Here Paul may refer to widows in general, but he probably refers to an order of widows who served the church, as in second-century Christianity. (Commentators disagree on this point.)
We should keep in mind that Paul addresses the values of ancient society for the sake of the church’s witness (5:7, 14; 6:1), not implying that all societies should share those values (which would, for example, look down on older women who had never married-5:10).
5:3. Honoring elders was important; “honor” here includes financial support (5:4, 16-18). By “widows indeed” (KJV, NASB) or “real widows” Paul means not simply those bereaved of husband but those both committed to the church’s ministry of prayer (5:5) and experiencing the stereotypical Old Testament plight of widows: destitution (5:4).
5:4. Adult children or other close relatives were expected to care for destitute widows, who had no opportunity to earn wages in ancient society. It was believed that one owed this care to one’s parents for their support during youth; Paul agrees. Judaism even understood this support as part of the commandment to honor one’s parents.
Under Roman law, a father could discard a newborn child; the child was not regarded as a person and member of the household until the father agreed to raise and support the child. This way of thinking no doubt contributed to children’s recognition of responsibility to parents. Early Jews and Christians, however, unanimously opposed abortion, infanticide and throwing out babies, seeing personhood as a gift of God, not of parents.
Caring for aged parents was a matter not only of custom but of law, and was common even in Western society until recent times.
5:5. The Jewish ideal for older widows, who received support from family or distributors of charity but whose only contribution to society was prayer (no small contribution), was that they be women of prayer (cf. Lk 2:37). (This is probably unrelated to the Roman image of Vestal Virgins’ prayers supporting Rome, although that image shows the ease with which the idea could have been grasped even in pagan culture.)
5:6. Here Paul probably refers to some sort of sexual immorality, perhaps becoming a mistress or indulging in lust (once remarried-5:11-a woman would not be considered a widow).
5:7. The Greco-Roman world as a whole was happy to find cause for scandals in minority and foreign religions, and libeled especially any sexual irregularities. Being “above reproach” (NASB, NRSV; also in 5:14) is crucial for the spread of the gospel (6:1). Although conflicting ideals about widows’ remarriage existed in antiquity (see comment on 5:9,14), all would view negatively a Christian’s committing immorality or violating a vow of celibacy.
5:8. Even pagans believed in supporting destitute widows who were relatives; it was believed that one owed support to one’s aged parents.
(Adapted from The IVP Bible Background Commentary: New Testament. Buy the book here.)
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