Re: set of a set etc.

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


.

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