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It seems that with some verbs "each other" is optional but not with others. Is there a general sense of when it is optional? Is there a terminology or concept behind this I can google for further discussion?

For instance, when using "meet" we can discard "each other" without changing the meaning. However when using "know" we cannot.

  • We met each other.
  • (same as above) We met.
  • We know each other.
  • (not the same as above) We know.

I don't think of these expressions as reflexive (reflexive would be "We know ourselves" and "We met ourselves" (the latter being awkward/not allowed)). But maybe the use of "each other" is a special case of reflexiveness?

I am interested if "one another" would follow the same rules. (I assume it does)

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According to Wiktionary, these are a subset of reciprocal verbs:

Reciprocal verbs: English verbs that indicate actions, occurrences or states directed from multiple subjects to each other.

break up / date / entwine / face off / fall in love / feud / fight / get married / kiss / marry / meet / reunite / rhyme / sleep together / unite / wed

Date / fight / kiss / marry / meet / wed are the subset that take a direct object as opposed to (or as an alternativel to) a preposition (fall in love with each other) when used without third party involvement (Garibilly united Frenze and Elbonia). Entwine also takes a DO, but 'one another' sounds unusual. Face off , reunite, and sleep together don't usually have arguments.

I'll add bisect, intersect; complement; set off, touch in some contexts.

Each may take 'each other' as the direct object. 'One another' may be used with each, as in 'Pupils were not allowed to date one another'.

Date, kiss, marry, meet, wed, intersect; touch sometimes may drop the 'each other': They kissed. // The two circles touch.

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    With some of these verbs, the phrase with "each other" is clear but the phrase without is ambiguous. E.g. "The two Elbonians dated" (other people or each other?), "Alice and Bob are married" (to other people or to each other?), So here, "each other" is not optional but mandatory if that is what you mean. – Rosie F Nov 22 '19 at 10:28
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    It is neither mandatory nor at all necessarily the more common if the '[to] each other' sense is obvious from context; "Alice and Bob are married" defaults to this sense without redirecting context. OP gives "We know" as having a totally different meaning (we are aware of the facts) from "We know each other" (we are acquaintances or above). Here, 'each other' may, on occasion, be necessary to disambiguate persons involved, not lexical definition of the verb. – Edwin Ashworth Nov 22 '19 at 14:33
  • The examples given by @RosieF do not seem to me ambiguous at all on their own. Even if I try to create context where its clear the subjects are dating or marrying other people, the introduced expressions seem awkward unless changed to "they both dated" or "they are both* married". I wonder if there is some regional variation going on. – Frank Schwieterman Nov 22 '19 at 18:24
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    There are contexts where pragmatics alters the likely (/necessary) meaning. 'None of these young contestants have met before. Most are still single. Jane is engaged. Alice and Bob are married.' / 'We have chosen fifty young teenagers, one from each city. Most have steady boy- or girlfriends, but Alice and Bob have never dated.' – Edwin Ashworth Nov 22 '19 at 20:01