Re: infinity

guenther vonKnakspot wrote:
> William Hughes wrote:
> > guenther vonKnakspot wrote:
> > > step...@xxxxxxxxxx wrote:
> > > <snip>
> > > > > Are you saying then that one single performance of the experiment
> > > > > delivers one single vase which is empty for person A and simultaneously
> > > > > is not empty for person B, because A does not know which balls were
> > > > > removed while B does?
> > > >
> > > > No. How did you come to that conclusion?
> > > >
> > > > A ball is either removed or it is not. If you describe
> > > > exactly how the balls are removed than there is one and
> > > > only one answer
> > >
> > >
> > > Then it would appear that you did not follow my articles. Let me repeat
> > > for you. Suppose the balls are not labeled on the outside but inside,
> > > so that person A who is performing the experiment does not see which
> > > balls he is putting out, and which ones he is taking out. Person B has
> > > a device which enables him to see which balls are being put into the
> > > vase and which ones are being taken out. Person A performs the
> > > experiment every morning, untill person B determines that the
> > > experiment performed is exactly the one described as experiment 1 by
> > > the OP. Now we have a situation in which A would end up with a non
> > > empty vase (he has been dropping 10 indistinguishable balls into the
> > > vase and taking one out all morning long) while B knows that for every
> > > natural number n the ball labelled n has been taken out of the vase. So
> > > which one is it, is the vase empty or not?
> > >
> >
> > Why do you think that A will end up with a non empty vase?
> > Depending on which balls A removes he may end up with any
> > number of balls in his vase from 0 to infinity. A does not
> > know what is going to happen. B waits for a day when A uses
> > (unintentionally since A cannot read labels) a strategy that
> > leads to an empty vase. Both A and B agree that the vase
> > is empty. (B knows the order in which A removed the balls,
> > A doesn't, but the fact that the balls can be labelled means
> > that this order exists.)
> >
> > -William Hughes
>
> Because there is no reason for A to end up with an empty vase. A has
> been dropping 10 balls into the vase and taking one out. The whole
> contention that B finds the vase to be empty is that B knows that for
> any n in the set of natural numbers, the ball labelled n is not inside
> the vase.
>

But the whole point is that it is possible to perform the operation
"drop 10 balls into the vase, take one out" an infinite number of
times and end up with an empty vase. A knows this.
So A is not surprised to see an empty vase, even though he
does not know exactly how this happened. It is not necessary
for A to know how he got an empty vase for A to know that the
vase is empty.

-William Hughes

.

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