On Wed, 12 Sep 2001, Chen Yixiong, Eric wrote:
Actually it isn't Godel's (which just says some statements can't be found definitively true or false - it is undecidable). However, Arrow's Impossibility Theorem does(!) do exactly what you want.
According to the Theorem page at: http://www.personal.psu.edu/staff/m/j/mjd1/arrowimpossibilitytheorem.htm
I think I did not draw parallels to my writings below.
???? That sentence is without meaning as worded.
The theorm seems to apply for democratic systems, but here I write about systems in general.
But that's exactly(!) why Arrow's applies. Fairness (ie democratic) as individual choice (ie vote). The fact that there are no democratic (ie fair) mechanisms by which to make selections is what damns Crypt-Anarchic-Capitalist-Libertarian (CACL) thought. A good example is to apply voting theory to David Friedmans law by contract examples. One can cast CACL thought as democratic thought except for a single difference. Democratic thought requires all to be responsible to the same set of rules and policies. CACL doesn't. CACL thought has three fundamental flaws. One, it requires individuals to behave in a manner inconsistent with their biology. People ain't rational in any sort of consistent manner. Second, it says that if we get rid of government people will resolve their own problems. However, this statement can be turned into a 'democratic election' (ie the participants have their own choices to make - a vote) yet we can prove mathematically that such a solution is impossible if there are more than two (2) participants. Now I don't know about you but anything worthy of the label 'society' must have more than two (2) people involved. Finaly, it assumes that all issues and decisions one makes in life can be reduced to 'economic' decisions. While that is certainly possible it is clear that not all issues are deal with equitably in such a manner. (It's also applicable to Tim May's commentary a while back about the 'solved n-division' problem (which can also be shown to be a vote if the remainder is indivisible or can't be re-connected) and the fact that he seems to think that the solution that is out there now is universal. When in fact it applies to such a small fraction of n-division problems as to be worthless. The proof is in the 'remainder' and it's characteristics. Most of reality doesn't comply with the requirements for 'fair divisibility' - too granular.)
I think we had referred to different versions of Godel's Theorem, where I use this version : "No system of rules can have both completeness and consistency (including social systems applied to humans)".
But a social system isn't (just) a 'system of rules'. It also has beliefs and various cause-effect and dependency issues related to environment and biology that cause Godel's to be inapplicable. The fact that it consists of anything(!) more than a system of rules is enough to invalidate Godel's. Godel's simply isn't applicable to a broad enough set of examples. Though Godel's may keep you from proving it). The reality is that the concept of 'social system' is entirely too broad for the conept of 'self-consistent language' to be applied. Where did the requirement for 'consistency' in a social setting come from in the first place? And what does 'consistency' actually mean in that context? A naive interpretation might be that they always make decisions the same way or perhaps the same selection. Either will fail because it won't respond to changes in the environment. Clearly in conflict with the premise of being 'consistent'. -- ____________________________________________________________________ natsugusa ya...tsuwamonodomo ga...yume no ato summer grass...those mighty warriors'...dream-tracks Matsuo Basho The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage@ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------