Bertrand Russell was a very interesting fellow, who led a full and conscious life.

## The Logician’s Tale

I first came across Russell in *Gödel, Escher, Bach*. He was portrayed as being at the centre of a vigorous discussion on the potential for consistency and completeness in mathematics.

The story goes roughly like this.

Gottlob Frege was a logician who wrote two books about the use of set theory as the basic operations of mathematics. It was a magnificent work, but Russell came up with a counter example (generally termed Russell’s Paradox [link]) which fatally undermined Frege’s work just prior to the publication of the second volume. Frege still published it, but with an afterword that acknowledged the truth of Russell’s discovery.

Russell (in collaboration with Alfred North Whitehead) then began a related effort to build a consistent and complete proof of mathematics, taking (for example) several hundred pages to prove that 1 + 1 = 2. This effort was also based on set theory, modified with specific qualifications to rule out the paradox that Russell himself had described.

However, after the book was published, a young German mathematician by the name of Kurt Gödel then proved that the idea of a consistent and complete proof of all of mathematics was impossible: he published two papers, the upshot of which was that a mathematical system which was consistent could not be complete, while one which was powerful enough* to have a shot at completeness could not be consistent. In other words, in order to contain no potential for contradictions a system would have to be weak enough to not be useful.

I love Gödel’s result, because it (and Turing’s formulation of it in his work on the Halting Problem) says a lot about how there are some things in computing which are simply impossible. That is wonderful thing to know, because software has no physics but you have to obey the laws of mathematics just like everyone else.

This story is expounded upon in much more length in the book *Logicomix* which I was delighted to receive for Christmas. It’s not just about Russell but it is told with Russell as the narrator, and goes into splendid detail on the mathematico-philosophical developments of the early 20th century.

*Logicomix* also describes the work of Wittgenstein in a way that I almost understood. I tried to follow Wittgenstein a few years ago and got very lost. So, recommended for providing a number of useful maps.

## The Public Philospher

Russell was also well known as a public philosopher, educating the public on his ideas and those of other philosophers. It is in this vein that I offer another Russell nugget, his ten commandments:

- Do not lie to yourself.
- Do not lie to other people unless they are exercising tyranny.
- When you think it’s your duty to inflict pain scrutinize your reasons closely.
- When you desire power examine yourself closely as to why you deserve it.
- When you have power use it to build up people not to constrict them.
- Do not attempt to live without vanity, since this is impossible, but choose the right audience from which to seek admiration.
- Do not think of yourself as a wholly contained unit.
- Be reliable.
- Be just.
- Be good-natured.

These seem like good rules to follow, with or without the Abrahamic ten commandments in your life.

Go forth and live well.

[*] where “powerful enough” can be broadly described as “having the potential for self-reference”.