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Aland, Kurt. (1961). "Chapter Eight: The 'Oikos - Formula.'" In Did the Early Church Baptize Infants? (Translated by G. R. Beasley-Murray). (pages 87-94). Eugene, OR: Wipf & Stock. (Personal Library)
Much of modern apologetic work for infant baptism is predicated on the "oikos - formula," considering that a group would be baptized together as a household (Aland 1961, p. 87). Aland reviews the use of οἶκος in the New Testament, observing that out of 112 instances, only nine refer to 'family', i.e. the people who are in the house.Three of these instances make generic references such as greetings (Aland 1961, p. 88). In 1 Corinthians 1:16 and Acts 18:8 the word refers to the household of Crispus, baptized by Paul. Aland takes the baptismal reference there to apply only to Crispus. However, in 1 Corinthians 1:16 Paul did baptize the household of Stephanas. There is no mention there of the composition of either household. The remaining instances relate to the conversions of Cornelius, of Lydia, and of the prison keeper in Philippi. Aland observes that we know nothing of the composition of the households except for that of Lydia, and that all we know of her household is that there is never a husband mentioned (Aland 1961, p. 89).
In Aland's opinion, the argument for a household baptism necessarily including infants is weak, based on the examples of the households. While it is a possibility, there is no reason based on the evidence to conclude the presence of infants within the households (Aland 1961, p. 90). He concludes, "The elevation of this 'oikos-formula' to a theological status seems to me to be utterly unsatisfactory" (Aland 1961, p. 91). Aland thus considers Jeremias' argument that it was an established norm to be unwarranted (Aland 1961, p. 92).
Aland finally reviews the claim that the oikos-formula represented a ritual norm reflected in the Septuagint. Out of approximately 1600 occurrences, about 40 passages refer to a household. This does not strike Aland as sufficiently frequently to make a conclusion, especially as to the specific presence of infants (Aland 1961, p. 93).