In Cantor's diagonal argument, the contradiction originates from the hidden presumption that the definition of Cantor's number is complete. The contradiction shows that the definition of Cantor's number is incomplete. Thus Cantor's diagonal argument is invalid. [Chaohui Zhuang: "Wittgenstein's analysis on Cantor's diagonal argument", philpapers (2010)]

On Friday, 3 December 2021 at 08:56:05 UTC+1, WM wrote:
> In Cantor's diagonal argument, the contradiction originates from the hidden presumption that the definition of Cantor's number is complete. The contradiction shows that the definition of Cantor's number is incomplete. Thus Cantor's diagonal argument is invalid. [Chaohui Zhuang: "Wittgenstein's analysis on Cantor's diagonal argument", philpapers (2010)]

It's clearer with the nested intervals: take the limit of the sequence, just don't take the limit of the indices.

But Hilbert and his full hotels that aren't full is even worse, not even the excuse of a nervous break-down.

Anyway in the context of three centuries of frauds and progressive self-enslavement: the history of western incivilization in a nutshell.

Julio

fredag 3 december 2021 kl. 09:13:55 UTC+1 skrev ju...@diegidio.name:
> On Friday, 3 December 2021 at 08:56:05 UTC+1, WM wrote:
> > In Cantor's diagonal argument, the contradiction originates from the hidden presumption that the definition of Cantor's number is complete. The contradiction shows that the definition of Cantor's number is incomplete. Thus Cantor's diagonal argument is invalid. [Chaohui Zhuang: "Wittgenstein's analysis on Cantor's diagonal argument", philpapers (2010)]
> It's clearer with the nested intervals: take the limit of the sequence, just don't take the limit of the indices.
>
> But Hilbert and his full hotels that aren't full is even worse, not even the excuse of a nervous break-down.
>
> Anyway in the context of three centuries of frauds and progressive self-enslavement: the history of western incivilization in a nutshell.
>
> Julio

None of this is enslavement and are you too dumb to understand how infinity works, just like WM?

WM wrote :
> In Cantor's diagonal argument, the contradiction originates from the hidden
> presumption that the definition of Cantor's number is complete. The
> contradiction shows that the definition of Cantor's number is incomplete.
> Thus Cantor's diagonal argument is invalid. [Chaohui Zhuang: "Wittgenstein's
> analysis on Cantor's diagonal argument", philpapers (2010)]

"I have not found in Wittgenstein's Philosophical Investigations
anything that seemed to me interesting and I do not understand why a
whole school finds important wisdom in its pages. Psychologically this
is surprising. The earlier Wittgenstein, whom I knew intimately, was a
man addicted to passionately intense thinking, profoundly aware of
difficult problems of which I, like him, felt the importance, and
possessed (or at least so I thought) of true philosophical genius. The
later Wittgenstein, on the contrary, seems to have grown tired of
serious thinking and to have invented a doctrine which would make such
an activity unnecessary. I do not for one moment believe that the
doctrine which has these lazy consequences is true. I realize, however,
that I have an overpoweringly strong bias against it, for, if it is
true, philosophy is, at best, a slight help to lexicographers, and at
worst, an idle tea-table amusement." -- Bertrand Russell

On 12/3/2021 1:55 AM, WM wrote:
> In Cantor's diagonal argument, the contradiction originates from the hidden presumption that the definition of Cantor's number is complete. The contradiction shows that the definition of Cantor's number is incomplete. Thus Cantor's diagonal argument is invalid. [Chaohui Zhuang: "Wittgenstein's analysis on Cantor's diagonal argument", philpapers (2010)]
>

"...Wittgenstein..., an idle tea-table amusement." -- Bertrand Russell