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.`

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On 8/24/2012 6:39 AM, Roger Clough wrote:

Hi Stephen P. KingHmmmm. I guess I should have know this, but if there are unproveablestatements,couldn't that also mean that the axioms needed to prove them havesimply beenoverlooked in inventorying (or constructing) the a priori ? If so,then couldn't thesemissing axioms be suggested by simply asking what additional axiomsare neededto prove the supposedly unproveable propositions? Roger Clough, rclo...@verizon.net <mailto:rclo...@verizon.net> 8/24/2012Leibniz would say, "If there's no God, we'd have to invent him soeverything could function."----- Receiving the following content ----- *From:* Stephen P. King <mailto:stephe...@charter.net> *Receiver:* everything-list <mailto:everything-list@googlegroups.com> *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 <mailto: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 <mailto: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 --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email toeverything-list+unsubscr...@googlegroups.com.For more options, visit this group athttp://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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.