Symbolism, Imagery, Allegory
If Tevye's saying something, chances are it's a quotation from the Torah or midrash (what a bunch of rabbis wrote to explain Torah verses).
He relies on his quotations for everything: they show that he's a smart and educated guy, they make even his most wrong-headed advice sound wise, they help take him away from heavy-duty emotional stuff, and—most importantly—they let him lord it over other people.
For example, check him out here, as he stops himself from crying at his wife's deathbed:
[Golde] didn't understand a word I was saying, and spoke in a whisper. "I am dying, Tevye. Who will cook supper for you?" Her eyes would have moved a stone to tears.
But Tevye is not a woman, and so I answered her with a saying and a commentary and a chapter and another midrash. (8.7-8)
Boy, that's a lot of Biblical words to cram into the conversation when all Golde wants to do is have her husband say that he loves her, or something. Way to totally misread the scene, Tevye.