thus WE HAVE A SOURCE FOR THE INCONSISTENCY IN ZF

thus ZFC IE SKOLEM PARADOX

thus an axiom which was invented ad hoc to outlaw a paradox in naive set
theory is it self impredicative

and will lead to paradox in set theory ie ZFC

The australian philospher colin leslie dean points out a source in ZF thus
ZFC for its inconsistency ie the skolem paradox

 the separation axiom is impredicative - and leads to inconsistency in
ZFC-  is doubly interesting as zermelo introduced it  to outlaw the
russell paradox which showed naive set theory to be inconsistent

http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
3. Axiom schema of specification (also called the axiom schema of
separation or of restricted comprehension): If z is a set, and \phi\! is
any property which may characterize the elements x of z, then there is a
subset y of z containing those x in z which satisfy the property. The
"restriction" to z is necessary to avoid Russell's paradox and its
variant

poincare and russell argued that impredicative statements led to paradox
in mathenmatics

now
the separation axiom of ZFC is impredicative thus we would expect that ZFC
would end in paradox and it does due to the skolem paradox

solomon fefermanhttp://math.stanford.edu/~feferman/papers/predicativity.pdf

"in ZF the fundamental source of impredicativity is the seperation axiom
which asserts that for each well formed function p(x)of the language ZF
the existence of the set x : x } a ^ p(x) for any set a Since the
formular
p may contain quantifiers ranging over the supposed "totality" of all the
sets this is impredicativity according to the VCP
this impredicativity is given teeth by the axiom of infinity "

On May 18, 10:45 pm, "elsiemelsi" <cyprin... at (no spam) nosam.yahoo.com> wrote:
thus WE HAVE A SOURCE FOR THE INCONSISTENCY IN ZF

You say "the inconsistency in ZF" as though the PRIOR EXISTENCE
of such a thing had ALREADY been established. IT HAS NOT.
You personally ARE NOT AWARE OF ANY inconsistency in ZF.
If you are, you can give A PROOF OF A CONTRADICTION from ZF.
Since you can't, you just plain CAN'T SAY this.

thus ZFC IE SKOLEM PARADOX

A paradox is not the same thing as a contradiction or an
inconsistency. In this particular use, the term has philosophical
connotations about expectations. THOSE are what are contradictory.
ZFC itself does not actually prove any contradictions relating to
the Skolem paradox.

thus an axiom which was invented ad hoc to outlaw a paradox in naive set
theory is it self impredicative

That's right.

and will lead to paradox in set theory ie ZFC

How would YOU know that? It is NOT like YOU a prove a contradiction
from ZFC.