This question is a valid one, since the process Mormons describe to gain a spiritual witness (called a "testimony" by Mormons) of the truthfulness of the LDS church (reading the scriptures, living the commandments, prayer and fasting) is the same process that has led many other individuals to other beliefs.

How can Mormons be sure that their spiritual witness is any more valid than someone else's? Moreover, how can either person (Mormon or not) be sure what they believe to be a "spiritual witness" is other than a purely psychological phenomenon?

Here's how I have come to terms with it.

First, realize that you cannot know what other people are feeling, and you are not responsible for their actions. What you are responsible for is your own actions, which must be based on your own intellect and feelings. So, basically, you must do what you believe is right. So, for example, if testimony and faith in general can be explained by psychological phenomena (which I will admit is possible), *your* testimony and faith are still personal to you, and may or may not be the same thing others describe.

Second, again because you cannot see into other people's minds, you cannot see the basis for their faith. Therefore, it is important to not judge them. They often are doing the same thing you are doing-- trying to live the best they can according to the knowledge and spiritual promptings (or their perception of them) they have received.

This being said, I do have a strong belief in the truthfulness of the gospel, and of the LDS Church. The belief has come through study, and personal experiences. So, since I do believe that the LDS church is the only church ordained of God, I naturally believe that other religions do not have all the truth. Moreover, I believe that if a person will "experiment upon the word" (as it mentions in the Book of Mormon, in Alma chapter 32), they will increase their own faith and testimony to accept a more complete truth, so to speak. And, in fact, I have seen this happen a number of times. However, I also recognize the chance that I might just be completely mistaken, which is why my second point about not judging is important.