Re: set of a set etc.
The last point is a key one I think -- by this route, everything is a class
to Quine, which simplifies some things. It's important to keep in mind that
this is just the way Quine's axioms work. Many (probably most) other
axiomatic systems don't consider x = {x} to be true, even if x is an
individual. So there's no one true answer to the question about what this
means, it depends on the axiom system you're using. But there's no argument
when talking about multi-element sets: for Quine as for everyone else, the
set {x,y} is different from the set {{x,y}}, since the first has two
elements, and the second has one element.
--Mark
just learning about sets, so if this is a dumb question please pardon me.
In your last sentence, is {x,y} different from {{x,y}} because the first
has two elements (x and y) and the second has one element, the set
{x,y}? So, would you say that the second has one element, and that one
element contains two elements? Or would that not be valid?
thanks
k wallace
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