The australian philosopher colin leslie dean points out Mathematicians are
in deep crisis for 2 reasons

1) Skolems paradox

2) Godels incompleteness theorem is meaningless as he does not tell us what statements true



1) skolem discovered a paradox which makes set theory inconsistent

of which freankel and most mathematicians at the time saw

http://www.math.ucla.edu/~asl/bsl/0602/0602-001.ps.

and that

"most mathematicians followed fraenkels skepticiam


wiki states the paradox/contradiction thus

Skolem's paradox - Wikipedia, the free encyclopedia



[some will say only appears to be a contradiction but this comes from the belief that skolem gave a solution to the paradox - see below to see his solution destroys set theory and is not accepted]

note it says there is a contradiction in set theory ie that must make it inconsistent

note most mathematicians at the time including Abraham Fraenkel saw it as an antinomy

some argue that Skolem gave a solution to the paradox but this is not accepted as it destroys set theory

Peter Suber, "The L?wenheim-Skolem Theorem"

in regard to skolem relativism attempt at resolution - which is at
present is not accepted


Skolem himself admits his relativistic solution it destroys set theory

http://www.math.ucla.edu/~asl/bsl/0602/0602-001.ps

(John von Neumanns states

"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."

of which a few mathematician also agreed[/quote]
you have only two options
skolems paradox shows ZFC is inconsistent
or you accept skolems solution and thus ZFC is destroyed

now rather than solving the paradox before moving on with set theory
mathematicians just ignored it and used set theory for all sorts of
proofs

Now mathematicians are in crisis for there is now so much invested in
set theory that the skolem paradox threatens the very foundations of
mathematics

so some mathematician now try to argue away the paradox by saying it is
not a contradiction
but
skolems paradox want go away it is at present unable to be disproved
and modern maths is buried so much in rubbish for useing set theory they cant get out




2)
mathematician have so much invested in godels incompleteness theorem
much maths is reliant on it
but at the time godel wrote his theorem he had no idea of what truth was
as peter smith admit s the Cambridge expert on Godeladmits

but truth is central to his theorem
as peter smith kindly tellls us

http://assets.cambridge.org/97805218/57840/excerpt/9780521857840_excerpt.pdf

you see godel referes to true statement
but G?del didn't rely on the notion
of truth



now because G?del didn't rely on the notion
of truth he cant tell us what true statements are
thus his theorem is meaningless

this puts mathematicians in deep crisis because all the modern idea derived from godels theorem have no epistemological or mathematical worth for we dont know what true statement are

Gödel's incompleteness theorems - Wikipedia, the free encyclopedia...

without a notion of truth we dont know what makes those statements true
thus the theorem is meaningless

and modern mathematics is in deep **** for useing a meaningless theorem