If it is said:
Granted, the Quran does not indicate that the intended purification and removal of defilement actually occurred. Nevertheless, the Prophet’s supplication—may Allah bless him and grant him peace—that this be granted to them (1) indicates that it did occur, for his supplication is answered (2).
The reply is:
The point is that the Quran does not establish his claim that purification and the removal of defilement occurred (3), much less establish infallibility and the Imamate. As for adducing the hadith as evidence, that is a separate matter.
We further say regarding the second point:
Grant that the Quran indicates their purity and the removal of defilement from them (4), just as an answered supplication (5) must bring about (6) the purification of those for whom it was made and the removal of defilement from them. Even so, none of this indicates infallibility from error. The proof is that, through what Allah commanded the Prophet’s wives—may Allah bless him and grant him peace—He did not intend that none of them would ever commit an error, for errors may be forgiven for them and for others. The context of the verse indicates that He wills to remove from them defilement—that is, foulness such as indecencies—and to purify them completely from indecencies and other sins.
Purification from sin takes two forms, as in His words:
“Purify your garments.”
[Surah al-Muddaththir: 4]
And His words:
“Indeed, they are people who keep themselves pure.”
[Surah al-Aʿrāf: 82]
For He said