Sola Meta-scripture?

 "There is," writes the Thomist philosopher Walter Farrell,

an infinite chasm between the unspeakable things that are too base, too irrational for words and the ineffable things that are too high, too intelligible for the framework of speech.

Heights and depths, with a vertical abyss in between. And here we are. 

Speech, it seems, is too rational to reach down to the infrarational or up to the transrational. It only works in the temperate zone in between.  

Now, math is a language, but Gödel forever proved its insufficiency in mapping -- in a way that is both consistent and complete -- anything beyond itself, for any formal system contains assumptions that cannot be justified by the system. 

Does this mean we are sealed in tautology and absurcularity? In other words, is knowledge just the expansion of an otherwise closed circle?

As part of my continuing education, yesterday I read a book called Ideas at the Intersection of Mathematics, Philosophy, and Theology, hoping for some answers. Lately we've been talking about psychic integration, and the author -- who is both Christian and a mathematician -- was troubled by the lack of integration between the two:

There just had to be fruitful ways for either bringing Christian faith to bear upon the math I was learning in college or for bringing the math I was learning in class to bear somehow on my faith. 

However, there are "relatively few people interested in finding places where the Christian faith might intersect with mathematics." 

Concur. Most mathematicians -- like most people -- just breeze past Gödel as if nothing has happened: "the philosophy of mathematics has little or no influence upon 99% of mathematicians."

Am I the only one who cares about the rules?! 

Unfortunately, I didn't get much out of the book, but the author does bring Gödel to bear on the impossibility of sola scriptura, and you can probably see how. He begins with the Westminster Confession of Faith, which claims that  

The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit or traditions of men.

But supposing the inviolability of the incompleteness theorems, no formal system can be self-justifying, independent of other axioms from outside the system: "the whole counsel of God cannot be deduced from an enumerable set of axioms allegedly given expression by scripture." 

when a person is going to begin talking about his or her formal theory in a meta-theoretical way, then that person will either have to begin saying things that are untrue or things that are unprovable -- at least from within that formal theory. And this uncanny property is not restricted to arithmetical systems. 

As it pertains to sola scriptura, "the proposition that one is being asked to confess" 

must be added as an additional axiom -- to those propositions that are said to be expressly set down in scripture, except this one will not be set down in scripture... 

I don't blame anyone for saying So what?, but that's all I got this morning.