Re: Contradiction in mathematics Hilbert's paradox of the Grand Hotel outlaws ZFCs axiom of infinity

On Mar 21, 1:24 am, byron <spermato...@xxxxxxxxx> wrote:
On Mar 21, 5:47 am, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

Moreover, specifically, you've not shown that the thought experiment
Hilbert's Hotel entails that Z set theory is inconsistent.

colin leslie dean has shown the skolem paradox proves ZFC is
inconsistent
dont
say skolem solved the paradox
as skolems solution is not accepted because it destroys ZFC- as skolem
noted himself

(1) You said Hilbert's Hotel proves ZFC is inconsistent. Now you've
switched to Skolem's paradox.

(2) It's not been shown that Skolem's paradox proves that ZFC is
inconsistent. What sequence of formulas that is a proof in the
language of set theory of a sentence P & ~P do you claim to exist?

(3) Skolem, despite his criticisms of set theory, did not claim that
his result proves that ZFC is inconsistent. Especially in the quote
you provided, Skolem does not claim that ZFC is inconsistent:

Skolem states "I believed that it was so clear that axiomatization in
terms of sets was not a satisfactory ultimate foundation of
mathematics that mathematicians would, for the most part, not be very
much concerned with it. But in recent times I have seen to my surprise
that so many mathematicians think that these axioms of set theory
provide the ideal foundation for mathematics; therefore it seemed to
me that the time had come for a critique."

Even John von Neumann noted that Skolems relativism was one more
reason to upset set theory and destroy it

"At present we can do no more than note that we have one more reason
here to entertain reservations about set theory and that for the time
being no way of rehabilitating this theory is known." – ([[John von
Neumann]"The Bulletin of symbolic logic" Vol.6, no 2. June 2000, pp.
148http://www.math.ucla.edu/~asl/bsl/0602/0602-001.ps.

Again, in that quote Von Neumann does not claim that set theory is
inconsistent. Moreover, though he says that "FOR THE TIME BEING" there
is no known way to rehabilitate set theory, he does not advocate that
set theory be "destroyed".

Abraham Fraenkel noted that Skolems relativism did not satisfactoraly
disprove the antinomy and that there was no agreement as to his
relativist solution

"Neither have the books yet been closed on the antinomy, nor has
agreement on its significance and possible solution yet been reached."
– ([[Abraham Fraenkel] in "Einleitung in die Mengenlehre" 3rd ed p.
333, 1928, quoted in "The Bulletin of symbolic logic"" Vol.6, no 2.
June 2000, pp. 147http://www.math.ucla.edu/~asl/bsl/0602/0602-001.ps

Again, nowhere in that quote does Fraenkel say that ZFC, or ordinary
set theories, are inconsistent.

You seem to conflate "Theory T is inconsistent" with "There are
various important bases of criticism of theory T."

MoeBlee
.

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