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Topic: Russell's Paradox
Replies: 15   Last Post: Jul 3, 1996 8:49 PM

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hawthorn@waikato.ac.nz

Posts: 14
Registered: 12/12/04
Re: Russell's Paradox
Posted: Jun 19, 1996 8:01 PM
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In article <4q59nn$8kg@tor-nn1-hb0.netcom.ca>, dchris@netcom.ca(Dan Christensen) writes:
> In <zunger.834989322@rintintin.Colorado.EDU>
> zunger@rintintin.Colorado.EDU (B. L. Z. Bub) writes:
>

>> ... in ZF it is possible to prove that Russell's construction is not
>> a set, and so no contradiction arises therefrom.


I have never seen this paradox as much of a paradox myself.
And you don't need monsters like ZF to knock it on the head.

It suffices to note that

S = `the set of all sets that are not members of themselves'

is not properly defined. We can consider a set to be a rule
which sorts objects into two piles - member and non-members.
The definition above is not a set, not because of some fancy
ZF exclusion, but simply because the purported rule fails to
adequately specify in which pile the object S belongs. The
rule is incomplete! One can turn S into a valid set simply by
specifying what it does to S. But if you do this, the paradox
vanishes. The Russell paradox is no more a paradox than the so
called Zeno paradox, and you don't need to retreat into formalism
as ZF does to get rid of the problem.

Ian H







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