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

From: Eray Ozkural exa (examachine_at_gmail.com)
Date: 11/28/04 

Date: 28 Nov 2004 14:17:37 -0800

"Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message news:<87wtw7pa62.fsf@phiwumbda.org>...
> 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>.

I've read all the notes, yes. Cantor proposes a solution.

Maybe Galileo's paradox still persists, though.

> 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.)

Lecture notes, inspired by textbooks he teaches. Philosophy is not
like technology, it doesn't date that quickly. But thanks for the
caution: I should be looking in the textbooks myself.

If the current poster did not think that there could be more
preferable formalizations of "infinity", he would not suggest looking
in Galileo's paradox. He would have deemed it "solved".

Regards, 

--
Eray Ozkural

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