Date: Mar 3, 2013 4:33 PM
Subject: Re: Matheology � 222 Back to the roots
WM <firstname.lastname@example.org> wrote:
> > > Question: Do you find your characterization of the situation in
> > > finished infinity not silly?
Nowhere nearly as silly as WM's characterizations which require for
every sequence a last but both concrete and evanescent member.
> > > Don't you see a mathematical
> > > contradiction of the sentence: There are all FIS of d in the list but
> > > not in one single line?
Only if there is a fixed last line rather than, as in real math, for
each line a successor, just as for each natural there is a successor.
> > Not at all. Clearly
> > there are all FIS of d in one single line
> > iff there is a last line.
> > I do not consider the sentence
> > "There is no last line"
> > to be a contradiction.-
> But "there are all FIS" is not a contradiction
But "there are all FIS in one single line" IS a contradiction, when, as
here, for each line there is a successor line longer than the line
WM seems to want to live in a mathematical world where one can never
have a situation where the existence of each member of a set of objects
requires the existence of a successor object in the set distinct from
both the object itself and from all its predecessor objects in the set.
Since that sort of situation abounds in standard mathematics,
WM is out of it.