The most horrifying journey, this is what doubting 'everything' does.

[Mystic]

Reason itself is self-justifying. The moment you try to provide reasons against it, reasons to not reason, you've already been defeated.

There is no reason not to reason, but it's about distinguishing proper ways and non-proper ways.  We have limited time in life.  We can't reason about everything. True reason will never misguide from my perspective, because it's connection and reliance on God's Guide.
The false claimants of reason and perception can get us many things true, and borrow from the light in their own existence.
Your paradigm doesn't take account possibility of Djinn and Angels, and portals to the darkest spirit and portals to the leader and Guide,  you are explaining the paradigm purely from an Atheistic stand point.
Since Djinn have incredible powers and minds,  and telepathy, relying on a false energy source and false imperfect mind way to reason, won't make us get all facts wrong, but mix truth with falsehood.
From my perspective, we humans rely on either Angels or Devils or Djinn inbetween, there is a relationship between the two, but most people don't perceive it.
The evil friend (Qareen) doesn't leave me but so doesn't the Guide abandon me.
And I am learning reaching true conclusions is not sufficient to rely on that process of thinking even if you are certain.
Tranquility lies in holding to the pure spring of blessed light, and not to mix with it anything else from impure sources.
Harder said then done.
But again, you think of axioms and reason and all that, from secular perspective.
I don't believe that perspective.
Undisiplined thinking which rules my soul too much even if reaches true conclusions can be bad, if we are wasting time, and not acting to what we already know.
I really got to go. 
I know I didn't prove anything I said, just showing my framework.