Perhaps the definition of faith most widely quoted by Latter-day Saints is the one given by Alma: "Faith is not to have a perfect knowledge of things; therefore if ye have faith ye hope for things which are not seen, which are true." (Alma 32:21.) This definition is even more complete and meaningful than the definition given by Paul as recorded in our present New Testament: "Now faith is the substance of things hoped for, the evidence of things not seen." (Hebrews 11:1.)
It is interesting to note that both of these prophets include hope as an element of faith; yet, as Alma points out, faith is more than mere hope or the "desire to believe." (Alma 32:26-27.) On the other hand, faith is not knowledge, "for if a man knoweth a thing" he has no need to exercise faith or even to believe, for "he knoweth it." (Alma 32:18.) Alma's comparison of faith to the planting of a seed beautifully and clearly illustrates this principle. (Alma 32:28-43.) One of the best expositions of the distinctions between belief, faith, and knowledge is that given by Elder James E. Talmage:
The terms faith and belief are sometimes regarded as synonyms; nevertheless each of them has a specific meaning in our language, although in earlier usage there was little distinction between them, and therefore the words are used interchangeably in many scriptural passages. Belief, in one of its accepted senses, may consist in a merely intellectual assent, while faith implies such confidence and conviction as will impel to action. Dictionary authority justifies us in drawing a distinction between the two, according to present usage in English; and this authority defines belief as a mental assent to the truth or actuality of anything, excluding, however, the moral element of responsibility through such assent, which responsibility is included by faith. Belief is in a sense passive, an agreement or acceptance only; faith is active and positive, embracing such reliance and confidence as will lead to works. Faith in Christ comprises belief in Him, combined with trust in Him. One cannot have faith without belief; yet he may believe and still lack faith. Faith is vivified, vitalized, living belief.. . . Neither belief nor its superior, actual knowledge, is efficient to save; for neither of these is faith. If belief be a product of the mind, faith is of the heart; belief is founded on reason, faith largely on intuition . . .
The mere possession of knowledge gives no assurance of benefit therefrom. It is said that during an epidemic of cholera in a great city, a scientific man proved to his own satisfaction, by chemical and microscopical tests, that the water supply was infected, and that through it contagion was being spread. He proclaimed the fact throughout the city, and warned all against the use of unboiled water. Many of the people, although incapable of comprehending his methods of investigation, far less of repeating such for themselves, had faith in his warning words, followed his instructions, and escaped the death to which their careless and unbelieving fellows succumbed. Their faith was a saving one. To the man himself, the truth by which so many lives had been spared was a matter of knowledge. He had actually perceived, under the microscope, proof of the existence of death-dealing germs in the water; he had demonstrated their virulence; he knew of what he spoke. Nevertheless, in a moment of forgetfulness he drank of the unsterilized water, and soon thereafter died, a victim to the plague. His knowledge did not save him, convincing though it was; yet others, whose reliance was only that of confidence or faith in the truth that he declared, escaped the threatening destruction. He had knowledge; but, was he wise? Knowledge is to wisdom what belief is to faith, one an abstract principle, the other a living application. Not possession merely, but the proper use of knowledge constitutes wisdom. (Articles of Faith, pp. 96-100.)