Thread: ZFC invalid due to axiom of seperation Rus paradox stands

ZFC invalid due to axiom of seperation- russell paradox still stands

the australian philospher colin leslie dean points out poincare and russell argued that impredicative statements led to paradox in mathenmatics

zermelo ad hoc introduced the axiom of seperation to outlaw the russell paradox which showed naive set theory to be inconsistent
but this axiom is invalid as it is impredicative
thus it cant be used to outlaw russells paradox
thus russells paradox still stands




http://en.wikipedia.org/wiki/Zermelo...kel_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 seperation axiom of ZFC is impredicative
solomon ferferman

http://math.stanford.edu/~feferman/p...dicativity.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 "


thus by useing an invalid axiom ZFC becomes invalid

hmmm... When are you and your crackpot ideas finally going to be banned?

lol.

I wish the naysayers would post a rebuttal instead of pretending that the arguments are crazy, as if they understood the subject.

@ Shubee

Look at you taking the intellectual highground

My "lol" was an expression of amusement at the way arcane mathematician replied to the post - my instant thoughts on the thread's claim to show the "invalid" status of one of the fundamental systems of maths was that it was likely to be verbiage. I'm sure arcane mathematician would agree. But why is this thread just verbiage? I'm no mathematics professor but I do study maths and have some common sense.

If this truly was a proof that the ZFC axioms for set theory were "invalid", then it would not be posted on a popular internet forum, it would be discussed in a university or research setting. Similarly, my experiences with forums is that you get people who romantically hold that they have found the "solution" to a problem that has been unsolved or a flaw in a theory that has long been accepted because they think they have stumbled across something that no one has ever thought of. Look for example at the number of flawed Fermat's Last Theorem proofs that appear all over mathematics forums...99% of the time they are wrong. This person also seems to quote wikipedia. If this was a true and proper proof, they would write down the fallacious premises themselves rather than quoting them from a source that is seen by many academics as not completely intellectually rigorous and trustworthy. Hence my scepticism.

X

Originally Posted by Shubee

I wish the naysayers would post a rebuttal instead of pretending that the arguments are crazy, as if they understood the subject.

As if you understood the subjects you claim to have a higher understanding in than the PhD's of the fields, while showing blatant ignorance and a lack basic understanding of elementary concepts in said fields...