Uniqueness and unicity can be synonyms when they are used to describe something that is “unique”, meaning something that is distinct from all other things.
Are these terms interchangeable, or do they carry slightly different meanings?
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
Mathematicians (whose native language is not English) may use unicity, modeled after the French unicité, in place of the preferable word uniqueness.
In a similar way, foreign mathematicians also use compacity in place of compactness. Even if the mathematician is a native speaker of English, if his teacher was foreign, he may still have picked up compacity and unicity.
Another one is analiticity. But there is no (common) English word analiticness, so in this case I guess there is no avoiding analiticity.
All three of uniqueness, uniquity, and unicity are attested by the Oxford English Dictionary, each with several centuries of citations. There is no especial difference in meaning between them; there is, however, a staggering difference in frequency.
Here’s what you should therefore do:
Use uniquity only when you wish to rhyme with such words as iniquity, or when you wish to express the antonym of ubiquity using a form closely parallel to that word.
Use unicity only when you wish to rhyme with such words as complicity, or when you wish to express the antonym of multi-city. ¹
Use uniqueness everywhere else.
If you don’t use uniqueness, you are apt to perplex readers for one of two reasons:
What it all comes down to is that uniqueness is the only one in common use, as shown by this Google N-gram:
Click graph to go directly to full Ngram.
That means that uniquity and unicity are “special-effects” words only, with uniqueness doing all the real work to express “one-of-a-kindness” in the language.
“We need a multicity solution to our traffic problems during rush hour. A unicity approach just won’t work.”
There are dictionaries which register more or less all words, whether they are "dictionary corpses" or not. The Longman Dictionary of Contemporary English has only unique and uniqueness, neither unicity nor uniquity. By the way, also the smaller Concise Oxford Dictionary has only uniqueness. I should say unicity and uniquity are dictionary corpses a journalist may dig out and revive to sweep his readers of their feet with his exquisite vocabulary or a poet may use these corpses when he is in need of a special rhyme.
PS I refer to my edition of The Concise Oxford Dictionary of Current English in bookform, 9th edition, 1995.