Hi Roger,
The point is that there exist (provably!) statements that are
infinite and thus would require proofs that can effectively inspect
their infinite extent. We could argue that induction allows us to
shorten the length to a finite version but this does not cover all. For
instance, consider a proposed theorem that states that there exists a
certain sequence of digits in the n-ary expansion of pi. How does one
consider the proof of such a theorem? Constructability (by fiite means)
is the key to our notions of "understanding", etc. and have lead some
people to reject all math that does not admit constructable proofs. This
is a HUGE problem in mathematics and by extension philosophy.
On 8/24/2012 6:39 AM, 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?
Roger Clough, [email protected] <mailto:[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 <mailto:[email protected]>
*Receiver:* everything-list <mailto:[email protected]>
*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] <mailto:[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] <mailto:[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
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
--
Onward!
Stephen
http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
