Nearness, n.
The state or quality of being near; -- used in the various senses of the adjective.
Shades of meaning
Fernald has no entry of its own for nearness; he lists it under approximation.
Where he writes about it:
Nearness, neighborhood, and propinquity are commonly used of place; approximation, of mathematical calculations and abstract reasoning; we speak of approach to the shore, nearness to the town, approximation to the truth. — from approximation