Re: is there a set of all ordinals

obviously there was a set of all ordinals in Burali-fortis day as they came
up with the paradox did canto accept such a set

In Russells day there was a set of all sets
which destroyed naive set theory
so to avoid it set theory just introduced an axiom

Axiom schema of specification

which wiki says
"The restriction to z is necessary to avoid Russell's paradox and its
variants. "

so was there a set of all sets which has just been dissalowed due to an
ad hoc axiom


--
Message posted using http://www.talkaboutscience.com/group/sci.logic/
More information at http://www.talkaboutscience.com/faq.html

.

Relevant Pages

  • Re: Resolving the paradoxes of set theory
    ... > Paradox refers to a specific and historically definitive set of ... This is exactly the point of modern axiomatic set theory. ... > this axiom there would be no basis for claiming it false in ZFC. ... Is the set of all valid sets not a valid set? ...
    (sci.logic)
  • Axiom of choice is invalid and rubbish
    ... "as soon as zermelo brought out the axiom in 1904 mathematicians said it ... consistent with the axioms of set theory -[but the axioms of set theory ... Acceptance of it brings about paradox in maths ie skolem, ...
    (sci.logic)
  • Re: Resolving the paradoxes of set theory
    ... In order to demonstrate the power set you need to either use symbols ... not an "unrestricted comprehension axiom" it is, rather, the existence ... This is why it is peculiarly prone to paradox. ... conceivably eliminate the known paradoxes from naive set theory. ...
    (sci.logic)
  • Godels incompleteness theorm proven wrong
    ... either lead to paradox or end in paradox. ... axiom of reducibility but this axiom was rejected as being invalid by ... Thus just on this point Godel is invalid as by using an axiom most people ... Godel proved that mathematics was inconsistent ...
    (sci.math)
  • Godels incompleteness theorem proven invalid
    ... axiom 1V - axiom of reducibility- in his proof. ... either lead to paradox or end in paradox. ... Thus just on this point Godel is invalid as by using an axiom most people ... Godel proved that mathematics was inconsistent ...
    (sci.math)