[1] **viXra:1401.0149 [pdf]**
*submitted on 2014-01-22 05:43:50*

**Authors:** Antonio Leon

**Comments:** 14 Pages.

It is proved in this paper the undecidable formula involved in Gödel's first incompleteness theorem would be inconsistent if the formal system where it is defined were complete. So, before proving the formula is undecidable it is necessary to assume the system is not complete in order to ensure the formula is not inconsistent. Consequently, Gödel proof does not prove the formal system is incomplete but that, once assumed it is incomplete, it is possible to define an undecidable formula within the system. This conclusion makes Gödel's incompleteness theorems devoid of substance.

**Category:** Set Theory and Logic