An externalist view of "proof" cannot adequately work with
  regards to the subjective, internal-view-to-the-outward.

  That's the crux of the problem with an exclusively objective
  process.

  How can brains with cognitive biases come together and decide
  what is or is not a cognitive bias without being cognitively
  biased? Agreement?

  Woo. Agreement. Challenge the assumptions behind the system from
  WITHIN which you are working. It's helpful, even if later you
  decide to return back to it.