Axioms are faith, whether presented without recourse to scripture or not.
I am beginning to suspect that you don't read the posts, and simply respond in a knee-jerk fashion.
I asked you to point out ANY axioms that I have used thus far.
I state it once again,- I have used NONE.
Zero. Zilch. Nada.
So, there is no question of "axiom" or "faith" in the First Principles post.
Vedantic axioms fail the falsifiability criterion, hence are NOT SCIENTIFIC.
Once again, you responded without reading.
I clearly stated that science ( including "falsifiablity" ) requires a subject-object dichotomy.
In that sense, it is science that has not yet
attained Non-duality/Advaita , rather than the other way round.
Aside from this fact, the LOGIC used in Vedanta is non-different from scientific analysis.
This is qualitatively different than saying "there is a pink elephant onj the dark side of Uranus which visits my refrigerator and is invisible when you open the refrigerator or put any detection equipment in it".
That is not falsifiable EVEN though there is a subject-object duality involved.
THAT is unscientific.
Not so with Advaita, which demonstrates the logic of non-duality from first principles with NO axiom.
If you find that objectionable, prove it.
That states that "truths" are a set of statements whose structure is allowed by the rules of construction of those statements. But given ANY set of axioms, some truths (i.e. statements with valid structure), will be left out, i.e. couldn't be derived from those chosen axioms. If you change the axioms, new set of "truths" get left out. If you try to include all the truths, you end with contradictions.
I can understand your new-found fascination with Kurt Godel, but you are barking up the wrong tree.
Once you can show me ANY axiom used, Godel's model is applicable.
Since NO axiom has been used, the "Incompleteness Theorem" doesn't apply.
For example, Euclid's axioms were considered self-evident by him. Until Lobachevsky, Riemann etc showed that they are not self-evident at all. In fact changing those axioms gives rise to many new kinds of non-euclidean geometries.
Wrong analogy in the first place.
This is the reason why I refrain from posting serious analysis.
Euclidean axioms are not
self-evident because it involves axioms about OBJECTS.
There is no such axiom in the First Principles Post.
Either you understand that, or you don't.