LI recently had a discussion with an engineer during the course of which the subjects of God and mathematics were raised. Not for the first time, LI was struck by the difference in what mathematics means for us, and what it means for engineers. Engineers take mathematics to be primarily the efflorescence of that domain of knowledge that deals with discrete units and their relationships. Numeration, in other words, is the primary element of the mathematical. But for LI, mathematics defined by a set of functions (the variable, Successor of, etc.), a set of definitions, and a set of axioms. Our engineering friend was claiming that everything wasn�t mathematically determined. Her point was that LI held to a view similar to Quine�s � a sort of neo-Pythagorianism, in which everything eventually dissolves into number.
Now, we do think there is something to be said for the idea that, theoretically, everything can be translated into mathematics. But we also see logical faults with that view, starting with the term �everything,� which seems semantically dependent on the �All� of set theory. In other words, our proposition is invalid to the extent that it assumes what it wants to claim. Goedel�s work shows that there are limits to the All within mathematics. In the set of All statements generated by mathematics, at least one of them is unproveable � that which asserts the closure of the system. However, there�s nothing in Goedel that addresses the question of the complete translatability of assertions about the world into mathematics. In other words, there�s nothing to guide us in contemplating the possibility of a non-mathematical All. Such an All would, we think, be something like Spinoza�s God. This God, by the way � and any other God � is limited by mathematics, too: even God can�t count the uncountable numbers. Omniscience, in other words, has been quietly proven, in Western culture, over the past two hundred years, to be a characteristic that is not possessed by any intelligence � that, in fact, contradicts intelligence. For almost fourteen hundred years, omniscience was the great constitutive principle of European thought � it is funny how quietly it crumbled. In a sense, Darwin, Newton, and Einstein are reconcilable with the patriarchal God of Jerusalem � but Cantor, Goedel, and Bohr aren�t. Our hypothetical, non-mathematical All can�t know All about itself, and remain an All. It is as if God were some great egg, a Humpty Dumpty, who can only exist when he has his great fall, The Divine moment is just that moment of contact, when the shell is forever broken.