Re: The Idea of Structure as Data and Conditions

[Colin McLarty <colin.mclarty@case.edu>]

Something has gone entirely wrong here.

The axiom of regularity forbids x\in x.

colin



On Mon, May 28, 2012 at 11:15 PM, Fred E.J. Linton <fejlinton@usa.net> wrote:
> On Mon, 28 May 2012 07:25:19 PM EDT, Florian Lengyel
> <florian.lengyel@gmail.com>, protesting my assertion that
>
>>> Virtually no one ever wants to restrict attention to functions that
> respect
>>> (preserve or reflect) membership (other than "preserve" between ordinals).
>
> remonstrated that
>
>> Within set theories that satisfy the axiom of regularity, one's attention
>> is restricted to functions that both preserve and reflect self-membership.
>>
>> f(x) \in f(x) iff x\in x
>
> Hereto, I in turn ask: Why only self-membership? why not membership outright
>
> -- f(x) \in f(y) if (and/or only if) x \in y -- ?
>
> And how often, really, do we actually impose either of those restrictions? (Or
>
> did FL inadvertently omit a "sometimes" between "is" and "restricted" :-)   ?)
>
> Cheers, -- Fred
>

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