On 2/17/2013 9:14 PM, Charlie-Boo wrote: > On Feb 17, 8:36 pm, Jeff Barnett <jbb...@comcast.net> wrote: >> Graham Cooper wrote, On 2/17/2013 4:07 PM: >> >>> Is any definable collection a set? >> >>> That is the usual meaning of Naive Set Theory. >> >> I suggest we don't need your definition. The world (99%) tells the >> student to consult "Naive Set Theory," Paul R. Halmos (1960) D. von >> Nostrand. For the rest (1%) the term means ZF sans Choice and Continuum. >> Why would you think of tossing your definition out here? And why Prolog >> at all? Speak the common language. >> -- >> Jeff Barnett > > That was 60 years later. Russell wrote to Gottlob Frege with news of > his paradox on June 16, 1902. The paradox was of significance to > Frege's logical work since, in effect, it showed that the axioms Frege > was using to formalize his logic were inconsistent. Specifically, > Frege's Rule V, which states that two sets are equal if and only if > their corresponding functions coincide in values for all possible > arguments, requires that an expression such as f(x) be considered both > a function of the argument x and a function of the argument f. In > effect, it was this ambiguity that allowed Russell to construct R in > such a way that it could both be and not be a member of itself.
So you do pay attention!!!
I thought so from your remarks in another thread. But, very often your remarks toward set theory have seemed anti-mathematical. I see now that you merely see the same problem with the same "urban legend" from a different background.