Wei and Brent:

considering Wei's Q#1 and 2 the thought occurred to me
(being almost a virgin in thinking in mathematical
constructs) that this looks as an even harder problem
than Chalmers's famous neurological "hard problem".
For me, at least. 
With the Q#3 I would ask "who is I?" Mathematically of
course. Otherwise we don't know. That would require a
mix of 1st and 3rd person notions which is confusing.
Same with Q#4. 
A dilemma of a subset like: validity of a legal
position" is easier, because it is only 3rd person
related (except for an inclusion of "my opinion" into
So I can't wait for a solution to Brent's addition:
 "how to formulate such meanings in math constructs?"
Especially in self reference to the formulator "I".

Physical existence (for me) is no more plausible than
a mathematical existence: both are figments of the
mind upon (maybe poorly perceived) impacts we can use
only as interpreted for ourselves. 

John M

--- Wei Dai <[EMAIL PROTECTED]> wrote:

> Is there a difference between physical existence and
> mathematical existence? 
> I suggest thinking about this problem from a
> different angle.
> Consider a mathematical substructure as a rational
> decision maker. It seems 
> to me that making a decision ideally would consist
> of the following steps:
> 1. Identify the mathematical structure that
> corresponds to "me" (i.e., my 
> current observer-moment)
> 2. Identify the mathematical structures that contain
> me as substructures.
> 3. Decide which of those I care about.
> 4. For each option I have, and each mathematical
> structure (containing me) 
> that I care about, deduce the consequences on that
> structure of me taking 
> that option.
> 5. Find the set of consequences that I prefer
> overall, and take the option 
> that corresponds to it.
> Of course each of these steps may be dauntingly
> difficult, maybe even 
> impossible for natural human beings, but does anyone
> disagree that this is 
> the ideal of rationality that an AI, or perhaps a
> computationally augmented 
> human being, should strive for?
> How would a difference between physical existence
> and mathematical 
> existence, if there is one, affect this ideal of
> decision making? It's a 
> rhetorical question because I don't think that it
> would. One possible answer 
> may be that a rational decision maker in step 3
> would decide to only care 
> about those structures that have physical existence.
> But among the 
> structures that contain him as substructures, how
> would he know which ones 
> have physical existence, and which one only have
> mathematical existence? And 
> even if he could somehow find out, I don't see any
> reason why he must not 
> care about those structures that only have
> mathematical existence. 

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