"We exist, things exist, and we are aware that things exist, and are aware that we exist."

Yes we exist. To me the most important aspect of existence is the fact that we are subjected to existence and exist. We do not get to choose.

"To think otherwise, and imagine consciousness has primacy, is a fallacy, irrational, and objectively unprovable."

In being subjected to reality and not allowed to choose existence creates the idea of objectivity. Not sure that as a principal objectivity can be proved to be anything more than a conscious utopia dream that can never be realized in fact. Thus to me such is very shaky ground on which to depend on for a place for minds to stand.

"Hence the Primacy of Existence axiom, which places consciousness as secondary." All things that exist : exist subjectively.

The order we see in the universe denies the Primacy of Existence axiom. Order requires consciousness and is inexplicable when seen as an accident. Not a chicken and the egg problem at all once it is realized that with subjectivity there must be a agent that is not subjected to reality, but exist in and of its own accord.

"objective universe"

Is not a physical object that exist. It is an idea that is easy to disprove.

Using the scientific method Objectivity cannot be proven nor can anything really be proven. Axioms only have value in so far as they explain reality. The use of imagination to have objectivity is not actually a condition that can be reasoned about. First one must be able to examine a thing to know that it exist. So if objectivity exist lets put it on the table and examine it.

I really enjoyed your post. Thanks for sharing it with us!