Re: Obections to Cantor's Theory (Wikipedia article)

Han de Bruijn wrote:

> Daryl McCullough wrote:
>
> > Instead of using the term "size" to refer to sets, we could
> > refer to the "bloppitude".
> >
> > Instead of using the words "infinite", we could use the term
> > "mega-bloppity".
> >
> > Nothing of any importance about mathematics would change
> > if we substituted different words for the basic concepts.
> > In contrast, your arguments are about nothing *but* terminology.
> > To me, that shows that there is no actual content to your
> > arguments.An actual mathematical argument does not depend on word > > choice.
> >
> > As a challenge, see if you can express your claims about
> > infinite sets, or infinite naturals, or set size, or whatever,
> > *without* using the words "infinite", "larger", "size", etc.
>
> This clearly represents the formalist (Hilbertian) view on
> mathematics as a "senseless game with symbols".
>
> Han de Bruijn

Would you please say exactly where Hilbert said that mathematics is a
"senseless game with symbols"?

And the remarks of the poster to whom you responded do not "clearly
represent" that he considers mathematics to be a "senseless game of
symbols". On the contrary, I take him to be saying that mathematics is
made senseless by appropriating mathematical terminology in vague,
equivocal, and inconsistent ways. I understand the poster's point to be
that one's mathematics shouldn't depend on the suggestiveness of
metaphorical jargon, but rather on defintions and proof. Set theorists
express ideas through the relations among primitive and defined terms,
not by relying upon penumbral associations of the terms. You missed
that point and made a strawman of the poster's view and Hilbert's views
too.

MoeBlee

.

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