"Who knows the knowing of not-knowing?" (Zhuangzi 22:7; Mair)
Not surprisingly, the 22nd chapter of the Zhuangzi, "Knowing Wanders North", has a great deal to say about not-knowing. The question above is preceded by this: "Not-knowing is deep and knowing is shallow; not-knowing has to do with what is intrinsic, knowing has to do with what is extrinsic." There is a great deal 'out there' that is knowable, yet knowing is embedded in not-knowing 'in here'. How do I know that I know? I know.
Descartes' famous "I think, therefore I am" is knowing denying that it cannot know itself. A more accurate presentation of the problem might have been "I exist, therefore I think I exist". But even this assumes what it cannot know, namely that there is existence. It is here that the more practically minded say, just shut up and live already! Philosophical Daoism says the same, only it finds joyous release in exploring the depths of the unknowablity of this phenomenon of existing. The previous quote is preceded by one of those rhapsodic outbursts so typical of the Zhuangzi: "Let us try and wander together in the palace of not-even-anything, merging together into one single assertion that is nowhere brought to a halt! . . . Coming and going, I know not where I come to rest. I come and I go in it, never knowing where it all ends. Soaring through the vastness, the Great Understanding enters into me, never understanding where it comes to a halt!" (Ziporyn) (It bears remembering that in the Inner Chapters this 'Great Understanding' is presented as a hypothetical.) Here is the knowing of not-knowing, the understanding that requires no understanding, the living that is free to live freely, the one intrinsic assertion, "Thankfully, yes!"
I am reminded of the happiness of fish. Their happiness cannot be known extrinsically, as other, but only intrinsically, as mutually experienced. We are happy together. All that is, is happy together. The trees dance, the rocks sing, empty space scintillates.
We are inclined to explore not-knowing as a problem of knowing; Zhuangzi does so, but as an invitation to a more ‘mystical’ immersion in life. Knowing demonstrates not-knowing, but it is still just knowing that it does not know, until it leaves knowing behind.
You can check out Scott's writings on Zhuangzi here.