In the monotheistic tradition, how is the idea of the saint alike and different from the Greek idea of a hero? What are examples of Hebrew, Christian, and/or Islam saints?
An understanding of sainthood will actually differ per Protestant or Catholic view; however, both understandings of sainthood are rooted in the Greek concept of a hero. The term saint comes from the Greek word hagioi, meaning holy. According to Protestant understand, God commands all of His followers to be holy in doing and thinking as He would do and think. We especially see the biblical command for all of God's followers to be holy that Protestants go by in 1 Peter 1:15-16: "But just as he who called you is holy, so be holy in all you do; for it is written: 'Be holy, because I am holy'" (NIV). What's more, in Paul's letters, he frequently reminds the members of the churches under his care that they have been "sanctified in Christ Jesus [and] called to be saints, with all who in every place call on the name of Jesus Christ our Lord" (1 Corinthians 1:2). The word sanctification comes from the Greek word hagiasmos, which has the same root as the word saint and means holiness. Hence, to be sanctified is to be made holy, and the Pauline argument that the Protestants go by is that all who follow Jesus have been made holy ("What is a Saint?"). This concept of being made holy fits the Greek concept of heroism in that heroes, through self-sacrifice for the greater good, were made divine.
The Catholic concept of sainthood is slightly different in that they do not believe all followers have been made saints. According to their doctrine of canonization and beatification, only certain people are made holy. A Catholic may be named as a candidate for sainthood after that person's death, and a process of evaluation begins, which is the process of canonization. The person's bishop will begin by researching the person's life and writings to see if that person's life can indeed be thought of as holy. Next, the person is investigated by a "panel of theologians at the Vatican" ("How Does the Church Choose Saints?"). If both the panel and the cardinals of the Congregation for the Causes of Saints agree, then that person will be decreed "venerable," meaning worthy of honor. Finally, the person is declared to be a saint only if the process of beatification is completed. According to the process of beatification, a holy person in heaven will be able to grant miracles. Hence, if the deceased person through petition does grant one miracle, then it is viewed as proof that the person is indeed holy, in heaven, and a saint. The Catholic doctrine of canonization of saints also fits the idea of Greek heroism in that those who proved to be heroic through deeds of great courage and self-sacrifice were thought to be either demigods or made into demigods, meaning part human and part god, and capable of doing the miraculous.