Le 10-août-07, à 14:26, David Nyman a écrit :

> On 09/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>> 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.
> Thank you for asking, it's very important to ensure full understanding
> at all points.  My maths are indeed a bit rusty, but fortunately
> resources are easily available as needed to refresh the memory.  Would
> you be happy with the wikipedia treatment of 'function'?
> http://en.wikipedia.org/wiki/Mathematical_function

It is ok. I will say more in a post on the difference between the 
layman and the logician.

>> 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
> How can I best demonstrate this to your satisfaction?  I accept the
> validity of the demonstration in the UDA (which I believe that I'd
> already intuited as a consequence of the 'solipsism of the One') that
> the first person or reflexive OM must be indeterminate with respect to
> its third person manifestations.

OK. Have you seen that this is going to made physics a branch of 
"intensional number theory", by which I mean number theory from the 
points of view of number ... ?

>  However, I also wanted to ask
> whether it was important in this context to define in detail the
> content and informational limits of a given OM (e.g. its temporal
> scope or 'duration')?

? The third person OM are outside time and space. time and space will 
emerge from the way OMs combine each other. They do combine through 
their intrinsic relative content eventually. But here we are 

>> 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?
> OK indeed.
>> 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.
> Do I need Franzen's book too?

Hmmm.... The problem with the logicians is that they have a tendency to 
write beautiful books (and often quite expensive).
So yes, buy or find an exemplar of Franzen's book, but honestly I could 
mention some other good book. But in our context Franzen's book could 
be a good if not the best beginning. His other book on inexhaustibility 
is quite interesting too, even as an introduction to PA (the 
Escherichia Coli of the "lobian machine").
OK. Don't buy it if you decide to buy only one book on Godel, and let 
me think which is the best one. But if you are willing to buy/read two 
books, then get it asap.

>> 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?
> Alright!
>> 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.
> OK, again in terms of 'the One', since all the 'reconstitutions'
> exist, they must all indeed play a role in the 'account' (which can be
> synonymous with narrative or story).

Here there is something not quite correct I think. But I must go. The 
idea is that "all the reconsititution exist in many histories" will 
have just a statitistical effect of the first person view of the way 
the OM (re)combine. Again this is a (grandmother) anticipation.

>> By the first person indeterminacy, your future will be determined by
>> the most probable comp histories going through your actual state.
> By 'probable' you refer to the elusive measure?

The not so much elusive measure :)    Yes.

>> 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.
> i.e. from the third person pov?

Yes. Together with the impact for the other views.

>> 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.
> IOW you adopt the view from the inside out?  I would like to
> understand this securely.  It seems to me that you're saying that
> focusing on self-reference relies on the intrinsic self-location of
> first person 'pages' within the 'Library of Babel' of the UD's output.
>  Given this, how do such pages then 'cohere' into 'narratives through
> time'?

It is the other way round. It is from the logico-arithmetical coherence 
of the OMs that the subjective first person feeling of time (and 
irreversibility) will emerge. But this is what I have to show you 
(again, this is an anticipation).

>> 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".
> I think we may have to come back later to this question of subjective
> time.  But for now I rely on you to set the agenda of our more
> structured modus operandi.

Ok thanks.



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