Thesis (M.A.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / As is so often true in history, the importance of an event cannot fully be judged or appreciated unless it is being weighed in light of the prevailing situation of the period. Godel's discovery came at a time when mathematicians generally were looking for a means by which they might fully axiomatize arithmetic, as we have done with geometry. They hoped to be able to find an assvrance that the proof of any arithmetic fact might he proven using only the axioms and rules of inference that had been set up for the system. Those primarily concerned in this endeavor were a group known as the Formalists (since they wished to completely formalize basic mathematics) and David Hilbert. In addition to showing the complete axiomatization of our arithmetic system, they hoped further to exact a proof of the consistency of the axiomatized system [TRUNCATED]. / 2031-01-01