I flipped to a random part of The Man who Mistook His Wife for a Hat, and I ran across this passage:
Eyes Right!
Mrs. S., an intelligent woman in her sixties, has suffered a massive stroke, affecting the deeper and back portions of her right cerebral hemisphere. She has perfectly preserved intelligence -- and humour.
She sometimes complains to the nurses that they have not put dessert or coffee on her tray. When they say, 'But, Mrs. S., it is right there, on the left', she seems not to understand what they say, and does not look to the left. If her head is gently turned, so that the dessert comes into sight, in the preserved right half of her visual field, she says, 'Oh, there is it -- it wasn't there before'. She has totally lost the idea of 'left', with regard to both the world and her own body. Sometimes she complains that her portions are too small, but this is because she only eats from the right half of the plate -- it does not occur to her that it has a left half as well. Sometimes, she will put on lipstick, and make up the right half of her face, leaving the left half completely neglected: it is almost impossible to treat these things, becasue her attention cannot be drawn to them ('hemi-inattention' -- see Battersby 1956) and she has no conception that they are wrong. She knows it intellectually, and can understand, and laugh; but it is impossible for her to know it directly.
Knowing it intellectually, knowing it inferentially, she has worked out strategies for dealing with her imperception. She cannot look left, directly, she cannot turn left, so what she does is to turn right -- and right through a circle. (emphasis mine)
It sounds like the default way for English speakers to deal with
this distinction between two types of knowing is to add adverbs. (It's still awkward, and I wish we had established verbs to take care of it, as per JohnQPublik's comment in that post.) So far I've seen academically/viscerally (me) and intellectually+inferentially/directly (Sacks) -- any other examples? (I should read the rest of this book. Apart from it being fascinating, neurological-disorder-land sounds like a good place to find this distinction in practice.)
I use know for "know academically" and ken for "know viscerally", when the distinction is important, which is not often. Most of the time the important distinction is between knowing and not knowing, rather than between knowing and kenning. Know is my default word.