Profundity, n.; pl. -ties.
Etymology: [L. profunditas: cf. F. profondite. See Profound.]
The quality or state of being profound; depth of place, knowledge, feeling, etc. "The vast profundity obscure." Milton.
Shades of meaning
Fernald has no entry of its own for profundity; he lists it under wisdom.
Where he writes about it:
Insight, judgment, profundity or depth, reason, sagacity, sense, and understanding are native qualities of mind, tho capable of increase by cultivation. — from wisdom