Le 08-août-07, à 15:26, David Nyman a écrit :

>
> On 30/07/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>> Meanwhile I would suggest you read the book by David
>> Albert: "Quantum Mechanics and Experience"
>
> OK, I've ordered it.


Good.




>
>> I can compare only the "logic of probability/credibility one" of  
>> nature
>> (more or less quantum logic) and the logic of "probability/credibility
>> one" extracts from the discourse of the self-observing machine. It  
>> *is*
>> technical. It cannot be a starting point, I think.
>> In my opinion, the starting point is Church thesis. Once you are back,
>> tell me and I can do that.
>
> OK


I hope you will not mind if I ask you "stupid" question, like "Do you  
know what mathematicians mean by "function?".
Sometimes I realize that some people does not grasp what I say because  
they just miss some elementary vocabulary, or they have a problem with  
the notation.
Of course anyone can ask any questions. Math is something easy (the  
easiest of all sciences) but if you miss a definition then it *looks*  
difficult.





>
>>> The following may not be
>>> relevant in this context, but I'm particularly interested in  
>>> something
>>> you said elsewhere ('simulation argument') about how comp can relate
>>> OMs (and presumably the multiverse structures associated with them)
>>> geometrically 'through time'.
>>
>>
>> If this is not relevant in this context, I ask what is relevant ... ?
>
> I was referring only to its relevance as a a starting point.  However,
> it appears that you think it is.

OK, it is important, but cannot be used as a starting point. We will  
get it soon after Church thesis.



>
>> Now, as I said some days ago, I think that a way to link more
>> formally my work and the everything discussion can consist in defining
>> a notion of basic atomic third person observer moment.
>
> It would help me if you would define the content of this fundamental
> OM concept rather specifically for the purpose of this discussion.


OK. But for this I need to be sure you grasp well the UD argument, at  
least the seven first step. The steps will always refer to the 8-steps  
presentation of the summary PDF Slides available here:
http://iridia.ulb.ac.be/~marchal/publications/ 
SANE2004MARCHALAbstract.html




>
>> The UDA, plus
>> Church thesis + a theorem proved in Boolos and Jeffrey (but see also
>> and better perhaps just Franzen's appendix A) makes it possible to
>> define the comp third person OMs by the Sigma1 sentences of
>> arithmetical language. Those have the shape ExF(x) with F(x)  
>> decidable.
>> For example ExPrime(x) (a prime number exists), Ex(x = code of
>> triple(a,b,c) and machine a gives c on argument b),
>
> Is there a 'grandmotherly' way of making it intuitively compelling
> what makes it possible for the OM to be defined thus?



Well, the UDA can already be seen as a 'grandmother' way of making this  
intuitive. What you have to understand is the turing-universality of  
addition and multiplication, in the first order logic framework. I will  
explain this in all detail, but I have to begin with Church thesis. I  
propose we try to organize ourself through a well defined sequence of  
posts, which we can from time to time transform into a pdf, so that we  
can refer to the pages of that pdf, instead of post messages with  
fragile addresses. OK?





> In your various
> debates with Peter, I guess I've picked up essentially that such truth
> statements stand here for 'existence'.  Yes?

Peter was putting too much philosophical weight to the notion of  
existence. Recall that the "ontic base of reality" will just be te  
numbers, and that when I say a number exist, I mean it in the usual  
sense of elementary high school arithmetic. The key point is that a  
machine which can prove all the true sigma1-sentence is turing  
universal. this is already well explained in Torkel Franzen's book (in  
his first appendix).  Again, don't worry I will explain. Now, to  
eliminate redundancy in the explanations, I insist we organize ourself.  
I have already explain many of those things, but never in a way so that  
I can easily refer to the (too many) posts. All right?


>
>> ... This last
>> example show that the notion of Sigma1 sentences is rather rich and
>> encompasses full computability. So the very restricted notion of
>> Sigma1-proof (restricted from  the point of view of provability) is
>> already absolutely universal with respect to computability. A machine
>> is universal iff the machine is Sigma1 complete, i.e. is capable of
>> proving all true Sigma1 sentences.
>
> Could you expand more slowly on the particular importance of 'full
> computability' here.  Sorry if I'm being slow, but I want to make sure
> I get the intuitions as you intend them.


I will perhaps begin by that important question. Never apologize for  
being slow. It is a symptom that you try to understand the real thing.  
It is normal to be slow.



>
>> Such  a machine codes automatically
>> a Universal Dovetailer: to be a UD accessible state is Sigma1.
>> So the measure we are searching can be put on the set of Sigma1
>> sentences. Intuitively, from UDA, the weight for each Sigma1 sentences
>> should be given by the "number" of proof going trough those sentences
>> (including the many infinite proofs of some false sigma1 sentences).
>> Now we can search for some equivalence relation on those proofs, but
>> this is known to be very hard, and that is why I prefer to interview
>> the universal lobian machine directly, and content myself with the
>> corresponding logic of "certainty".
>
> Is a more 'grandmotherly' form of all this possible to begin with?
> I'm remembering the idea of the roadmap, in terms of which the
> destination, and the journey towards it, could first be set out in
> more general terms, in order to make the problems and their possible
> solutions as intuitively compelling as possible at the outset.  It
> seems to me often that I get the general drift, and some of the main
> ideas, but there's still some confusion as to the whole picture.
> Could there be a sort of master 'storybook' version - a narrative of
> the key points into which the emerging formal detail could be fitted?


The idea is really this: if you are in front of a running (and thus  
never stopping UD), the seven steps shows that, taking comp seriously,  
to make any 100% prediction, you have to take into account all the  
reconstitutions of yourself (which exist by the comp hyp) and their  
continuations.
By the first person indeterminacy, your future will be determined by  
the most probable comp histories going through your actual state.
The problem then will consist in defining what is a "probable comp  
history". This is a very difficult problem: for example, when can we  
say that two computations are equivalent, etc.
The trick I have done is to abandon the idea of searching directly a  
measure on the computations, and, instead, to isolate the mathematical  
structure for the "certain-propositions" by using the self-referential  
logics.



>
>> Yes and No.
>> Yes for two reasons: 1) if we assume comp, the UDA shows we have to
>> recover knowledge from infinities of computations in the UD* (the
>> "block" universal dovetailing. And FOR does presuppose comp.  2) in  
>> the
>> arithmetization of the UDA, the notion of knowledge coherent with the
>> UD thought experience is just given by the older definition of
>> knowledge as true justified opinion (in platonism, but also in a lot  
>> of
>> east and west rational account of mystical experiences). It is a gift
>> that we arrive formally here at temporal-like logic of evolving first
>> person knowledge.
>
> Do you mean that first person knowledge by definition can emerge only
> in an 'evolutionary' way -


No, from a third person view.
Yes, from a first person view.



> i.e. that it must necessarily be restricted
> 'in time', as opposed to some all-encompassing atemporal form (e.g.
> the 'knowledge' of the One, if it had a pov)?

The first person will feel herself restricted 'in time' indeed.  
Somehow, she creates subjective time/consciousness. But from the ontic  
view, with the "block-all-computations" (alias UD*) there is no time.  
 From the material (first person plural view) pov, it is an open problem  
if there is an "objective time".

Bruno



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


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