On 24 Aug 2012, at 12:39, Roger Clough wrote:
Hi Stephen P. King
Hmmmm. I guess I should have know this, but if there are
unproveable statements,
couldn't that also mean that the axioms needed to prove them have
simply been
overlooked in inventorying (or constructing) the a priori ? If so,
then couldn't these
missing axioms be suggested by simply asking what additional axioms
are needed
to prove the supposedly unproveable propositions?
You can add the new statement, but then you get a transformed machine,
and it will have new unprovable statement, or become inconsistent.
Tkae the machine/theory having the beliefs:axioms:
1)
2)
Suppose the machine is consistent.
Then the following below is a new consistent machine, much richer in
probability abilities:
1)
2)
3) "1) + 2)" is consistent.
But the one below:
1)
2)
3) "1) + 2) + 3)" is consistent.
which can be defined (the circularity can be eliminated by use of some
trick) will be inconsistent, as no machine can ever prove consistently
his own consistency.
Bruno
Roger Clough, [email protected]
8/24/2012
Leibniz would say, "If there's no God, we'd have to invent him so
everything could function."
----- Receiving the following content -----
From: Stephen P. King
Receiver: everything-list
Time: 2012-08-23, 13:28:00
Subject: Re: Emergence
Hi Richard,
You mean "provable statements" not "truths" per se... I guess.
OK, I haven't given that trope much thought.... I try to keep
Godel's theorems reserved for special occasions. It has my
experience that they can be very easily misapplied.
On 8/23/2012 1:24 PM, Richard Ruquist wrote:
Stephan,
Strong emergence follows from Godel's incompleteness because in any
consistent system there are truths that cannot be derived from the
axioms of the system. That is what is meant by incompleteness.
Sounds like what you just said. No?
Richard
On Thu, Aug 23, 2012 at 1:20 PM, Stephen P. King <[email protected]
> wrote:
Hi Richard,
Ah! http://en.wikipedia.org/wiki/Strong_emergence
"Strong emergence is a type of emergence in which the emergent
property is irreducible to its individual constituents."
OK, but "irreducibility" would have almost the same meaning as
implying the non-existence of relations between the constituents
and the emergent. It makes a mathematical description of the pair
impossible... I don't think that I agree that it is derivable from
Godel Incompleteness; I will be agnostic on this for now. Could you
explain how it might?
On 8/23/2012 1:10 PM, Richard Ruquist wrote:
It is said that strong emergence comes from Godel incompleteness.
Weak emergence is like your grains of sand.
On Thu, Aug 23, 2012 at 12:48 PM, Stephen P. King <[email protected]
> wrote:
Hi Richard,
Pratt's theory does not address this. Could emergence be the
result of inter-communications between monads and not an objective
process at all? It is useful to think about how to solve the
Sorites paradox to see what I mean here. A heap is said to emerge
from a collection of grains, but is there a number or discrete or
smooth process that generates the heap? No! The heap is just an
abstract category that we assign. It is a name.
On 8/23/2012 9:44 AM, Richard Ruquist wrote:
Now if only someone could explain how emergence works.
Can Pratt theory do that?
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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