The Holy Ghost
Apostles do not have the responsibility to convince others of their call--that's the Holy Ghost's job. Consider the actions of the apostle Peter:
- He bore testimony of Christ
- The Holy Ghost ratified Peter's words to his hearers (or at least those who were willing to listen)
Now when they heard this, they were pricked in their heart, and said
unto Peter and to the rest of the apostles, Men and brethren, what
shall we do? (Acts 2:37)
Peter was then able to teach them what they needed to do to retain not just the witness but the gift of the Holy Ghost:
Then Peter said unto them, Repent, and be baptized every one of you in
the name of Jesus Christ for the remission of sins, and ye shall
receive the gift of the Holy Ghost. (Acts 2:38)
Luke's record indicates that for those who followed through, the gift of the Holy Ghost did indeed come upon those to whom it was bestowed by the apostles' laying on of hands (see Acts 8:17-20).
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Signs
The Lord's messengers are indeed regularly accompanied by signs. In some cases, the New Testament records signs given through or in validation of the apostles' divine authority; in other cases the record is silent on this matter.
It is noteworthy, though, that:
- Mark 16 indicates that signs shall follow them that believe not them that believe shall follow signs
- In Acts 2, it wasn't after the manifestation of the gift of tongues--which surely got people's attention--but after Peter's testimony of Christ, that the listeners were pricked in their hearts by the Holy Ghost and willing to act. After their conversion, signs and manifestations of God's power did occur.
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Summary
One who is called as an apostle of Jesus Christ should testify of Christ, and aid people in participating in the ordinances & covenants of the Gospel of Jesus Christ, so that they may receive the gift of the Holy Ghost, and more abundantly experience the blessings and transformation God offers.
How many of the people who saw the Red Sea part remained faithful and diligent in obeying God and His representative, Moses?
The power of the Holy Ghost, the gift of the Holy Ghost, and the transformative process that results from those who embrace these invitations to act, are far more convincing than anything else.