Category Archives: General

The last three posts explored the consequences of being able to express sentences like… G: “This sentence is not provable.”  …within certain systems.  Specifically, we argued as follows.  If G is false, then it is provable.  But this contradicts the assumption that our system is accurate … Continue reading →

As my inaugural post for the blog, I thought I would give a very high altitude look at Gödel’s First Incompleteness Theorem.  In the early twentieth century German mathematician David Hilbert (1862-1943) put forward a proposal to formalize mathematics in axiomatic form, together with … Continue reading →