The relevant part here, I find, is that he is invoking much earlier concepts of art/aesthetics -- the use of the words "dimly, briefly" echo the "clear but confused" of Descartes and Leibniz and the way such matters of (a)perception are discussed by later philosophers (up to Kant) -- note that in the "clear or obscure" distinction, there was nothing to be gained from the "obscure" direction.

The other direction for interpreting Solzhenitsyn is mysticism, but that's just, for the most part, Platonism with a new value system. I mention this (mysticism) because of the "revelations unattainable by reason" section, but that sort of formulation also shows up in considerably more rational(ist) philosophers. Anyway, this is just a rambling.

As for intuition (and math to an extent): Kant, Husserl, Merleau-Ponty.

I lose myself
In the jungle of words.

And find myself again
In the wonder
Of the word.

-- Rose Ausländer (loosely translated)