From: Lee Corbin (lcorbin@tsoft.com)
Date: Tue Jun 18 2002 - 12:51:18 MDT
Rafal writes
### Lee Corbin wrote:
If Platonic reality were enough, then it would completely
wipe out all our reasons for doing anything. As Greg Egan
hinted at in his absurd Theory of Dust (in Permutation
City), your life will continue (has continued--is continuing)
in timeless platonic space regardless of what happens in
the actual execution. So why save a little girl from Nazis?
Why strive to build a friendly AI? Whether you fail or
succeed, and it's all happening in platonic space anyway
then who gives a shit?
### I think we can have our mathematical cake and eat it too,
### if we conceive of some of the Platonic entities as incom-
### plete - e.g. since certain sets can be defined (or define
### themselves, or exist) only in relation to other, simpler
### sets, we could imagine that there is an "edge" to mathe-
### matics - the sets which use all simpler sets (those are
### frozen, timeless, like the set of all integers from 1 to 100)
### in their definition.
Well, there is a tradition in set theory of defining sets
recursively like this. A little like Russell's theory of
types, but much better. (Von Neumann also defined the
integers this way, as you know.)
So in many developments (see Potter's "Set Theory" or Knuth's
"Surreal Numbers") each new set of numbers is defined for a
new *day*. That is, on each "day" you can use all the sets
produced on previous days in the construction.
However there are at least omega (countably infinite) days.
There may even be uncountably many days! I don't recall.
So your "edge" could be taken to mean some sort of "present
day" or "present time".
### One of the edge sets could be the set of all numbers fully
### describing the current state of the multiverse. The set of
### numbers describing fully the state of the multiverse tomorrow is
### not a part of mathematics, it doesn't mathematically exist yet
This is hyper-weird, IMO. I say that any object that we can talk
about and discover properties of exists just as much as the number
17 does. This includes *all* of the enormously large cardinals
that have been *discovered* so far. And we should decree that
OUR act of discovery has NO EFFECT on them! How could it when
our friends in Andromeda can discover them too?
### (unless we live in a simulation within a meta-multiverse which
### already went through the stage containing ourselves eons ago).
Well, okay, this admission---or the possibility that this is true
---puts us right back where we are, in Cantor's full paradise.
### I imagine that this process of derivation at the edge
### of mathematics can give rise to our experience.
Totally weird. Doesn't one of your patient's experience cease
when you've given him or her sufficient anesthesia? Doesn't
one's experience come to an end if one really dies? What possible
link is there or could there be between our *experience*, which
is locally determined by neurons (or by Turing quadruples if
we're uploaded just so), and the eternal timeless truths of
mathematics? Don't you need to postulate a mechanism here?
(Good luck.)
### The arrow of time runs from the simple sets, to infinities
### of unimaginable ordinality, and they do get bigger with every
### tick of the clock. Even the integer fully encoding Lee's mind
### is not finished - every time you ask it something, it adds more
### digits (according to rules inherent in itself and other numbers),
### and therefore it's conscious.
Well, show me a real number that's not "finished", and I'll show
you one that has omega more digits (e.g., yours plus the decimal
part of root 2). Now are you going to give me credit for having
created a brand new real number? Or are you going to be reasonable
and admit that that particular real number already existed?
Besides, you *never* get to ask an integer that encodes my mind
anything. Not really. You must ask an actual running process
(e.g. me, uploaded or not). If you do as the integer apparently
bids you to do, i.e., delve into it and ask your questions, it
isn't *really* answering you at all! That's a lie. It only
appears to be answering you only because all integers already
exist, and that's just the integer that happens to have a lot
of stored answers.
Lee
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