The Math Forum

Search All of the Math Forum:

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

Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 14
Registered: 12/12/04
Re: Russell's Paradox
Posted: Jun 19, 1996 8:01 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <4q59nn$>, 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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.