Günther Greindl wrote:
> 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?)
There's no compelling reason the everything, or "The Everything", should be
well defined. In fact all our theories to date have contingent aspects,
usually in the form of boundary conditions, that are not defined by the
theory. But mathematical structures are different, they don't have
contingent parts. So if a mathematical set is not well defined then we
don't know what we're talking about when we discuss it.
> 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.
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