
Re: I Bet $25 to your $1 (PayPal) That You Can’t P rove Naive Set Theory Inconsistent
Posted:
Feb 17, 2013 10:14 PM


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.
CB

