Re: Epistemology 201: The Science of Science

From: aeo6 (aeo6_at_cornell.edu)
Date: 02/21/05 

Date: Mon, 21 Feb 2005 10:15:49 -0500

Allan C Cybulskie said:
>
> "robert j. kolker" <nowhere@nowhere.net> wrote in message
> news:37ebq0F5bcpooU1@individual.net...
> >
> >
> > Allan C Cybulskie wrote:
> > > I've already dealt clearly with that. It's merely a word game, since
> > > infinity is the largest number that we can talk about. But that does
> not
> > > allow us to go beyond that and draw any inferences beyond "we can't talk
> > > about the extra elements because we don't have a terminology for it).
> >
> > Not a word game. A < B (in the sense of cardinality)
>
> In short, the cardinality is less in this case. What does this have to do
> with number of elements, or any of the analysis I provided?
>
> > According to you anything you cannot comprehend is a word game.
>
> Stephen asked me what infinity + infinity was. Since I expect that he would
> not have approved of an answer of "2 * infinity", I saw the question as only
> possible leading to the answer "infinity", and then to the reply that
> therefore the set (0,1) has a number of elements equalling infinity and the
> set (0,2) has a number of elements equalling infinity, and so there was no
> reason to claim that the set (0,2) had to have more elements. But that's a
> word game based on the fact that we won't say "2 * infinity", not an actual
> argument.
>
> Surely
> > the sign of a less than first rate intellected. I suggest you give up on
> > mathematics and take up floor polishing, dish washing or even computer
> > programming.
>
> This is probably more ironic than you know.
>
> Besides, who said I was all that interested in mathematics? I merely
> exercise my right to not allow people playing word games to pull the wool
> over my eyes.
>
>
>
Thank you Allan. You are obviously no less than a first rate intellect
as far as I can tell. Probably the only way to see beyond Cantor is to
NOT be a mathematician by trade. I guess my problem here is that I HAVE
been trying to say infinity+infinity=2*infinity, as long as you're
talking about the same infinity consistently. I'm not sure why people
have such a hard time conceiving ratios between infinite sets that are
less than a power-set ratio. Even when there are an infinite number of
rationals for each natural number, they are assigned the same
cardinality, because of this counting method. It's nice to hear that
someone else detects double-speak when it comes to mathematicians
interpreting Cantor's cardinalities, vis a vis number/size/cardinality.
Either I'm not crazy, or at least I'm not alone.

Thanks! 

-- 
Smiles,
Tony

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