Axiom of Consciousness
The Axiom of Consciousness states that consciousness exists--in particular, that any assertion pertaining to reality implies the existence of a conscious entity making that assertion. For example, the assertion, "The sun is shining," implies the existence of a conscious entity that is claiming that the sun is shining, thus showing that consciousness exists. (This implication remains valid whether or not the assertion is true or false--in this case, whether or not the sun is actually shining.)
As with any other axiom, any claim that the Axiom of Consciousness is false is immediately self-defeating: such a claim implies the existence of someone making that claim, which in turn implies that consciousness exists, validating the Axiom. The existence of consciousness is prerequisite to any assertion whatsoever.