Self-Application

The seventh rule of discussion is self-application.

In mathematics, this line runs from Cantor through Russell to Godel and Turing.

Cantor uses the diagonal method.

Russell shows the paradox of the set of all sets that are not elements of themselves. In its popular form, this is known as the barber paradox: the barber shaves all and only those who do not shave themselves. Who shaves the barber?

In Godel and Turing, this line leads to fundamental limitations of formal systems and computation.

The meaning for my discourse is this: a system that describes thinking is itself part of thinking. It cannot stand outside the field it describes. Therefore, it must obey the rules that it imposes on other forms of thinking.