I have seen a statement:
- We have a Christian duty to serve each other.
Is this statement correct?
Because 'each other' is used for two persons and 'one another' for more than two persons.
"We have a christian duty to serve each other. Is this statement correct**?** Because each other is used for two persons and one another for more than two persons.
This seems to be an invented "rule" that has no basis in fact.
The OED gives "each other" as synonymous with "one another" and remarks:
each other pron. used as a reciprocal pronoun (as object and in the genitive) = one another. … Some commentators on usage restrict each other to two parties and one another to more than two, but such a distinction is seldom found in actual use.
This seems linked to the concept of "clusivity", which is missing from English.
Broadly speaking it is the distinction of whether the speaker and/or the addressee are included in the group referred to by "we".
So, if "we" is meant to include the speaker and addressee, "each other" seems appropriate. If "we" is meant to exclude the speaker, the addressee or both, "each other" would be lacking the "other".
As has already been pointed out by other contributors to this page and the related one, it is debatable whether there is a rule that restricts each other to binary relationships.
However, even if it is assumed, for the sake of argument, that there is such a rule, the quoted sentence can be interpreted in a way that is compatible with it. It is possible that somebody who makes this exhortation about our Christian duty, thinks of each instance of 'serving' as something that will take place between exactly two people, even though the exhortation is addressed to a group ('we') that has a large number of members. Everybody in that large group has the duty to serve others, but one can think of each specific acts of serving as directed at one other person at a time. So interpreted, the exhortation is compatible with the (alleged) rule.