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Question: Why did Oliver Cowdery and David Whitmer accept Hiram Page's seer stone revelations as authoritative?
The Lord used this incident as a way to teach Oliver the proper order of revelation in the Church
This event is discussed in the Doctrine and Covenants and Church History Seminary Teacher Manual (2013):
In 1830, the Prophet Joseph Smith encountered a challenge because Church members did not understand the order of revelation in the Church. Hiram Page claimed to receive revelations for the Church through the medium of a special stone, and some Church members, including Oliver Cowdery, believed him. Shortly before a Church conference that was held on September 26, 1830, the Lord revealed truths that helped Oliver Cowdery and others understand the order of revelation in the Church.
Oliver was actually directed by the Lord to correct Hiram Page in this matter. It was a "teaching moment" for Oliver:
11 And again, thou shalt take thy brother, Hiram Page, between him and thee alone, and tell him that those things which he hath written from that stone are not of me and that Satan deceiveth him;
12 For, behold, these things have not been appointed unto him, neither shall anything be appointed unto any of this church contrary to the church covenants.
13 For all things must be done in order, and by common consent in the church, by the prayer of faith.
14 And thou shalt assist to settle all these things, according to the covenants of the church, before thou shalt take thy journey among the Lamanites. (D&C 28:11-14).
- "Lesson 34: Doctrine and Covenants 28," Doctrine and Covenants and Church History Seminary Teacher Manual, 2013.