Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: I Bet \$25 to your \$1 (PayPal) That You Can’t P
rove Naive Set Theory Inconsistent

Replies: 7   Last Post: Feb 18, 2013 1:48 PM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: I Bet \$25 to your \$1 (
PayPal) That You Can’t Prove Naive Set
Theory Inconsistent

Posted: Feb 18, 2013 1:48 PM
 Plain Text Reply

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.

Date Subject Author
2/17/13 Graham Cooper
2/17/13 Charlie-Boo
2/17/13 Graham Cooper
2/17/13 Charlie-Boo
2/17/13 Bernice Barnett
2/17/13 Charlie-Boo
2/18/13 fom

© The Math Forum at NCTM 1994-2018. All Rights Reserved.