I have had the opportunity to reflect on the notions of indeterminacy and incompleteness within various fields associated with mathematics. I initially gained a reading comprehension on paradoxes, emphasizing Russell's paradox of the library. I then studied first order logic, using propositional calculus as a means of examining a formal system which is consistent and complete for the purpose of comparison and future reference. I explored various proofs utilizing the essence of Cantor's diagonal argument, which allowed me the opportunity to better comprehend the ideas of infinity, contradiction, incompleteness, and indeterminacy. All this led to a Halting version proof of Gödel's Incomplete Theorem. I examined the proofs of Gödel's two incompleteness theorems and concluded with a discussion on Chaitin's Omega.
Wu, S. (2006). Gödel and Beyond: A Treatise on the Notion of Indeterminancy (Undergraduate honors thesis, University of Redlands). Retrieved from http://inspire.redlands.edu/cas_honors/44