Re: Logarithm of transfinite numbers

Do you ever remove more than one at a time? No. Does the vase
become empty? According to you.

So far we understand each other.

So, how many balls were in the vase right before it became empty?

Please define "right before". You can answer that with an Iteration #
for some n, or if you prefer, give me a time T. Once I know what you
mean by "right before", I can happily give you answer.

Yes, you have a contradiction here. According to the gedanken,
you must have had -9 balls in order to empty the vase.

The gendanken says nothing of the kind. The only contradiction here is
with the false assumption that there is a last iteration before the
process ends. And this is a false assumption that you are making, not
I. The gendanken, once freed from your erroneous proposition, quite
contently and consistently empties all the balls from the bin, one at
at time, Ball #n at Iteration #n.

I didn't label the balls. I don't need labels.

No of course you don't! The labels are entirely your undoing here!
You want to change the problem and ignore the labels, because you know
(whether you wish to admit it publically or not), these labels entirely
throw out your whole theory.

You ask about the labels. I say they don't matter. The balls are
all labeled '1', okay. It doesn't matter. This is one of many reasons
I cannot ascribe to transfinite set theory.

So instead of honestly answering the question as given, with the
labels, you choose instead to pretend they don't matter. But if they
didn't matter, you wouldn't have a problem answering the questions,
would you? They matter all right. They matter so deeply that your
house of cards crumbles with their admission. You so desperately want
to avoid the labels, but I'm not letting you. If they truly don't
matter, then you should be able to answer the damn question.

But you can't, can you? All these many months of posting and hours
upon hours of investing yourself into this group, you are finally
seeing a flaw, a crack in your armor. You would rather throw out the
thought experiment than face the possibility that this past year's
postings have all been in vain.

I know you still deeply believe that the growth of 9n balls per
iteration leads to an infinite number of balls at the end. And I know
you believe deeply that your system is equi-consistent, at least until
recently. But now, you are finding that there are unnatural
side-effects to your theory, and it's here that I am asking you to have
the courage of your convictions and intellectual courage to honestly
answer these tough questions.

Ever vigilant,

Jonathan Hoyle

.

Relevant Pages

  • Re: Logarithm of transfinite numbers
    ... with the false assumption that there is a last iteration before the ... You want to change the problem and ignore the labels, ... It doesn't matter. ... iteration leads to an infinite number of balls at the end. ...
    (sci.math)
  • Re: Logarithm of transfinite numbers
    ... you must have had -9 balls in order to empty the vase. ... with the false assumption that there is a last iteration before the ... You want to change the problem and ignore the labels, ...
    (sci.math)
  • Re: Logarithm of transfinite numbers
    ... become empty? ... you must have had -9 balls in order to empty the vase. ... You want to change the problem and ignore the labels, ... It doesn't matter. ...
    (sci.math)
  • Re: Logarithm of transfinite numbers
    ... Where the labels go, so go the balls. ... Yes, the balls disappear. ... one is removed, one at a time, with Ball #n being removed at Iteration ...
    (sci.math)
  • Re: infinity
    ... > Virgil said: ... > My point is that the labels don't matter. ... > number of the balls going in and out and you have the answer. ...
    (sci.math)