ABSTRACT
Arithmetical truth is unaxiomatizable. This profound limitative result is due to Godel. It is perhaps the most important foundational result ever established, a beautiful triumph of the flowering of rigorous thinking in its first three decades of the twentieth century. The chapter aims to provide for the philosophical beginner the most succinct and accessible proof possible of the unaxiomatizability of arithmetical truth. It discusses formulae and sentences are understood to be in the first-order language of arithmetic. For purposes, one particular model will hold our attention: the so-called standard model for arithmetic. The philosophical reader is asked to take it on trust, as a straightforward theorem of mathematics. Its proof is absolutely straighforward – it is a proof by mathematical induction.
