Talking to Mormons 101
What you are up against
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Enormous cultural pressure -- the missionaries travel in twos and have supervision from the local stake leaders. They have left families and girlfriends at home and may not be allowed to return if they leave Mormonism. They cannot marry until they return from their mission, so if they leave their faith they are also leaving their girlfriends. The missionaries watch each other to make sure they don't lose their faith or fall into sin. If one detects a problem with the other, they will report to the stake president and the missionary may be removed without notice. The missionaries are never alone during their mission. They are even encouraged to leave the bathroom door open slightly when they use the restroom or shower so that they will be less inclined to sexually gratify themselves since someone else could catch them.
Detailed training and argumentation techniques -- the missionaries are trained to talk to Christians (especially Baptists) about Mormonism. They use many of the same terms and lingo that Christians use, but often radically redefine what the words mean. It is often very frustrating to go around in theological circles because you are literally speaking different relgious languages. Make a habit of defining every Christian term as you use it the first time. Try not to use churchy talk to avoid this trouble if possible.
A plan to undermine your faith even if they don't win you over -- Mormon missionaries will often try to undermine your faith even if they suspect that you will not convert. They want to break your faith so that you will consider them spiritual authorities in the future. As you mentioned, they like to use the term "Elder" when referring to each other to give themselves an air of authority. Ask their first names and have them call you by your first name to break down the pretense and of authority. That will put you on an equal playing field.
Your goals
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To learn more about Mormonism -- this is just about guaranteed. If your discussions continue and you ask good questions and present your faith clearly, you will become well-versed with Mormonism.
To learn more about your faith -- you will definitely learn more about your faith, especially what aspects of your faith are essential and what is not. You will need to focus on the most important doctrines, the nature of God, the person of Christ, the desperate nature of being lost and responsible for sinning against God and the way of faith - not works - to a new life in Christ.
To lead Mormon missionaries to Christ -- This should always be your goal, but in reality it is not very likely to happen. Beyond all of the pressure to stay Mormon and the way their partner and the stake leader monitors them, they will be transfered out or forbidden to talk to you before they are likely to come to Christ.
Dangers
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It is much easier to win an argument than it is to be a witness -- since you have the truth on your side, you may be able to put them in a position where you show how ridiculous their beliefs are... If you find yourself in that situation, make the point quickly and move on to your next point. (You've won the "point" and further rubbing it in will actually embarrass them and have the opposite effect. Once I was talking to some missionaries and they wanted me to read a passage out of "Pearl of Great Price", one of their "inspired" books. I did a bad thing and actually read the passage in context and it taught how everything that is alive has a spirit and can become a god and rule over their own worlds creating in their own image. I asked, "Does that mean that a potato can become a god?" They balked. I asked the question again. Finally one of them said yes after a long silence. I started laughing and pressed the point about there being celery gods, tuna gods, potatos gods, flea gods, oak gods, tarantula gods and duck gods. They sat in embarrassed silence and I realized that I had embarrassed them and they were now closed to hearing any more from me until the next time we met.) At the end of your session, you can "wrap up" by mentioning your "concerns" with their belief system and include the point as an issue.
It is much easier to drive a Mormon into atheism than toward Christ -- it is possible for a modestly experienced Christian to triumph over a Mormon in a debate and demonstrate that their religion is false. Unfortunately, since their religion is a house of cards based on Joseph Smith and his "infallible" teaching, they are liable to toss their faith away after their mission tour instead of coming to Christ. Remember, they've been convinced that mainstream Christians are completely deceived and misled by false teaching and they are not likely to respect Christian doctrine even if they don't trust their own. The best method I've found is to work on small but important areas of doctrine and gradually replace their faulty Mormon teaching with Bible teaching. I can be tricky and is very time-consuming, but when you do it you put a little truth time-bomb in their hearts that the Holy Spirit can use to convict them after the pressure is off and they have a chance to reflect on their mission and their faith.
