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
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
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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