The Lord does not leave honest seekers in the dark, void of divine assistance; he provides evidence upon which to build houses of faith. "All belief is founded on evidence," Elder Orson Pratt explained. "A true faith is founded on true evidence; a false faith on false evidence. And in no case can a man have faith, either true or false, unless it is the result of true or false evidence. The greater the evidence, the greater will be the faith resulting from that evidence" (Pratt, 48; cf. Heb. 11:1; McConkie, 166). Korihor had every reason to have faith in God; as Alma pointed out, he had evidence from the prophets and the scriptures as well as the order of the cosmos (Alma 30:44; cf. D&C 88:45–47). But he rejected that evidence and thereby laid the foundation for his own destruction. Near the end of the Nephite saga, Mormon prayed with all his heart for the deliverance of his people, but his prayers were "without faith, because of the hardness of their hearts" (Morm. 3:12). Mormon was unable to exercise faith in their behalf because his people, who refused to accept divine evidence of the truth, offered no evidence that they intended to repent of their wickedness or change their ways.
Alma explained that to have "faith is not to have a perfect knowledge of things" but to have a "hope for things which are not seen, which are true" (Alma 32:21 italics added; cf. Ether 12:6; Heb. 11:1). Sincerity and devotion to a cause are not sufficient; saving faith can only be exercised in that which is true. Thus no matter how committed the Zoramites were to their liturgy atop the Rameumptom (Alma 31), their false beliefs concerning God could not result in faith unto life and salvation. Their refusal to believe in the coming condescension of God the Son precluded salvation, no matter how consistently they cried out to their deity in their weekly ritual.
In the scriptures, there is no distinction between true faith and true belief; belief is a synonym for faith. To have faith in Christ is to believe in Christ, to "believe that he is, and that he created all things, both in heaven and in earth; [to] believe that he has all wisdom, and all power, both in heaven and in earth" (Mosiah 4:9). The Nephite prophets labored diligently to invite their people "to believe in Christ, and to be reconciled to God" (2 Ne. 25:23), "for the Lord covenanteth with none save it be with them that repent and believe in his Son, who is the Holy One of Israel" (2 Ne. 30:2). The Nephites were called upon to "believe in Christ, and view his death, and suffer his cross and bear the shame of the world" (Jacob 1:8). Truly, "whosoever shall believe on the Son of God, the same shall have everlasting life" (Hel. 14:8; cf. Morm. 7:10).