> > wrong corey. I haven't any idea who Russell is, or what 'all wisdom' means.
> > i think the corey you want is corey lindsey.
>
> sorry, no idea here either.
>
> ---corey
Bertrand Russell was a mathematician/philosopher who is famous for
writing the _Principia Mathematica_ with A.N. Whitehead.
This is a monumental attempt to reduce all mathematics to
symbolic manipulation. It took them over 100 pages to prove
the big theorem 1+1=2. Russell also wrote _A History of Western
Philosophy_ and got kicked out of the Cambridge (or was it Oxford)
faculty for the heinous crime of not believing in Christianity.
Russell's Paradox (1902) shows that there is something wrong
with the concept of "the set of all sets". To understand this, first
observe that a set is a collection of objects, some of which may
themselves be sets. For example, S = {1,6,{1,3}} is a set with three
elements. Note that 3 is not an element of S, but {1,3} is. Also,
{1,6} is a subset of S, but not an element of S.
Now it is conceivable that a set could be an element of itself. For
example, the set of all sets (if there is such a thing) is itself a set,
so it is an element of itself. Of course that's not the same as being
a subset of itself--every set is a subset of itself!
Now consider the set A consisting of all sets that are not elements
of themselves. Is A an element of itself? If so, then A is one of
those sets that is not an element of itself, and we have a contradiction.
If not, then A is not one of those sets that is not an element of itself,
so A is an element of itself, again a contradiction. We must conclude
that there is no such thing as the set of all sets which are not members
of themselves. But then there can't be any such thing as the set of all
sets either, because if there was we could construct A. This is Russell's
Paradox.
The easiest way out of this is to forget about doing any set theory!
But if you feel you must do set theory, probably the best thing to do
is to assume that sets are constructed one level at a time.
Day 0--the (mathematical) universe consist of primitive elements, say
the letters of the alphabet, and no sets.
Day 1--all possible sets of primitive elements are formed.
Day 2--all possible sets consisting of objects born on Day 0 or Day 1 are
formed. For example, {a,b,{a,c},{x,y,z}} is born on day 2.
So you never speak of "the set of all sets" (if you do your eyeballs will
turn black...) but instead assume you are working at some stage of set
construction. If you want you can let this process go on for infinitely
many days, but it is never "done". Or you can stop at some finite stage.
In fact, there are some mathematicians, called Intuitionists, who think
that we shouldn't allow infinite sets. So you're an Intuitionist, Dan!
The drawback of this is that most "useful" mathematics (like calculus)
becomes much more difficult or impossible.
You could apply the same idea to wisdom if your model wisdom is
sufficiently similar to set theory. If "pieces of wisdom"
can be treated as sets, then it seems to make sense that any
collection of pieces of wisdom is another piece of wisdom,
so in particular you could talk about "all wisdom" being
the piece of wisdom consisting of all pieces of wisdom. But
as Russell's Paradox shows, this would not be wise! ;-o)
The easiest way out of this dilemma is to suppose that at any
given time we are at some stage of "wisdom construction".
So we can refer to the collection of all pieces of wisdom
that have been constructed so far, but we don't refer to that
collection as a piece of wisdom itself, until the next stage.
Now if you are willing to imagine that there can be infinitely
many stages, in fact any infinite ordinal number of stages,
then you could have wisdom construction up to any stage.
Maybe "enlightenment" is just getting to the first infinite ordinal.
--Bill Haloupek haloupekb@uwstout.edu http://www.mscs.uwstout.edu/~billh/home.html My employer doesn't share my opinions, my webpage is under construction, and my life is based on a true story. Will solve math problems for food.