It is always possible for believers to be taken in by Mormons. It is a very deceptive and demonic religion with many traps. If you feel you are having too many doubts or problems talking to the Mormons, call off your appointments. God will not be displeased and you will be better for it. Not everyone is meant to work with cultists. Some people have special gifts and personalities that give them the patience and detactment necessary to work with these seriously deceived people.
Preparation
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Pray. Pray. Pray. Pray. Pray. -- You are going up against spiritual darkness and the power of the enemy. You need wisdom from God, the power of the Holy Spirit and the compassion of Jesus to do this work.
Have your own King James Bible handy -- Mormon missionaries (the common Salt Lake LSD variety) use only the King James. They say it is authoritative as "correctly interpreted" but that's not really true. (My Mormons got so frustrated with me because I was always quoting Bible to them. They originally told me that my Bible had "many plain and precious things" removed and that their books restored those doctrines. I always responded that it was very strange that my Bible with "missing parts" was able to refute their "complete gospel". They got so frustrated by my use of my incomplete Bible that they finally confessed that they thought the King James had faulty doctrine and was useless. That gave me the opportunity to show they how deceptive they were at the first study when they claimed to believe the Bible and hold it as one of their standards of faith and practice.)
I suggest that you read some of the material at Watchman Fellowship to prepare yourself for the Mormon worldview and terminology:
http://www.watchman.org/lds/index.htm
I've found the Watchman Fellowship to be a very helpful source. I've supported their ministry and have purchased hard to find materials there. They take great pains to be very accurate with their materials.
What to expect
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Two Mormon males - usually one will do most of the talking while the other one will assist. Often one is less experienced and is learning from the other.
A series of study guides - the first guide is designed to sound nice and Christian, but is designed to make the unwary Christian believe that they need some sort of earthy prophet to lead the church. They will quote from the book of Amos about the need to know the Lord's will through a prophet. They will ask a bunch of leading questions that expect yes or no answers. Don't even answer quickly. Think about your answers first because the questions are designed to lead you down a path without considering the ramifications of your responses. I rarely answered yes or no but instead stated my understanding of the situation.
The missionaries are sternly instructed not to deviate from the study guides. If you take them off topic, they may or may not answer your question and they will dutifully continue the study. You will not have much of an opportunity to share your side until the end of the "lesson" where they press for a commitment to read a selection from the Book of Mormon and pray for God to give you a "burning in your bosom" that the Mormon message is true.
Issues
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The main issue will be authority -- Who has authority to give the proper interpretation of scripture? They also make much of successionism (the doctrine of authority for the sacraments or ordinances that is allegedly passed from Jesus through an ordained priesthood to the present day). Of course most Baptists believe that our authority comes directly from Jesus Christ and there is no priestly line of special powers necessary. Ultimately the real question is whether you should continue in your faith or toss everything you know based on the questionable testimony of Joseph Smith, Jr. and a "burning in your bosom" that you allegedly receive when you pray about whether or not the Book of Mormon is true.
Suggested method
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Hit the main issues of authority, the trustworthiness of scripture (don't fall into the trap of claiming inerrancy because you will have a very difficult time convincing them -- they have a whole ream of "errors" that you will spend refuting and miss the important point of showing that the Bible is reliable -- inerrancy won't save them, but Jesus can! They may embrace inerrancy after they believe.), the nature of God, the Trinity (they will beat on the doctrine of the Trinity since most Christians don't have a working knowledge of the doctrine), the person and work of Christ, and the need for salvation by grace through faith.
Discussions will often go around the mulberry bush unless you make them stick to the point. Keep a notepad handy so you can write down their objections as a matter of discussion once your finish making your point. Otherwise you won't get to finish and the whole thing will descend into an argument with no one's mind changed and an opportunity missed.
The end result of your discussions
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Don't be disappointed in your discussions if there is no visible change in your Mormon friends. The Spirit can work with them long after they leave if you sow the seed of the word of God in their lives.
I will pray for your appointment.