Wordwizard

1) Sally was dancing with Paul with a black jacket on, not with Paul with the blue jacket on.
2) Sally was dancing with the Paul with a black jacket on, not with the Paul with the blue jacket on.

Let us say we are at a party where there are two Pauls. I want to say which Paul Sally was dancing with. Which sentence should I use?

Gratefully,
Navi

You should use 2), which is pretty unambiguous.

1) could be parsed as meaning that Sally was wearing a black jacket while dancing with Paul, whereas she was not wearing a blue jacket while dancing with Paul. It is also unclear whether the second mention of Paul in this version of the sentence relates to the same Paul or to a different one.

Preceding the names with "the" precludes any misunderstanding about who was wearing the jackets and whether or not Sally was dancing with the same Paul.