Hi, Yotam,
Here's my take on "transrational." As Wilber often points out, pre-rational and transrational thinking and awareness are often confused, simply because both are non-rational. But transrational awareness is a non-rational form of cognition which transceds and encompasses rational thinking. Transrational insights, when they are expressed, are often expressed in rational language; Wilber is masterful at this. But of course some traditions may chose enigmatic forms of expression, to reveal the limits of and point past conventional rational thought.
In pre-rational awareness, we may think affectively and by association, rather than through the use of inductive reasoning. The pre-rational worldview may be coherent, but its coherence is on the level of resonance and reflection, meaningful correspondences, affective associations, and so on. This field of "coherence" may appear seamless and holistic, but it is pre-rational.
In transrational awareness, we may return to a holistic sense of things, but our holistic perspective now encompasses rationality and the ability to relate the items of our awareness through complex logical relationships. In transrational awareness, while we can use logic, we can perceive the limitations of our logical constructs, as well as the limits of our pre-rational, affective associations.
My understanding is that at the upper limits of rational awareness, we are capable of seeing and thinking from multiple perspectives at once. We move from a somewhat linear perspective of cause and effect, to more open and decentered forms of reasoning. We may be able to think things through using classical "excluded middle" logic, but we also have access to "included middle" logic (built on models of transcendence and inclusion). I see this as the "vision logic" stage.
In transrational awareness, we can become aware of connections that transcend or run deeper than normal causal chains, but in this case, the perspectives which disclose particular causal chains are seen as subsets of a more encompassing awareness.
I expect my explanation here is not without its flaws, but this is my general understanding at this time.
Best wishes,
Balder
May the boundless knowledge that time presents and space allows illuminate the native perspectives of your original face.