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 ;-))

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

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

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