"Some years ago...two missionaries came to me with what seemed to be a very difficult question, to them. A young Methodist minister had laughed at them when they said that apostles were necessary today in order for the true church to be upon the earth. And they said the minister said, 'Do you realize that when they met to choose one to fill the vacancy caused by the death of Judas, that they said it had to be one who companied with them and had been a witness of all things pertaining to the mission and resurrection of the Lord? How can you say you have apostles, if that be the measure of an apostle?'
"And so these young men said, 'What shall we answer?' I said to them: 'Go back and ask your minister friend two questions.
First, how did the Apostle Paul gain what was necessary to be called an apostle? He didn't know the Lord; had no personal acquaintance. He hadn't accompanied the apostles. He hadn't been a witness of the ministry, nor the resurrection of the Lord. How did he gain his testimony sufficient to be an apostle?
Now the second question you ask him: How does he know that all who are today apostles have not likewise received that witness?'
"I bear witness to you that those who hold the apostolic calling may, and do, know of the reality of the mission of the Lord."
("Born of the Spirit," address to seminary and institute faculty at Brigham Young University, 26 June 1962, 13). Quoted in New Testament Institute Manual, p. 137.
I know the apostles DO know the Lord Jesus Christ.
(For more first-hand witness accounts, see the testimonies given by two other apostles, in two of my previous blog posts: The Resurrected Christ, 4/21/2009, and Boyd K. Packer You're Good Enough post #2 10/10/2009).