Re: Zenkin's paper on Cantor (reply of Dr. Zenkin)

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 11/27/04 

Date: Sat, 27 Nov 2004 16:46:13 +0100

examachine@gmail.com (Eray Ozkural exa) writes:

> "Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message news:<87d5y1vm2f.fsf@phiwumbda.org>...
>> examachine@gmail.com (Eray Ozkural exa) writes:
>>
>> > "Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message news:<87fz2zfzid.fsf@phiwumbda.org>...
>> >> > Since there is the observed antinomy of the infinitely big,
>> >> > unfortunately "size of a set" is far from being an obvious concept.
>> >>
>> >> What antinomy is that?
>> >
>> > Dear Jesse, search for the paradox of the infinitely big on google.
>> > I'm sure you will find a few philosophers who have better command of
>> > English than I have.
>>
>> Can't find anything. Can you name some names? Give a hint of what
>> the actual antinomy is? Give some reference more specific than
>> Google?
>
> http://ls.poly.edu/~jbain/philmath/philmathlectures/M01.Intro.pdf
>
> There are probably better expositions than these slides, but that's
> the best thing I could find.

Certainly, you should check out the rest of the site. That way,
you'll see that his solution to the *apparent* paradoxes of infinite
sets is to follow Cantor. As far as I can tell, he presents the slide
you refer to for historical reasons and to motivate the later
discussion on Cantor.

See
<http://ls.poly.edu/~jbain/philmath/philmathlectures/M05.Cantor.pdf>.

In any case, let's not confuse lecture notes with philosophy of
mathematics research. Why not point me to a recent publication on
paradoxes of infinitely big written by a working philosopher of
mathematics?

(Not that Bain is or isn't a working philosopher of mathematics, but
lecture notes aren't a good indication of current issues in
philosophy.) 

-- 
Jesse F. Hughes
"Well, you know as soon as you have a new number I will be happy to
add it to the list.  Don't try those childish tit-for-tat games with
me."                          -- Ross Finlayson on Cantor's theorem.

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