D_A

14 hours ago, Strange said:

!

Moderator Note

This probably deserves a thread of its own. Let us know if it fits better in Mathematics, rather than Philosophy.

 

That may be because such a set cannot exist (which is the of the paradox).

Also, a set of abstract concepts (ie. sets) is pretty hard to visualise, anyway. The paradox probably works better when written in mathematical (set theoretical) notation. (I think there is an error in ydoaP's description, as well.)

Yes please! I'd like to get the post moved to the math section if possible, as I'd like to challenge the mathematicians among us fairly with this case as well.

7 hours ago, Carrock said:

A non mathematical example from memory (I remember better doing it this way than copy and paste*):

 

* and will learn from SF if my understanding is inadequate.

Thank you for your attempt to help, Carrock. However, I'm still struggling.

You start your post with the words, "A non mathematical example". As soon as you start the argument with this presumption, the rules of the (rigid) set theory are no longer applicable (at least according to my logical thinking).

The librarian is free to include a reference in the catalogue (of catalogues which don't include themselves) to itself, for instance. Or, he/she could just throw the whole lot into the bin out of pure frustration, for that is a tap into the vastness of possibilities that root out of human imagination. In real-life, a human being can come-up with solutions outside of set theory logic for such practical problems.

The gist of my argument is that (I feel) your example example is not a fair real-life implementation of Russel's paradox.

P.S.

I didn't understand the last part of your post: "* and will learn from SF if my understanding is inadequate."

On 9/20/2013 at 3:03 PM, ydoaPs said:

So, let's take a look at a specific set: the set of all sets which are not members of themselves. The set of all cats is not a member of the set of all cats-it's a set of cats, not of sets! So, it goes in! Likewise, any set consisting of no sets will go in this set of all sets which are not members of themselves.

 

So, we pose a question: Is this set of all sets which are not members of themselves (from here on out, we'll call it 'R') a member of itself? If R is a member of R, then it fails to meet the requirements to be in R, so it isn't a member of R. That's a contradiction, so that's no good. That means R must not be a member of itself. But what happens if R is a member of itself? If R is a member of itself, it meets the requirement to be in R. Since R is the set of ALL sets meeting this requirements, it goes in. Again we have R both being a member of itself and not being a member of itself. So, either way, we get a contradiction. This means something is logically impossible. But we got this result simply from the definitions of sets and members and from the very conceivable idea that you can group whatever you want together.

 

This is a situation in which something is conceivable, but logically impossible. This means it is not the case that whatever you can imagine is possible. Crackpots, take note: the fact that you can imagine something in no way implies that it is possible. It doesn't matter how clear your perpetual motion device/unified theory/God/electric universe is, imagining it doesn't cut the mustard. This is one of the reasons you NEED the math.

Greetings everyone,

This is my very first post here, and it comes out of pure curiosity. I see that the OP's argument draws from Russel's paradox. 

However, I'm having  a very hard time "imagining" a set of all sets that is not a member of itself.  On the contrary, I can perfectly imagine a set of all cats (like a big balloon filled with cats, for instance).

The challenge for me is that Russel's paradox is an abstract mathematical concept, and I am not able to imagine anything physical out of it.

Quoting the OP, "...from the very conceivable idea that you can group whatever you want together." Again, although grouping things is conceiveable for me, a set of all sets that is not a member of itself is not physically conceivable for me.  The thread title reads, "If I can imagine it, it is a possibility."

Anyone who wishes to help me out here is grandly welcomed!