Re: set of a set etc.



Mark Nudelman wrote:
> Stephen J. Herschkorn wrote:
> > Jasper wrote:
> >
> >> The description is what I would call formal, not conceptual. "My cat"
> >> and the set of my cat {My cat} are different conceptually. My cat
> >> likes milk. The "set of my cat" does not, yet the two denotations
> >> are closely related. What is the conceptual relationship between the
> >> two?
> > Your cat is a member of the set of your cat. The set of your cat is
> > not a member of your cat.
> >
> > Sets are collections. A collection is distinct from the objects
> > therein (usually). Put a ring in a box. The box contains the ring;
> > the box and the ring are not the same thing.
>
> Just to confuse matters, W.V.O. Quine in "Set Theory and Its Logic" defines
> the law of extensionality and notes that a consequence of it is that there
> is only one memberless object. That is, since extensionality says that two
> things are identical if they have the same members, and indivduals do not
> have members, all indivduals are identical to the empty set and to each
> other. To avoid this, he could treat an individual as a different sort of
> object than a set, but instead he defines "x \in y" as meaning "x = y" when
> y is an individual. A consequence of this is that individuals are identical
> to their unit sets, that is, x = {x} but ONLY when x is an individual. Of
> course, he retains x =/= {x} when x is a set. He takes some pains to show
> why this is harmless, but it does seem rather odd.
>
> --Mark

Yes it does. Thanks for the input and the reference. What do you make
of it?

Jasper

.

Relevant Pages

  • Re: Cantors definition of set
    ... 123 member of {123, apple, fritz the cat} ... apple member of ...
    (sci.logic)
  • Re: The purpose of RPCA
    ... Each cat has ... started horking my hairball posts in 1998, all of the rec cat groups were ... repeat offenders in your kill file. ... Rob isn't the only member with cancer, ...
    (rec.pets.cats.anecdotes)
  • Re: The purpose of RPCA (long, you might want to get a beverage)
    ... Kyla and her cat Mosey looked down and read the post ... Rob isn't the only member with cancer, ... Don't ask me for my picture. ... Pam, I'm sitting here in tears, and may I offer you a HUG for taking the ...
    (rec.pets.cats.anecdotes)
  • Re: Cantors definition of set
    ... 123 member of {123, apple, fritz the cat} ... apple member of ...
    (sci.logic)
  • Re: set of a set etc.
    ... >> and the set of my cat are different conceptually. ... > Your cat is a member of the set of your cat. ... Put a ring in a box. ... things are identical if they have the same members, and indivduals do not ...
    (sci.math)