For example, the altar is holy because it has been set apart for use in the temple, not because it has a certain shape or is made of a particular material. Any use of the altar not in line with its prescribed use as a holy object is forbidden. Similarly Israel is holy because it is chosen, not the reverse. Being called and set apart for particular divine purposes makes Israel holy, and that holiness puts them under solemn and divine obligation, the obligation to live up to the holiness to which they have been set apart. If Israel obeys God, that obedience is the proper response to their calling—to the fact that they are holy—but that obedience is not what makes them holy.
Similarly, a reasonable translation of the Greek word hagios in the New Testament might be not just "holy," but more informatively "one of God's people." As such, the saint is holy—in other words, set apart, even if not perfectly pure—and, therefore, he or she is obligated to God to be pure.
Surely the purity of character identified with saintliness is at least part of what the word saint intends. Members of the LDS Church have been called to be pure. That is expected of them. But, given the connotations of the word saint in the Hebrew Bible, we must remember that saint describes not just moral cleanliness (in the broadest sense), but also and especially a covenant relation to God. The chosen people—called saints in the Hebrew Bible, the New Testament, and today—are those who make covenant with God.
We see that in Exodus 19:3-6. There the Lord makes his covenant with Israel and says that by entering into the covenant (rather than because of any presumed purity) they will become a holy nation (goy qadosh). The Hebrew phrase translated "holy nation" in Exodus 19:6 could also be translated "a holy people," and by extension "a nation of saints," in other words a people covenanted to God.
Just as holy objects are those set aside for holy purposes, the saints are the people set aside for God's holy purposes. Presumably those purposes range beyond the purposes of the individuals who make up the nation, and presumably those purposes are not God's recognition of the moral superiority of those in his nation. Indeed, the Hebrew Bible goes out of its way to regularly show us people who are fallen and yet nevertheless the chosen people.
Mormons have no reason to assume that what was true of ancient Israel, true of the New Testament Church, and true of the people in the Book of Mormon is less true of ourselves: We are covenanted to God to be tools for his work, and by virtue of that covenant we (among others rather than instead of them) are chosen people. We are called saints. The covenant that makes us saints also obligates us to be pure. But it is no guarantee that we are.
James Faulconer is a Richard L. Evans Professor of Religious Understanding at Brigham Young University, where he has taught philosophy since 1975.