Outside of the set

Leibniz's belief in a universal digital coding embodied his principle of maximum diversity: infinite complexity from finite rules. "Nothing is a better analogy to , or even demonstration of such creation than the origin of numbers as here represented , using only unity and zero or nothing," he wrote to the Duke of Brunswick in 1697, urging that a silver medallion be struck (with a portrait of the duke on the reverse) to help bring the powers of binary arithmetic, and "the creation of all thing out of nothing through God's omnipotence," to the attention of the world.

Where does this meaning come in? If everything is assigned a number, does this diminish the meaning in the world? What Gödel (and Turing) proved is that formal systems will, sooner or later, produce meaningful statements whose truth can be proven only outside the system itself. This limitation does not confine us to a world with any less meaning. It proves, on the contrary, that we live in a world where higher meaning exists.

Turing's Cathedral, George Dyson