[extropy-chat] Possible Worlds Semantics

[Adrian Tymes]

--- Hal Finney <hal at finney.org> wrote:
> The topic is "common knowledge", information for which we can say
> that
> I know it, you know it, I know you know it, you know I know it, I
> know
> you know I know it, and so on, indefinitely.

> I will add an additional question, to get the analysis started: is
> the
> first part of the reasoning correct?  That is, suppose you were the
> first son in the example above, you opened your envelope to see
> $10,000,
> are you correct to say that you would pay $1 to switch?  This is
> before
> you even know that your brother is going to be asked.

The problem is, the answer to this relies on one crucial part of
non-common knowledge: what the contents are of the other brother's
envelope.  Each brother must decide based on the information that that
brother possesses.