In the early years of the 20

^{th}century, Bertrand Russell and Alfred North Whitehead set about axiomizing mathematics—boiling math down to its fundamental principles, modeling Euclid’s geometry. One of Russell’s main concerns was eliminating the paradox of self-reference. Toward this end, he and Whitehead penned their*Principia Mathematica*in three imposing volumes. A few decades later, Kurt Gödel showed up and ruined everything by showing that any formal system at a certain threshold of power can, in a sense, self-destruct.Gödel’s proof has two key points: that certain mathematical statements can be interpreted as statements about mathematics itself (which should only be possible in meta-mathematics), and that these statements can be condensed into a single statement which speaks about itself. Thus, any formal system of a certain sophistication carries the potential for self-reference, the very thing Russell was so eager to eliminate.

Don Ault likes to say that the

*Principia*was a turning point in the respective careers of Russell and Whitehead: Russell was only able to think before the*Principia*, and Whitehead was only able to think afterward. Whitehead penned his major philosophical works, and Russell became the doddering old man we see in__Prisoner’s Dilemma__.
## No comments:

## Post a Comment