Jesse Mazer wrote:
Also, I'm still confused about your original argument:
"Since you agree that the number of histories is on a continuum, you
must accept that no matter how large or small a segment of the
continuum is considered, the number of histories is the same. Hence
measure is the same for any observer."
What is the "number of histories" that is the same here? Weren't you
saying the number is infinity? And do you agree that in general it is
not correct to say that because two sets contain an infinite number of
elements, that means their measure must be the same?
I am only talking about the cardinality of the continuum as applied to
the number of histories and its implication regarding measure: Since the
number of histories included in the past of an observer - and consistent
with his present - has the same infinity as the continuum, then this
cardinality is the same for any observer. To ask an observer about his
own measure (when he is alive of course) is meaningless.
As an example consider the following hypothetical situation: suppose
that one of the greatest scientist such as Isaac Newton had never been
born. Classical Mechanics would still have been invented, but years
later, maybe centuries later and the course of our civilazation would
have been different. Surely his birth was an unlikely event. Does it
mean that our civilizaton has a low measure compared to retarded
civilization where he was never born? It sure does not "feel" like it -
from a first person point of view.
The only way to talk meaningfully about measure is when you can compare
two situations from a third person point of view: for example, if you
witness someone die from a freak event you could conclude that he
continued living in a world with lower measure than yours. This is a
third person point of view. However, from that person's point of view
(first person), the freak event never happened and therefore he will
consider his measure to be just as high as yours.