#
Earl Bertrand Arthur William Russell

Earl Bertrand Arthur William Russell was born into the English upper class in 1872.
He lived a very turbulant and long life, in which he broke down the foundation of logic, preached atheism,
made acquaintances with famous people like Winston Churchill and D.H. Lawrence, visited the prison several times
on behalf of his beleives, and wrote a huge bunch of books.

In his young years, he studied mathematics and later wrote a book together with another mathematician
on the foundations of mathematics. In their book, for example, they printed a one page proof, just to
prove that 1+1=2. While he was researching, he also found a paradox which today is called
Russell's Set Paradox. This is how it works:

First, we make a distinction between two types of sets. The sets which contain themselves as a member and the sets
which don't contain themselves as a member.

Let's look at an example: a pear belongs to the *set of pears*: the
*set of pears*, however, doesn't belong to the *set of pears*; it is not a pear itself and therefore doesn't fullfill the
criterion. This means that the *set of pears* is not a member of itself.

We now look at a different set, the *set of everything which isn't a pear*. In this set, you can find books, rats, or
president Bush; all these members aren't pears and therefore fullfill the criterion. Since you will find
everything in this set which isn't a pear, you will also find the *set of pears* and the
*set of everything which isn't
a pear* as members. That means that the
*set of everything that isn't a pear* contains itself as member.

Russell went a step further and looked at the *set of all sets which aren't members of themselves*.
So in this set, you will find the *set of pears*, the *set of presidents*,
and many other sets. You won't find the *set of everything which isn't a pear*,
since that set contains itself as a member and therefore doesn't fullfill the criterion. While Russell
was looking at this *set of sets which aren't members of themselves*, he
wondered if this set is a member of itself.

If it is a member of itself, it doesn't fullfill the criterion, so it can't be a member of itself.

On the other hand, if it isn't a member of itself, it does fullfill the criterion and
therefore has to be a member of itself.

So when Russell found this paradox, he suddenly had a proof that
logic, which he thought was the foundation
of mathematics, couldn't hold for itself. Today we of course know that
his paradox isn't a helpless case;
if we use **fuzzy logic** we can very well get an answer. Russell, however,
didn't know about fuzzy logic and
was deeply disappointed by mathematics. He gave up mathematics, but that
doesn't mean that he stopped turning
the world upside down. Throughout his life, which was 97 years long,
much too long actually for his adversaries,
he kept preaching his ideas as loud and as often as he could. He wrote
dozens of books, mathematical books,
philosophical essays, novels, and even junk. By the time he died in
1970, he had not only started a whole
new period in logic, but he also had a Nobel Prize for literature in his pocket.
He is a famous example to show that people with a great talent for mathematics
can also be great writers.