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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

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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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic 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.











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