I will not shut me from my kind, And, lest I stiffen into stone, I will not eat my heart alone, Nor feed with sighs a passing wind:
What profit lies in barren faith, And vacant yearning, tho' with might To scale the heaven's highest height, Or dive below the wells of Death?
What find I in the highest place, But mine own phantom chanting hymns? And on the depths of death there swims The reflex of a human face.
I'll rather take what fruit may be Of sorrow under human skies: 'Tis held that sorrow makes us wise, Whatever wisdom sleep with thee.
Well, now. It would seem that our Tenny is well on the road to recovery. He doesn't want to keep himself locked away from other people ("my kind")—he wants to be sociable.
If he doesn't engage with his fellow man, he apparently runs the risk of "stiffen[ing] into stone."
This makes sense. The more he separates himself from others, the more solitary and set in his ways he'll become—like the crotchety old man who yells at kids to get off his lawn.
The image of the stone nicely creates this picture of what the speaker could turn into.
Instead, he recognizes that there's nothing to be gained from "barren faith" and "vacant yearning." So, wallowing in his doubt and yearning for Arthur to be alive again won't do anybody one bit of good.
"Barren" and "vacant" work with the previous imagery of the stone to emphasize that his life could permanently be empty if he continues to wallow in his grief and not let anyone in.
In the end, sorrow leads to wisdom. It seems to be part of that "eternal process" Tennyson mentioned before. He's continuing to put things within a more optimistic perspective.