Re: Mathematicians are in deep *** for 2 reasons

rupert says

These "problems with Skolem's solution" have nothing to do with the
contention that ZFC has been proved to be inconsistent.

i say
but they do
you offered skolems solution to prove set theory is not in contradiction
note set theory is ZFC

but skolems solution is not accepted due to those problem
so set theory ie ZFC is inconsistent ie in contradiction (as fraenkle and
most of the mathematicians at the time saw it as an antinomy]


rupert says

He thought it cast doubt on set-theoretic foundationalism, yes. I've
given you some quotations from the appendix to Machover's book which
discuss this view. That's nothing to do with the contention that ZFC
has been proved to be inconsistent. No competent person thinks this.
That includes Abraham Fraenkel.

i say fraenkel said it created an antinomy in set theory that must mean
ZFC
John von Neumann said the paradox meant [ that there is] no way of
rehabilitating this theory is known

quote

"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." â?? ([[John von
Neumann]"The Bulletin of symbolic logic" Vol.6, no 2. June 2000, pp. 148
http://www.math.ucla.edu/~asl/bsl/0602/0602-001.ps.


rupert says


Why? You're the one who comes on here adovcating his views. It's your
burden to defend them.


i say

i have given my sources

you have given your skolem solution to back up your view that set theory
[which must mean ZFC] is not in contradiction

and i have shown you that solution is not accepted by Fraenkal most
mathematicians of his time John von Neumann etc
thus your only support that Skolem is not a contradiction is destroyed

thus set theory which is ZFC remians in contradiction ie inconsistent
becuase as suber and bunch point out


Bunch notes op cit p.167

â??no one has any idea of how to re-construct axiomatic set theory so that
this paradox does not occurâ??
Peter Suber argues that mathematician claim skolems paradox is not a
contradiction but they dont know how to prove it is not a contradiction

Most mathematicians agree that the Skolem paradox creates no
contradiction. But that does not mean they agree on how to resolve it.
[The Löwenheim-Skolem Theorem,
http://www.earlham.edu/~peters/courses/logsys/low-skol.htm#amb3]


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