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, rclo...@verizon.net
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 <stephe...@charter.net > 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 <stephe...@charter.net > 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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