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?

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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