Re: OT (sets and stuff)

Neo wrote:
> ... when there are no elements, there is
> nothing, no set and not an empty set. None of neo's Set Theory books
> denote the empty set as {} but more correctly with another symbol.

Why/how would/could another symbol be /more/ correct?

 From this it looks like you do not accept the 'tertium non datur'. If so, you are not alone.

To me, sets exist in the mind only. That is the way I have always looked at them. Like variables or even, numbers: 1+1=2. What does that have to do with reality? One cloud and another one can make a bigger one, not always two.

That is the thought I had when the teacher explained: 1+1=2 is always true. It goes for apples, oranges, candies and children.

Like variables and numbers, sets are, however, very powerful collective illusions.

I was - I really was - flabbergasted when Marshall took your 'empirical' glove and linked to a wikipedia article. There is IMO no such thing as empirical evidence for the existence of sets. They are an axiomatic construct.

Categories - to me it looks trivially obvious they are a construct of the mind. I'm not so sure about hierarchies, by the way.

> Neo can't see how to base
> things upon nothing but according to Keith and
> Bob, {} is a valid. So if my universal set has just one "element",
> namely {} then we have:
>
> U = { {} }

What makes this set U Universal?

> So what is NOT {}? According to Set Theory's Law of Complements, it
> should be the universal set. There seems to be a contradictions here
> as NOT {} equals {}.

What do you intend to signify with 'NOT {}'? Until I know that (and I know what you mean with {}), I don't/can't see a contradiction here.

> Can Mamma Keith explain without a whipping?

Please do not underestimate Keith.
Seriously inviting him to a challenge will do a better job getting him to contribute than this thin tease.

-- 
"The person who says it cannot be done
should not interrupt the person doing it."
Chinese Proverb.