While I concede to Frank the phrase "rhetorical affirmation," I must add that according to some, the linguistic source of rhetorical affirmation comes from the influence of Yiddish.
Leo Rosten, in his great book, "The Joys of Yiddish," writes of the rhetorical affirmation in the preface of the book, although he doesn't give it a name. There Rosten lists nine classic Yiddish linguistic devices that have invaded the English language, the last of which is answering a question with a question. The first eight are worthy of note and include:
- Blithe dismissal via repetition with an sh ("Fat-shmat, as long as she's happy");
- Mordant syntax ("smart, he isn't);
- Sarcasm via innocuous diction ("he only tried to shoot himself");
- Scorn through reversed word order ("already you're discouraged?");
- Contempt via affirmationa: ("My son-in-law he wants to be");
- Fearful curses sanctioned by nominal cancellation ("a fire should burn in his heart, God forbid!");
- Politeness expedited by truncated verbs and eliminated prepositions ("You want a cup coffee?");
- Derisive dismissal disguised as innocent interrogation ("I should pay him for such devoted service?") and to the point here,
- The use of a question to answer a question to which the answer is so self-evident that the use of the first question (by you) constitutes an affront (to me) best erased either by (a) repeating of the original question or (b) retorting with a question of comparably asinine self-answeringness.
Source: Rosten, Leo, "The Joys of Yiddish" (McGraw Hill 1968), pp xiv - xv.