Introduction
Elementary Arithmetic (EA) of Godel is a well-understood fragment of mathematical logic. It is an ideal vehicle for making an in-depth study of mathematical logic itself.
Incompleteness of EA is usually established by using a natural language (meta language) for the proof. Using a
natural language for a proof, obviously, has its risks. We
add three derivation rules to EA, call it Sentient Arithmetic (SA) , and attempt to prove the incompleteness of SA within itself, without using any meta language.