Tom Caylor writes:
> As I remember it, my interpretation/expansion of the "Yes Doctor"
> assumption is that 1) there is a (finite of course) level of (digital)
> substitution (called the "correct level of substitution") that is
> sufficient to represent "all that I am", and "all that I could be if I
> hadn't undergone a substitution", and 2) we (including the doctor)
> cannot know what the correct level of substitution is, therefore we
> have to gamble that the doctor will get it right when we say "Yes
> Doctor".
>
> Suppose that the level of substitution actually *performed* by the
> Doctor is S_p. Denote the *correct* level of substitution S_c. S_p
> can be expressed by a finite number, since the substitution itself can
> be expressed by a finite number (whatever is written on the tape/CD or
> other storage/transmitting device). We know what S_p is and it is a
> *fixed* finite number. But since S_c (*correct* level) is totally
> unknowable, all we "know" about it is our assumption that it is finite.
> The next *obvious* step in the logical process is that the probability
> that S_p >= S_c is infinitesimal. I.e. the probability that the doctor
> got it right is zilch. This is because most numbers are bigger than
> any fixed finite number S_p.
>
> So it seems that our step of faith in saying Yes Doctor in not well
> founded. It's definitely a bad bet.
>
> It seems that we need a stronger statement than S_c is finite.

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Surely an upper limit can be ascribed to S_c, probably way lower than the
Beckenstein bound for a brain-sized object.
Stathis Papaioannou
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