Russell's Paradox (aka bash the noob)

ExOffender

The set of all sets which are not members of themselves(SOASWANMOT): is it a member of itself?
This is a paradox because if the SOASWANMOT is a member of itself, it is disqualified, and as soon as it is disqualified, it is eligible, and as soon as... you get the picture. It must be one or the other, it cannot be both and cannot be neither.
So...
What about the set of all sets which are members of themselves (SOASWAMOT)? Again, it seems to me, it must be one or the other, can't be both, can't be neither. And yet... there is no determining causal factor to say.
Must be one or the other.
No determining factor.
Indeterminism?

I have no direct philosophical background, as I'm sure is clear. The only possible solution I can come up with is that there's some default setting in cases like this - like the 'absolute value' law in maths that prevents mensurative calculations returnng negative amounts.
Any thoughts? Be gentle...

simu

Tis a bit mind-boggling alright!

Sets are conceptual tools and have their limits as this thing shows (well, imho). There's another wording of it where it's put in terms of a catalogue that contains all the catalogues that do not catalogue themselves. So, it seems paradoxical but if you're talking about real-world things like catalogues, you have to take time as a factor - that makes things easier because all it boils down to is saying that catalogues, once printed, become outdated straight away!

I don't think that would satisfy the mathematicians, though!
(Guess who spends a lot of time in libraries looking at catalogues!)

/edit

What Russell himself said: http://www.philosophers.co.uk/cafe/paradox2.htm

Pherekydes

Russell was a twit.

sose wanmot (my spelling) doesn't exist.

Every (mathematical) group has an identity element.

solo1

That's just like saying that every number is divisible by one. It doesn't really mean anything - it's just something you have to do to make the numbers work out.

This statement is false.

Is it? It's the same problem. It's not a problem at all.

Fysh

Slow coach wrote:

Russell was a twit.

sose wanmot (my spelling) doesn't exist.

Every (mathematical) group has an identity element.

Uh, care to elaborate on that a little bit? I'm by no means an authority on the subject, but I suspect that if disproving Russell's notion only required comments such as the above then many folks would have gotten there before you.

Why does the SOASWANMOT not exist? It can be defined as a set, which is a theoretical construct that does not require any physical form. What's invalid about it? (I haven't done sets in ages, so I may be forgetting something here)

Sapien

Hermeneutics 101.

There is the possibility of an infinity of meanings that can manifest within the permutation of language, and likewise, notional constructs such as set theory. However, interpretation of meaning derives from the limitations of human existence, which is finite.

bonkey

I woulda said mathematics101 myself

These mind-boggling concepts are all dealt with under Gödel's Incompleteness Theorem.

Simply put - mathematics will allow you to indeterminable statements.

jc