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Tony Orlow wrote:
> Mike Kelly wrote:
> > Tony Orlow wrote:
> >> Mike Kelly wrote:
> > <snip>
> >>> Now correct me if I'm wrong, but I think you agreed that every
> >>> "specific" ball has been removed before noon. And indeed the problem
> >>> statement doesn't mention any "non-specific" balls, so it seems that
> >>> the vase must be empty. However, you believe that in order to "reach
> >>> noon" one must have iterations where "non specific" balls without
> >>> natural numbers are inserted into the vase and thus, if the problem
> >>> makes sense and "noon" is meaningful, the vase is non-empty at noon. Is
> >>> this a fair summary of your position?
> >>>
> >>> If so, I'd like to make clear that I have no idea in the world why you
> >>> hold such a notion. It seems utterly illogical to me and it baffles me
> >>> why you hold to it so doggedly. So, I'd like to try and understand why
> >>> you think that it is the case. If you can explain it cogently, maybe
> >>> I'll be convinced that you make sense. And maybe if you can't explain,
> >>> you'll admit that you might be wrong?
> >>>
> >>> Let's start simply so there is less room for mutual incomprehension.
> >>> Let's imagine a new experiment. In this experiment, we have the same
> >>> infinite vase and the same infinite set of balls with natural numbers
> >>> on them. Let's call the time one minute to noon -1 and noon 0. Note
> >>> that time is a real-valued variable that can have any real value. At
> >>> time -1/n we insert ball n into the vase.
> >>>
> >>> My question : what do you think is in the vase at noon?
> >>>
> >> A countable infinity of balls.
> >
> > 1) It's not clear to me what you mean by that phrase but I'll assume
> > the standard definition. Still, the question remains of which balls you
> > think are in the vase? Does every natural number, n, have a ball in the
> > vase labelled with that n?
>
> Conceptually, sure.
Yes or no? What is the set of balls in the vase at noon? Which balls
are in the vase and which are not?
> > 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.
But what relevence does this have to the statement "noon does not
exist"? What does that even *mean*?
When you've been saying "noon doesn't exist", you actually mean to say
"no insertion or removal of balls occurs at noon"?
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.
>The experiment's stated sequence logically precludes that the vase become
>empty.
It logically precludes that balls without a finite natural number on
them get added to the vase, but that doesn't seem to bother you. Ho
hum.
<snip more stuff about original experiment>
--
mike.
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