Gödel's Incompleteness Theorems are famous theorems in Mathematical Logic. In this article , I present a proof of $\textit{Gödel's First Incompleteness Theorems}$ based on concepts from $\textit{Computability Theory}$. The result suggests that $\textit{incompleteness}$ happens not only in $\textit{First Order Peano Arithmatic}$ but also in any Formal Theory that has the capability to reason about programs