[extropy-chat] Possible Worlds Semantics

[Ian Goddard]

Correction to my last post (a missing "NOT")...

--- Ian Goddard <iamgoddard at yahoo.com> wrote:

> > Suppose instead that the sons were not permitted 
> > to look at each other, but instead they had to 
> > write their confirmation of the deal on separate
> > pieces of paper and hand them to their father?  
> > What should they write?"
> 
> Given:
> 
> First son = A
> Second son = B
> 
> A's envelope has $10^4
> B's envelope has $10^3
> 
> Answer:
> 
> B should write: "If A wants to know if I say 'yes'
> to the switch, then I agree to switch."

 MAKE THAT: "... then I do NOT agree to switch."

 Or B could write: "If A wants to know if I want to
know if he wants to know if I say 'yes' to the switch,
then I agree to switch." 


> A should write: "If B wants to know if I want to
> know if he says 'yes' to the switch, then I do NOT
> agree to switch." 
> 
> Trying to explain my answer runs into describing a
> thicket of nested possible worlds where each brother
> needs to know what the other needs to know about
> the other in order to know/infer if the other has
> a higher or lower valued envelope. The critical 
> parameters are the max and min values and knowing 
> that someone with the max will necessarily say "NO 
> switch," and someone with the min will necessarily 
> say "switch." Given the indicated amounts, neither 
> can assume the other has the max or min. However, 
> the effect of those necessary answers flows through 
> the nested set of "other minds" in possible worlds 
> each builds in trying to sense what the other got.
> ~Ian
> 
> 

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