[extropy-chat] Is our Universe in a Brain?
Ian Goddard
iamgoddard at yahoo.com
Sat Apr 2 22:11:55 UTC 2005
Another way to ask ben's question [1] is: if the
common universe outside our brains is a dynamic model
within a computer, then how do we know whether or not
that computer is an *organic* computer like a brain?
Suppose (as I do) that all brains are organic
computers that build models of universes (such as
dreamscapes) [2], and suppose that our universe could
be a model in a computer, then it seems to follow that
the computer that is modeling our universe could be an
organic computer like a brain. Hmm...??? Well, I do
believe we can know that there is a modal-logic model
wherein all the statement in that argument are true
and thus are at least logically consistent. Here are
those statements in propositional modal logic:
1. b -> []c
2. u -> <>c
3. u -> <>b
Fleshed out in words:
1. If there is a brain (b), then necessarily there is
a computer (c).
2. If there is a universe (u), then possibly there is
a computer (c).
3. If there is a universe (u), then possibly there is
a brain (b).
A corresponding modal-logic model is the ordered
triple <W,R,I> where W = {1,2,3} a set of worlds or
states; R = { (1,2), (3,1), (3,2) } a set of ordered
pairs defining accessibility relations on W wherein 1
accesses 2, and 3 accesses 1 and 2; and I is an
interpretation function mapping the set of
propositional statements {b,c,u} onto W such that I(b)
= 1, I(c) = 2, and I(u) = 3 and where b = "there is a
brain," c = "there is a computer," and u = "there is a
universe."
In that model (which is more easily sketched on
paper), the valuation function V mapping the set of
our propositional statements {b,c,u} onto the set of
truth values {0,1} (where 0 = false and 1 = true) in
accord with the definitions of the modal operators
proves that:
1. V(b -> []c) = 1
2. V(u -> <>c) = 1
3. V(u -> <>b) = 1
So there exists a model for the statements in the
argument presented above. But that does not prove that
the argument is sound in reality, although it's at
least intuitively plausible (at least to me) and its
members are logically consistent. However, Mike's
point seems to be that there are knowable constrains
defining the limits of possible brains that ostensibly
rule out our universe being a model within some super
brain (ie, Yudkowskian arguments). [3] However, and
with only cursory consideration of this topic, I'd
posit if that's so, then brains are not the same as
computers (which contradicts my initial assumption and
which I'm thus inclined to reject).
~Ian
http://IanGoddard.net
"Since proofs need premises, it is impossible to prove
anything unless some things are accepted without
proof." Bertrand Russell
[1]
http://lucifer.com/pipermail/extropy-chat/2005-February/013883.html
[2] http://iangoddard.net/paranorm.htm
[3] http://lucifer.com/pipermail/extropy-chat/2005-February/013942.html
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