Now one could counter my proposition that the world is intelligible by questioning the equality of 'the real' with the intelligible. That there are aspects to the world beyond our capacity to know. For example we don't know the boundaries of our intelligence and our perceptual ability. That we live in Flatland without much gauge on our gauge.
I would agree with this - and refer to Stuart Kauffman's latest writings as brilliantly articulating that the unfolding of the living world is beyond reasonable grasp. Yet once that is understood the unknowable unfolding becomes more intelligible. But I interpret intelligibility as a sort of understanding - understandable even if it is essentially causally unknowable. The unknowable nature of the unfolding living world is not a result of a whimsical divine action or the mystery of a magic. Rather the unknowability lies in the fundamental nature of the world. So I would see that while the unfolding world is unknowable - it is intelligible - understandable - more so of course in retrospect than in prospect.
But maybe there is something different that the counter statement. For example in Jill Bolte Taylor's TED talk "My Stroke of Insight" - her left brain spoke intelligible while her right brain spoke subjective gibberish, or whether her conceptually unintelligible right brain experience presented another valid take on the world. The creative chora versus Plato - e.g. the Platonic dream that Eternal Reason presents us with the Real, versus the ever shifting and shifty comings and goings of feeling and dynamic creativity.
Now this counter is very interesting and actually gets to the heart of the matter. A great source for considering this is the RSA Animate video 'The Divided Brain by Iain McGilchrist. He points out that the brain processes two fundamentally & paradoxically different views. So what Taylor's 'stroke of insight' allowed was full unfiltered access to the right brain - this is much closer to the Buddhist view of the entanglement - the inter-beingness of the world, and the essential 'emptiness' of a self and all things. In some ways I imagine it as if she was accessing the nature of the world as it is in constant becoming from the foundation of superstrings on up to unfolding emergent levels of unpredictable wholes-becoming-more-than-sums-of-their-parts. This is part of what makes the world intelligible while yet being paradoxically beyond reasonable grasp.
I think this is the sort of view that is also linked to Kauffman's more spiritual musings e.g. the Re-invention of the Sacred. I would bet that Kauffman would have no problem accepting the view illuminated by Taylor's stroke of insight.
I think that what Kauffman, McGilchrist, Taylor and many others are pointing to is the need to move beyond a dualist imposition on our constructions of reality, the need to avoid this dualist trap. This is the radical epistemological move they are attempting - the embodiment of relativity-as-perspective-taking-and-context-shifting in an unfolding unknowable ontology-as-becoming.