Uniqueness Singularity is uniqueness.
Unique artifacts are rare, special, and singular.
We treasure them and form our knowledge around them. Uniqueness is a measure of rareness and not arbitrariness. Uniqueness, like most words we could choose, comes with some everyday bias that needs to first be dispelled, for it is often used to describe arbitrary distinctions. Colloquially, we call a teen with wild rebellious clothes and a face full of ornaments unique. And we call an artistic creation unique, even when we think that it is nothing at all special.