Jonathan,
I copied this from my essay blog site.
My essay was basically a two week effort. I happened to be rereading David Wallace's article that refutes the fatalism of Taylor when this idea leapt out at me. I was not planning on submitting an essay this cycle. So with a week of analysis and another week of writing I put this together.
There is a mathematical theory of unbounded but finite mathematics by Jan Mycielski, that I was recently made aware of. This is maybe useful for this work, for physics usually involves finite systems or involves finite numbers that are measured. I have been pondering whether some Godel numbering scheme that maps quantum numbers to integral solutions of Diophantine equations in this setting might lead to a finite and unbounded version of the Godel theorem. This might provide a more firm understanding of what my essay proposes.
Cheers LC