Is Everything well definable?

[Bruno Marchal]

Le 19-avr.-08, à 22:46, Günther Greindl a écrit :

>
> Dear Nichomachus,
>
>> decision. If she measures the particle's spin as positive, she will
>> elect to switch cases, and if she measures it with a negative spin she
>> will keep the one she has. This is because she wants to be sure that,
>> having gotten to this point in the game, there will be at least some
>> branches of her existence where she experiences winning the grand
>> prize. She is not convinced that, were she to decide what to do using
>> only the processes available to her mind, she would guarantee that
>> same result since it is just possible that all of the mutiple versions
>> of herself confronted with the dilemma may make the same bad guess.
>
>
> I have also thought along these lines some time ago (to use a qubit to
> ensure that all outcomes are chosen, because one should not rely on
> one's mind decohering into all possible decisions).
>
> The essential question is this: what worlds exist? All possible worlds.
> But which worlds are possible? We have, on the one hand, physical
> possibility (this also includes other physical constants etc, but no
> totally unphysical scenarios).
>
> I have long adhered to this "everything physically possible", but this
> does break down under closer scrutiny: first of all, physical relations
> are, when things come down to it, mathematical relations.
>
> So we could conclude with Max Tegmark: all possible mathematical
> structures exist; this is ill defined (but then, why should the
> Everything be well defined?)
>
> Alastair argues in his paper that everything logically possible exists
> (with his non arbitrariness principle) but, while initially appealing,
> it leads to the question: what is logically possible? In what logic?
> Classical/Intuitionist/Deviant logics etc etc...then we are back at
> Max's all possible structures.
>
> For all this, I am beginning very much to appreciate Bruno's position
> with the Sigma_1 sentences; but I still have to do more reading and
> catch up on some logic/recursion theory for a final verdict ;-))


You are on the right track :)



>
> One objection comes to mind immediately (already written above): why
> should the Everything be well defined?


I think you should ask Brian Tenneson. Personally I follow Plotinus and 
many Buddhist, Israelites, Muslims, and Christians, (and more) on the 
fact that the Big Picture (Brian's Universal set, I think) is not a 
member of what belongs to the Big Picture, so the everything cannot be 
described, nor really belonging to the everything.
Even restraining ourself to the mathematical universe (i.e. adopting 
mathematicalism), they are good reasons to believe that the whole of 
mathematics cannot be considered as a mathematical object. One reason 
is that all attempts to make the mathematical everything purely 
mathematical have failed. Set theories (like ZF) miss some mathematical 
object and also, in some sense, produce to much unwanted mathematical 
objects. Lawvere made an attempt to get the Big Mathematical Picture as 
a category, but he fails, although he (re)deiscovered the topos 
catehories in the process, which captures more the mathematician's mind 
than the mathematical reality (realities). The set theory NF does 
capture Universal Sets, but then I have doubt that it does it in a 
genuine sense, or if it is not in inconsistent theory.
Another reason is a not yet clear generalization of Gödel's 
incompleteness phenomenon along the line of Grim (ref in my thesis).
With comp, we have also a universal object (the universal machine), but 
again, like the toposes, it is more on the side of the "mathematician" 
than of the "mathematical reality". With comp (actually with the 
arithmetical comp, i.e. with the lobian interview) we have good reason 
to suspect that the notion of "truth (about) us"  *is* the big picture 
(Plotinus' One), but we can prove, then, that IF comp is true, and IF 
we are self-referentially correct (and thus lobian) then such a notion 
of truth cannot be expressed by any means by us. So I do thing that the 
everything, curiously enough, perhaps, does not belong to any 
everything thing we can defined (despite its name, probably because of 
its name).
I am not sure about the motivation of Brian for his search of a 
universal set. May be he could tell us a bit more?


bruno

PS I intended to comment some other posts but I have work to do, and I 
think this week I will be very buzy. I keep reading the list and 
absence or delay in comments does not reflect lack of interest but 
accumulation of time consuming jobs those days. Normally I will have 
more time next week. Best regards to all of you.
Ah ... A colleague of mine (the one who actually suggested me to look 
at that movie)  told me that "The Prestige" is the most 
anti-computationalist movie ever conceivable, and he gave me a very 
good argument! Cannot say more now without trigging the "spoiler alert" 
... :)


>
> To go back to your original question: to consider if both variants are
> chosen by the player of the game by herself (without qubit) seems to
> depend on which kind of Everything you choose. And that, I think, is 
> the
> crux of the matter.
>
> Cheers,
> Günther
>
> >
>
http://iridia.ulb.ac.be/~marchal/


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