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Floating quantifiers are quantifiers that can move away from the corresponding noun, such as "each" in "The boys hit each other" where it modifies "The boys". I am interested in prepositions in these bipartite reciprocal constructions, as in "They followed each others onto the stage" or "They waited for each other." These constructions are comparable to "They waited, each for the other." In this last example, the preposition is near its complement "the other", but in the earlier examples it is not.

Is there a term for these kind of "floating prepositions"? This term does not yield any results on Google Scholar.

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I don't see any floating of a preposition in your examples.

McCawley has some interesting remarks about reciprocal "each other". In the reference, click "next" until you get to occurrences 6-9, and especially 8, which mentions an analysis by Dougherty attempting to relate this "each" to the one that floats.

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The boys hit each other.

Each is not a 'floating quantifier' here (whatever that means), and each does not modify boys.

The reciprocal meaning is expressed by each in combination with other, and although each other is written as two orthographic words it is actually a single grammatical word. The two components are inseparable and thus form a compound reciprocal pronoun. In your example, the compound functions as direct object of hit.

You may be thinking of the 'spilt' construction as in

They are each required to consult with the other

which is semantically and syntactically different. Here "each" is a determinative and "other" a common noun, as opposed to a single compound pronoun.

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