Why are individual passages of the Qurʾān given the name "āyah"?

Imām Ibn al-Jawzī (d. 597/1201) summarized the scholars' opinions in his book "Zād al-Masīr" as follows:

1. The word āyah means sign. Therefore, an āyah is a marker that signifies the end of the speech before it and the beginning of the speech after it. [Abū ʿUbaydah]
2. It is called an āyah because it comprises a group of letters from the Qurʾān. Abū ʿAmr al-Shaybānī relates that the expression "the people went out with their āyah" means: as a group.
3. It is termed an āyah (sign) because it is wondrous. The reader, upon reciting it, can discern how distinct it is from human speech. This is similar to saying, "Such a person is a sign among signs (āyah min al-āyāt)," meaning: a wonder among wonders. [Ibn al-Anbārī]