Excerpt from a 2007 interview with Apostle M. Russell Ballard:1
You will not get to know it [whether the Book of Mormon is true] by trying to prove it archaeologically, or by DNA, or by anything else…Religious truth is always confirmed by what you feel. And that’s the way heavenly father answers prayers.
From a Wikipedia article on emotional reasoning: 2
Emotional reasoning is a cognitive process by which a person concludes that his/her emotional reaction proves something is true, regardless of the observed evidence.