Re: Anybody read and understood A. Garciadiego, BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC PARADOXES ?

On May 4, 3:38 pm, galathaea <galath...@xxxxxxxxx> wrote:
On Apr 22, 12:21 pm, philneo2...@xxxxxxxxx wrote:





On Apr 20, 9:12 am, translogi <wilem...@xxxxxxxxxxxxxx> wrote:

On Apr 19, 10:14 pm, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:

On 2007-04-19, philneo2...@xxxxxxxxx wrote:
The most important thing now is to trace the pernicious influence of
natural mathematics--the "mathematics" developed to cope with the
"paradoxes"--through the other disciplines. Try this paper:

Ryskamp, John Henry, "Paradox, Natural Mathematics and Twentieth-
Century Ideas" (April 14, 2006). Available at SSRN:http://ssrn.com/abstract=897085

As far as bizarre waffling goes this is not a bad piece. Alas, it has
nothing to do with the actual history (or content) of set theory, Gödel's
theorems, relativity and what not. A much better source on the history of
set theory is M. Hallett's _Cantorian Set Theory and Limitation of Size_.

--
Aatu Koskensilta (aatu.koskensi...@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

I don't understand the book,

I tried

According to the book there is something strange in Cantors paradox.
How can you contenate two infinite sets, for this you need to go to
the end of the first infinite set to contentate the beginning of the
second set.and that is a bit impossible. (you can not go to the end of
an infinite set)

I think you can "zip" two infinite sets
(for example the sets of even and odd numbers)
(first an even number) - (first odd number) -(the next even number) -
(the next odd number) -(the next even number) - (the next odd number)
and so on
but you can not put them after eachother.
(first all even numbers) then all odd numbers.

But i don't understand Cantors paradox enough to understand if that
undermines the whole proof.
(And am very doubtfull is it undermines all other paradoxes)- Hide quoted text -

- Show quoted text -

According to Garciadiego, there is no such thing as Cantor's paradox,
so what is "strange" about it? It's pretty clear that the supposed
"paradox" of Cantor is simply the result of misunderstanding of the
history. The real culprit here is the megalomaniac Russell.

I don't think you're reading very closely. Aatu has not read
Garciadiego, apparently, and Hallett does not discuss Garciadiego.
Hallett is a hagiographer of Cantor, and apparently Aatu is another
uninformed worshiper as well. Utterly ridiculous in this day and age,
with both Grattan-Guinness and Garciadiego now having published books
which undermine Cantor.

Remember, this is the same Cantor who, Garciadiego says, produced
ideas so unsound that they seem like the product of a "charlatan."
Still a fan of Cantor? Cantor is utter drivel and nonsense, and so is
the "natural" mathematics developed to "answer" the paradoxes.
Hilbert and Poincare are just as ridiculous as Cantor. Garciadiego
should make this perfectly clear to you.

You should read Grattan-Guinness on Poincare. Utterly scathing.

i just wanted to thank you for the reference on grattan-guinness

poincare has been one of the very few personalities
whose entire career i have studied in depth
and i have always looked for references and analyses of his ideas and
papers

g-g's book " the search for mathematical roots: 1870-1940 "
has also led me to realise i never pursued studying couturat
and probably should

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar- Hide quoted text -

- Show quoted text -

Welll, Grattan-Guinness is not the important one to read. Garciadiego
is. By the way, I have slightly updated my paper with a quote by
Einstein showing clearly his adoption of "natural" mathematics.

Ryskamp, John Henry, "Paradox, Natural Mathematics and Twentieth-
Century Ideas" (April 14, 2006). Available at SSRN: http://ssrn.com/abstract=897085

ALSO

Ryskamp, John Henry, "The Pratt-Ryskamp Exchange on Set Theory,
Paradox, Garciadiego and the Foundations of Computer Science" (May 2,
2007). Available at SSRN: http://ssrn.com/abstract=984129

.

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    ... nothing to do with the actual history of set theory, ... set theory is M. Hallett's _Cantorian Set Theory and Limitation of Size_. ... Garciadiego, apparently, and Hallett does not discuss Garciadiego. ... Hallett is a hagiographer of Cantor, ...
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