harm when he made his comment.

Actually I was replying, not even to Brian. But thanks.

> You bring up an interesting question: the relationship between Fuzzy
> logic and the MUH and you state that Fuzzy logic is a superset of
> deterministic logic. Isn't true that Fuzzy Logic can be implemented by
> means of a Turing Machine? Since a Turing Machine is purely
> deterministic it means that Fuzzy logic is actually a subset of logic.
> Hence the ad hoc introduction of Fuzzy logic may be unnecessary in the
> context of MUH.
> I don't think that the indeterminacy that we are considering here is
> fundamental or derives from an axiomatic approach. It is rather a
> consequence of living in many worlds simultaneously.

This is the key point. Tegmark believes that the physical universe 
could be a mathematical structure among others, which I can believe 
too. But with the coomputationalist hypothesis or its many weakenings, 
we have to take into account all mathematical structures supporting the 
self aware entities, to derive that particular mathematical structure. 
So we just cannot postulate a theory like "SWE", we have to derive it 
from a sum on all (sufficiently rich) mathematical structures. We just 
cannot consistently invoke a notion of existence of a "physical 
universe". This gives a clue why we believe or could believe in such a 
physical universe.

> When "I" make a
> measurement, a number of "I"'s make(s) a measurements. The result of 
> the
> measurement that each "I" perceive(s) defines the world where the "I"
> actually am (is). As you can see English is not rich enough to talk
> about "I" in the third person or in the plural.
> If there is a need for Fuzzy Logic, it would have to be a kind of logic
> adapted to deal with the MUH. I don't know enough to say if there is
> such a logic.

This puts light on the reason why the "explicitation" of comp (or its 
weakenings) is useful. The logic, in this case, has to be derived (by 
the UDA) from the sum invoked above. When the math are done we do find 
indeed a sort of quantum logic (ref in my url). It is an open problem 
if this logic is a fuzzy quantum logic. Evidences add up to think it 
could be a form of quantum credibility, instead of the "usual" quantum 
probability theory. This is related to the fact that we get the modal B 
logic (the "Brouwersche system") *without* the rule of necessitation. 
Much works remain, of course.



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