[Home]RealLife/Proof

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It is provable that, from our perspective as wikizens, there can be considered to be no RealWorld:

1) RealWorld is defined to be that which lies outside ToothyWiki (that which is not ToothyWiki)
2) This definition supposes an ordered field on the location in the nesting hierarchy (ie. A is outside B and B is outside C, hence A is outside C)
(PeterTaylor) Given the definition of "outside" in 1, you don't have an ordering at all, because the definition is symmetrical and partial orders are antisymmetrical. (Nor do partial orders have to be over fields, FWIW).
Look, I wrote this at 3:30am OK? It's not rigorous or we'd be in real trouble. - CorkScrew
Yes, I think PeterTaylor is neglecting point 10 below. Probably deliberately, but... --AlexChurchill
Anyway, the flaw is that the definition does *not* suppose an ordered field if you want to be picky. - CorkScrew
3) All ordered sets are infinite
(PeterTaylor) Not true. I present as a counter-example the empty set.
Oops, I meant field - CorkScrew
(PeterTaylor) Okay, then. Z_2.
What do you mean by Z_2?
The integers modulo 2.
Look, we did this in N&S. If an ordered field were finite then a<b => a+c<b+c would be false.
Ah, so an ordered field isn't just a field with a total ordering?
I meant a field with a relation "<" such that a<b => a+c<b+c for all a,b,c and a>0,b>0 => ab>0. I think. and Z_2 contradicts this as 0<1 but 0+1>1+1 mod 2
4) Hence there must be something outside RealWorld (in fact an infinite number of things).
(Vitenka) And haven't you mixed up field and set here?
5) Hence RealWorld + ToothyWiki is not exhaustive
6) But we have defined RealWorld as that which is not ToothyWiki
7) Contradiction hence the ordered field in qustion cannot exist
8) Hence there is not necessarily anything outside ToothyWiki - indeed, the concept of "outside" may have no meaning
9) Then, by Occam's Razor we can ignore the possibility of anything outside ToothyWiki without loss of generality
10) Only at SillyOClock could any of this make sense.



CategoryMaths CategoryWiki CategoryLanguageGettingInTheWayOfLogic

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Last edited April 7, 2004 7:20 pm (viewing revision 15, which is the newest) (diff)
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