Consider the phrase in the title in this paragraph:
“each has a thumb, followed in order by four fingers: the index (or forefinger), the middle, the third, and the so-called little finger.” (Swartz, Beyond Experience, pp. 204-205)
What are the conditions for its correct use? (Correct use is how it is commonly used by fluent speakers of english.) It is funny that I, as a fluent speaker of english, asks this question since I can and do use the phrase correctly. It is often the case that we can use a word correctly without being consciously aware of the conditions of its use. Some people call this usage intuitive. One could speculate that the pattern mechanisms in the brain that makes it possible to use such phrases correctly do not share their information with the consciousness.
As for the above phrase, I propose a theory for its use: A necessary and sufficient condition for its use is that the speaker/writer considers the name mentioned after the phrase questionable in a broad sense. In relation to the example above, presumably Swartz thought when writing that paragraph that that name of the little finger is somehow questionable. Perhaps little finger is a slang name or was at the time that book was written and Swartz preferred the non-slang name. I have not found a counter-example to this theory yet.