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Mike Kelly wrote:
> Tony Orlow wrote:
> > Mike Kelly wrote:
> > > Tony Orlow wrote:
<snip>
> > > 2) How come noon "exists" in this experiment but it didn't exist in the
> > > original experiment? Or did you give up on claiming noon doesn't
> > > "exist"? What does that mean, anyway?
> >
> > Nothing is allowed to happen at noon in either experiment.
>
> Nothing "happens" at noon? I take this to mean that there is no
> insertion or removal of balls at noon, yes? Well, I agree with that.
Hmm. Yes, there is no ball whose insertion time or removal time is
noon. But it seems to me that this "happen" is underdefined in a way
that can cause confusion. Does something "happen" to either of these
functions at x=0:
f(x) = 1 if x<0 ; 0 if x>=0
g(x) = 1 if x<=0 ; 0 if x>0
It seems to me that it is true (within the accuracy of normal
communication) to say that both f() and g() "drop from 1 to 0 at x=0"
even though the functions are different.
Similarly, it seems to me that clearly something "happens" (in any
normal sense) at noon in the standard vase problem - what happens is
that the frenzy of unending sequences of insertion and removal come to
a halt.
Good luck with the rest of this anyway... <g>
> How about this experiment, does noon "exist" in this experiment :
>
> Insert a ball labelled "1" into the vase at one minute to noon.
>
> ?
>
> >They both end up with countably many balls in the vase at noon.
>
> For now, I am going to try to restrict myself to discussing this new
> experiment, because I want to understand what "noon doesn't exist" is
> supposed to mean. And, again, your answer is ambiguous. I asked which
> balls are in the vase at noon, not the cardinality of the set of balls
> in the vase at noon. I then asked whether "noon exists", not whether
> anything "happens" at noon. Please try answering the questions people
> actually ask; it aids in communication.
Of course, using words with their standard meanings would also be a big
help - who knows what "countably" means in Tony's claim above.
Brian Chandler
http://imaginatorium.org
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